Examining Student Opinions on Computer Use Based on the Learning Styles in Mathematics Education

ERIC Educational Resources Information Center

Ozgen, Kemal; Bindak, Recep

2012-01-01

The purpose of this study is to identify the opinions of high school students, who have different learning styles, related to computer use in mathematics education. High school students' opinions on computer use in mathematics education were collected with both qualitative and quantitative approaches in the study conducted with a survey model. For…

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

ERIC Educational Resources Information Center

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

2002-01-01

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

Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

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

2013-01-01

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

Automatic mathematical modeling for space application

NASA Technical Reports Server (NTRS)

Wang, Caroline K.

1987-01-01

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

Using Construct Validity Techniques To Evaluate an Automated Cognitive Model of Geometric Proof Writing.

ERIC Educational Resources Information Center

Shotsberger, Paul G.

The National Council of Teachers of Mathematics (1991) has identified the use of computers as a necessary teaching tool for enhancing mathematical discourse in schools. One possible vehicle of technological change in mathematics classrooms is the Intelligent Tutoring System (ITS), an artificially intelligent computer-based tutor. This paper…

Will the digital computer transform classical mathematics?

PubMed

Rotman, Brian

2003-08-15

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

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

NASA Astrophysics Data System (ADS)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

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

A micro-computer based system to compute magnetic variation

NASA Technical Reports Server (NTRS)

Kaul, R.

1984-01-01

A mathematical model of magnetic variation in the continental United States (COT48) was implemented in the Ohio University LORAN C receiver. The model is based on a least squares fit of a polynomial function. The implementation on the microprocessor based LORAN C receiver is possible with the help of a math chip, Am9511 which performs 32 bit floating point mathematical operations. A Peripheral Interface Adapter (M6520) is used to communicate between the 6502 based micro-computer and the 9511 math chip. The implementation provides magnetic variation data to the pilot as a function of latitude and longitude. The model and the real time implementation in the receiver are described.

And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

ERIC Educational Resources Information Center

Street, Garrett M.; Laubach, Timothy A.

2013-01-01

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

The effects of geometric uncertainties on computational modelling of knee biomechanics

NASA Astrophysics Data System (ADS)

Meng, Qingen; Fisher, John; Wilcox, Ruth

2017-08-01

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.

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

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

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

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

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

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

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

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

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

A micro-computer-based system to compute magnetic variation

NASA Technical Reports Server (NTRS)

Kaul, Rajan

1987-01-01

A mathematical model of magnetic variation in the continental United States was implemented in the Ohio University Loran-C receiver. The model is based on a least squares fit of a polynomial function. The implementation on the microprocessor based Loran-C receiver is possible with the help of a math chip which performs 32 bit floating point mathematical operations. A Peripheral Interface Adapter is used to communicate between the 6502 based microcomputer and the 9511 math chip. The implementation provides magnetic variation data to the pilot as a function of latitude and longitude. The model and the real time implementation in the receiver are described.

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.; Mosher, R. A.; Bier, M.; Saville, D. A.

1981-01-01

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

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

PubMed Central

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

2016-01-01

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

The effects of geometric uncertainties on computational modelling of knee biomechanics

PubMed Central

Fisher, John; Wilcox, Ruth

2017-01-01

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models. PMID:28879008

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

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

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Epistemic Gameplay and Discovery in Computational Model-Based Inquiry Activities

ERIC Educational Resources Information Center

Wilkerson, Michelle Hoda; Shareff, Rebecca; Laina, Vasiliki; Gravel, Brian

2018-01-01

In computational modeling activities, learners are expected to discover the inner workings of scientific and mathematical systems: First elaborating their understandings of a given system through constructing a computer model, then "debugging" that knowledge by testing and refining the model. While such activities have been shown to…

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models

PubMed Central

Rejniak, Katarzyna A.; Gerlee, Philip

2013-01-01

Summary In this review we summarize our recent efforts using mathematical modeling and computation to simulate cancer invasion, with a special emphasis on the tumor microenvironment. We consider cancer progression as a complex multiscale process and approach it with three single-cell based mathematical models that examine the interactions between tumor microenvironment and cancer cells at several scales. The models exploit distinct mathematical and computational techniques, yet they share core elements and can be compared and/or related to each other. The overall aim of using mathematical models is to uncover the fundamental mechanisms that lend cancer progression its direction towards invasion and metastasis. The models effectively simulate various modes of cancer cell adaptation to the microenvironment in a growing tumor. All three point to a general mechanism underlying cancer invasion: competition for adaptation between distinct cancer cell phenotypes, driven by a tumor microenvironment with scarce resources. These theoretical predictions pose an intriguing experimental challenge: test the hypothesis that invasion is an emergent property of cancer cell populations adapting to selective microenvironment pressure, rather than culmination of cancer progression producing cells with the “invasive phenotype”. In broader terms, we propose that fundamental insights into cancer can be achieved by experimentation interacting with theoretical frameworks provided by computational and mathematical modeling. PMID:18524624

Mathematical modeling of swirled flows in industrial applications

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Learning and Teaching Mathematics through Real Life Models

ERIC Educational Resources Information Center

Takaci, Djurdjica; Budinski, Natalija

2011-01-01

This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

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

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Cellular automata-based modelling and simulation of biofilm structure on multi-core computers.

PubMed

Skoneczny, Szymon

2015-01-01

The article presents a mathematical model of biofilm growth for aerobic biodegradation of a toxic carbonaceous substrate. Modelling of biofilm growth has fundamental significance in numerous processes of biotechnology and mathematical modelling of bioreactors. The process following double-substrate kinetics with substrate inhibition proceeding in a biofilm has not been modelled so far by means of cellular automata. Each process in the model proposed, i.e. diffusion of substrates, uptake of substrates, growth and decay of microorganisms and biofilm detachment, is simulated in a discrete manner. It was shown that for flat biofilm of constant thickness, the results of the presented model agree with those of a continuous model. The primary outcome of the study was to propose a mathematical model of biofilm growth; however a considerable amount of focus was also placed on the development of efficient algorithms for its solution. Two parallel algorithms were created, differing in the way computations are distributed. Computer programs were created using OpenMP Application Programming Interface for C++ programming language. Simulations of biofilm growth were performed on three high-performance computers. Speed-up coefficients of computer programs were compared. Both algorithms enabled a significant reduction of computation time. It is important, inter alia, in modelling and simulation of bioreactor dynamics.

Some Computer-Based Developments in Sociology.

ERIC Educational Resources Information Center

Heise, David R.; Simmons, Roberta G.

1985-01-01

Discusses several ways in which computers are being used in sociology and how they continue to change this discipline. Areas considered include data collection, data analysis, simulations of social processes based on mathematical models, and problem areas (including standardization concerns, training, and the financing of computing facilities).…

Pedagogical Factors Affecting Integration of Computers in Mathematics Instruction in Secondary Schools in Kenya

ERIC Educational Resources Information Center

Wanjala, Martin M. S.; Aurah, Catherine M.; Symon, Koros C.

2015-01-01

The paper reports findings of a study which sought to examine the pedagogical factors that affect the integration of computers in mathematics instruction as perceived by teachers in secondary schools in Kenya. This study was based on the Technology Acceptance Model (TAM). A descriptive survey design was used for this study. Stratified and simple…

Approach to Computer Implementation of Mathematical Model of 3-Phase Induction Motor

NASA Astrophysics Data System (ADS)

Pustovetov, M. Yu

2018-03-01

This article discusses the development of the computer model of an induction motor based on the mathematical model in a three-phase stator reference frame. It uses an approach that allows combining during preparation of the computer model dual methods: means of visual programming circuitry (in the form of electrical schematics) and logical one (in the form of block diagrams). The approach enables easy integration of the model of an induction motor as part of more complex models of electrical complexes and systems. The developed computer model gives the user access to the beginning and the end of a winding of each of the three phases of the stator and rotor. This property is particularly important when considering the asymmetric modes of operation or when powered by the special circuitry of semiconductor converters.

Decision Support Tool for Deep Energy Efficiency Retrofits in DoD Installations

DTIC Science & Technology

2014-01-01

representations (HDMR). Chemical Engineering Science, 57, 4445–4460. 2. Sobol ’, I., 2001. Global sensitivity indices for nonlinear mathematical...models and their Monte Carlo estimates. Mathematics and computers in simulation, 55, 271–280. 3. Sobol , I. and Kucherenko, S., 2009. Derivative based...representations (HDMR). Chemical Engineering Science, 57, 4445–4460. 16. Sobol ’, I., 2001. Global sensitivity indices for nonlinear mathematical models and

Modelling Mathematics Teachers' Intention to Use the Dynamic Geometry Environments in Macau: An SEM Approach

ERIC Educational Resources Information Center

Zhou, Mingming; Chan, Kan Kan; Teo, Timothy

2016-01-01

Dynamic geometry environments (DGEs) provide computer-based environments to construct and manipulate geometric figures with great ease. Research has shown that DGEs has positive impact on student motivation, engagement, and achievement in mathematics learning. However, the adoption of DGEs by mathematics teachers varies substantially worldwide.…

Mathematical Modeling and Computational Thinking

ERIC Educational Resources Information Center

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

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

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

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

NASA Technical Reports Server (NTRS)

Gutierrez-Miravete, E.

1986-01-01

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

10 CFR 431.173 - Requirements applicable to all manufacturers.

Code of Federal Regulations, 2011 CFR

2011-01-01

... COMMERCIAL AND INDUSTRIAL EQUIPMENT Provisions for Commercial Heating, Ventilating, Air-Conditioning and... is based on engineering or statistical analysis, computer simulation or modeling, or other analytic... method or methods used; (B) The mathematical model, the engineering or statistical analysis, computer...

Reliability model derivation of a fault-tolerant, dual, spare-switching, digital computer system

NASA Technical Reports Server (NTRS)

1974-01-01

A computer based reliability projection aid, tailored specifically for application in the design of fault-tolerant computer systems, is described. Its more pronounced characteristics include the facility for modeling systems with two distinct operational modes, measuring the effect of both permanent and transient faults, and calculating conditional system coverage factors. The underlying conceptual principles, mathematical models, and computer program implementation are presented.

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

PubMed Central

Käser, Tanja; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; Richtmann, Verena; Grond, Ursina; Gross, Markus; von Aster, Michael

2013-01-01

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child's individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities. PMID:23935586

Recent literature on structural modeling, identification, and analysis

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1990-01-01

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

Automatic mathematical modeling for real time simulation system

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1988-01-01

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

Montgomery Blair Science, Mathematics and Computer Science Magnet Program: A Successful Model for Meeting the Needs of Highly Able STEM Learners

ERIC Educational Resources Information Center

Stein, David; Ostrander, Peter; Lee, G. Maie

2016-01-01

The Magnet Program at Montgomery Blair High School is an application-based magnet program utilizing a curriculum focused on science, mathematics, and computer science catering to interested, talented, and eager to learn students in Montgomery County, Maryland. This article identifies and discusses some of the unique aspects of the Magnet Program…

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

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

Toward integration of in vivo molecular computing devices: successes and challenges

PubMed Central

Hayat, Sikander; Hinze, Thomas

2008-01-01

The computing power unleashed by biomolecule based massively parallel computational units has been the focus of many interdisciplinary studies that couple state of the art ideas from mathematical logic, theoretical computer science, bioengineering, and nanotechnology to fulfill some computational task. The output can influence, for instance, release of a drug at a specific target, gene expression, cell population, or be a purely mathematical entity. Analysis of the results of several studies has led to the emergence of a general set of rules concerning the implementation and optimization of in vivo computational units. Taking two recent studies on in vivo computing as examples, we discuss the impact of mathematical modeling and simulation in the field of synthetic biology and on in vivo computing. The impact of the emergence of gene regulatory networks and the potential of proteins acting as “circuit wires” on the problem of interconnecting molecular computing device subunits is also highlighted. PMID:19404433

Correlation Educational Model in Primary Education Curriculum of Mathematics and Computer Science

ERIC Educational Resources Information Center

Macinko Kovac, Maja; Eret, Lidija

2012-01-01

This article gives insight into methodical correlation model of teaching mathematics and computer science. The model shows the way in which the related areas of computer science and mathematics can be supplemented, if it transforms the way of teaching and creates a "joint" lessons. Various didactic materials are designed, in which all…

AutoCAD-To-NASTRAN Translator Program

NASA Technical Reports Server (NTRS)

Jones, A.

1989-01-01

Program facilitates creation of finite-element mathematical models from geometric entities. AutoCAD to NASTRAN translator (ACTON) computer program developed to facilitate quick generation of small finite-element mathematical models for use with NASTRAN finite-element modeling program. Reads geometric data of drawing from Data Exchange File (DXF) used in AutoCAD and other PC-based drafting programs. Written in Microsoft Quick-Basic (Version 2.0).

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

NASA Technical Reports Server (NTRS)

Young, Gerald W.; Clemons, Curtis B.

2004-01-01

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

COMPUTER MODEL TECHNOLOGY TRANSFER IN THE UNITED STATES

EPA Science Inventory

Computer-based mathematical models for urban water resources planning, management and design are widely used by engineers and planners in both the public and private sectors. In the United States, the majority of the users are in the private (consulting) sector, yet most of the m...

SensA: web-based sensitivity analysis of SBML models.

PubMed

Floettmann, Max; Uhlendorf, Jannis; Scharp, Till; Klipp, Edda; Spiesser, Thomas W

2014-10-01

SensA is a web-based application for sensitivity analysis of mathematical models. The sensitivity analysis is based on metabolic control analysis, computing the local, global and time-dependent properties of model components. Interactive visualization facilitates interpretation of usually complex results. SensA can contribute to the analysis, adjustment and understanding of mathematical models for dynamic systems. SensA is available at http://gofid.biologie.hu-berlin.de/ and can be used with any modern browser. The source code can be found at https://bitbucket.org/floettma/sensa/ (MIT license) © The Author 2014. Published by Oxford University Press.

Data-Based Detection of Potential Terrorist Attacks: Statistical and Graphical Methods

DTIC Science & Technology

2010-06-01

Naren; Vasquez-Robinet, Cecilia; Watkinson, Jonathan: "A General Probabilistic Model of the PCR Process," Applied Mathematics and Computation 182(1...September 2006. Seminar, Measuring the effect of Length biased sampling, Mathematical Sciences Section, National Security Agency, 19 September 2006...Committee on National Statistics, 9 February 2007. Invited seminar, Statistical Tests for Bullet Lead Comparisons, Department of Mathematics , Butler

Mathematical modeling of heat transfer problems in the permafrost

NASA Astrophysics Data System (ADS)

Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

2014-11-01

In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

Agent based simulations in disease modeling Comment on "Towards a unified approach in the modeling of fibrosis: A review with research perspectives" by Martine Ben Amar and Carlo Bianca

NASA Astrophysics Data System (ADS)

Pappalardo, Francesco; Pennisi, Marzio

2016-07-01

Fibrosis represents a process where an excessive tissue formation in an organ follows the failure of a physiological reparative or reactive process. Mathematical and computational techniques may be used to improve the understanding of the mechanisms that lead to the disease and to test potential new treatments that may directly or indirectly have positive effects against fibrosis [1]. In this scenario, Ben Amar and Bianca [2] give us a broad picture of the existing mathematical and computational tools that have been used to model fibrotic processes at the molecular, cellular, and tissue levels. Among such techniques, agent based models (ABM) can give a valuable contribution in the understanding and better management of fibrotic diseases.

Distributed Algorithms for Probabilistic Solution of Computational Vision Problems.

DTIC Science & Technology

1988-03-01

34 targets. Legters and Young (1982) developed an operator-based approach r% using foreground and background models and solved a least-squares minimiza...1960), "Finite Markov Chains", Van Nostrand, , - New York. Legters , G.R., and Young, T.Y. (1982), "A Mathematical Model for Computer Image Tracking

A Model for Intelligent Computer-Aided Education Systems.

ERIC Educational Resources Information Center

Du Plessis, Johan P.; And Others

1995-01-01

Proposes a model for intelligent computer-aided education systems that is based on cooperative learning, constructive problem-solving, object-oriented programming, interactive user interfaces, and expert system techniques. Future research is discussed, and a prototype for teaching mathematics to 10- to 12-year-old students is appended. (LRW)

Comparing the Score Distribution of a Trial Computer-Based Examination Cohort with That of the Standard Paper-Based Examination Cohort

ERIC Educational Resources Information Center

Zoanetti, Nathan; Les, Magdalena; Leigh-Lancaster, David

2014-01-01

From 2011-2013 the VCAA conducted a trial aligning the use of computers in curriculum, pedagogy and assessment culminating in a group of 62 volunteer students sitting their end of Year 12 technology-active Mathematical Methods (CAS) Examination 2 as a computer-based examination. This paper reports on statistical modelling undertaken to compare the…

Studio Mathematics: The Epistemology and Practice of Design Pedagogy as a Model for Mathematics Learning. WCER Working Paper No. 2005-3

ERIC Educational Resources Information Center

Shaffer, David Williamson

2005-01-01

This paper examines how middle school students developed understanding of transformational geometry through design activities in Escher's World, a computationally rich design experiment explicitly modeled on an architectural design studio. Escher's World was based on the theory of pedagogical praxis (Shaffer, 2004a), which suggests that preserving…

Extension of transonic flow computational concepts in the analysis of cavitated bearings

NASA Technical Reports Server (NTRS)

Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

1990-01-01

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Using Agent Base Models to Optimize Large Scale Network for Large System Inventories

NASA Technical Reports Server (NTRS)

Shameldin, Ramez Ahmed; Bowling, Shannon R.

2010-01-01

The aim of this paper is to use Agent Base Models (ABM) to optimize large scale network handling capabilities for large system inventories and to implement strategies for the purpose of reducing capital expenses. The models used in this paper either use computational algorithms or procedure implementations developed by Matlab to simulate agent based models in a principal programming language and mathematical theory using clusters, these clusters work as a high performance computational performance to run the program in parallel computational. In both cases, a model is defined as compilation of a set of structures and processes assumed to underlie the behavior of a network system.

From Greeks to Today: Cipher Trees and Computer Cryptography.

ERIC Educational Resources Information Center

Grady, M. Tim; Brumbaugh, Doug

1988-01-01

Explores the use of computers for teaching mathematical models of transposition ciphers. Illustrates the ideas, includes activities and extensions, provides a mathematical model and includes computer programs to implement these topics. (MVL)

Videos | Argonne National Laboratory

Science.gov Websites

science --Agent-based modeling --Applied mathematics --Artificial intelligence --Cloud computing management -Intelligence & counterterrorrism -Vulnerability assessment -Sensors & detectors Programs

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim.

PubMed

Parasuram, Harilal; Nair, Bipin; D'Angelo, Egidio; Hines, Michael; Naldi, Giovanni; Diwakar, Shyam

2016-01-01

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N2a, N2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

Mathematical modeling of fluxgate magnetic gradiometers

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Oursland, Mark David

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

Modeling Criminal Activity in Urban Landscapes

NASA Astrophysics Data System (ADS)

Brantingham, Patricia; Glässer, Uwe; Jackson, Piper; Vajihollahi, Mona

Computational and mathematical methods arguably have an enormous potential for serving practical needs in crime analysis and prevention by offering novel tools for crime investigations and experimental platforms for evidence-based policy making. We present a comprehensive formal framework and tool support for mathematical and computational modeling of criminal behavior to facilitate systematic experimental studies of a wide range of criminal activities in urban environments. The focus is on spatial and temporal aspects of different forms of crime, including opportunistic and serial violent crimes. However, the proposed framework provides a basis to push beyond conventional empirical research and engage the use of computational thinking and social simulations in the analysis of terrorism and counter-terrorism.

Recent Evolution of the Introductory Curriculum in Computing.

ERIC Educational Resources Information Center

Tucker, Allen B.; Garnick, David K.

1991-01-01

Traces the evolution of introductory computing courses for undergraduates based on the Association for Computing Machinery (ACM) guidelines published in "Curriculum 78." Changes in the curricula are described, including the role of discrete mathematics and theory; and the need for a broader model for designing introductory courses is…

Computational modeling of the cell-autonomous mammalian circadian oscillator.

PubMed

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

2017-02-24

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

Mathematical Modelling of Optimization of Structures of Monolithic Coverings Based on Liquid Rubbers

NASA Astrophysics Data System (ADS)

Turgumbayeva, R. Kh; Abdikarimov, M. N.; Mussabekov, R.; Sartayev, D. T.

2018-05-01

The paper considers optimization of monolithic coatings compositions using a computer and MPE methods. The goal of the paper was to construct a mathematical model of the complete factorial experiment taking into account its plan and conditions. Several regression equations were received. Dependence between content components and parameters of rubber, as well as the quantity of a rubber crumb, was considered. An optimal composition for manufacturing the material of monolithic coatings compositions was recommended based on experimental data.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

PubMed

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

2017-08-01

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

The possibility of coexistence and co-development in language competition: ecology-society computational model and simulation.

PubMed

Yun, Jian; Shang, Song-Chao; Wei, Xiao-Dan; Liu, Shuang; Li, Zhi-Jie

2016-01-01

Language is characterized by both ecological properties and social properties, and competition is the basic form of language evolution. The rise and decline of one language is a result of competition between languages. Moreover, this rise and decline directly influences the diversity of human culture. Mathematics and computer modeling for language competition has been a popular topic in the fields of linguistics, mathematics, computer science, ecology, and other disciplines. Currently, there are several problems in the research on language competition modeling. First, comprehensive mathematical analysis is absent in most studies of language competition models. Next, most language competition models are based on the assumption that one language in the model is stronger than the other. These studies tend to ignore cases where there is a balance of power in the competition. The competition between two well-matched languages is more practical, because it can facilitate the co-development of two languages. A third issue with current studies is that many studies have an evolution result where the weaker language inevitably goes extinct. From the integrated point of view of ecology and sociology, this paper improves the Lotka-Volterra model and basic reaction-diffusion model to propose an "ecology-society" computational model for describing language competition. Furthermore, a strict and comprehensive mathematical analysis was made for the stability of the equilibria. Two languages in competition may be either well-matched or greatly different in strength, which was reflected in the experimental design. The results revealed that language coexistence, and even co-development, are likely to occur during language competition.

On dynamics of integrate-and-fire neural networks with conductance based synapses.

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IF models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

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

Bastian, Mark; Trigueros, Jose V.

Phoenix is a Java Virtual Machine (JVM) based library for performing mathematical and astrodynamics calculations. It consists of two primary sub-modules, phoenix-math and phoenix-astrodynamics. The mathematics package has a variety of mathematical classes for performing 3D transformations, geometric reasoning, and numerical analysis. The astrodynamics package has various classes and methods for computing locations, attitudes, accesses, and other values useful for general satellite modeling and simulation. Methods for computing celestial locations, such as the location of the Sun and Moon, are also included. Phoenix is meant to be used as a library within the context of a larger application. For example,more » it could be used for a web service, desktop client, or to compute simple values in a scripting environment.« less

Optimal Cost Avoidance Investment and Pricing Strategies for Performance-Based Post-Production Service Contracts

DTIC Science & Technology

2011-04-30

a BS degree in Mathematics and an MS degree in Statistics and Financial and Actuarial Mathematics from Kiev National Taras Shevchenko University...degrees from Rutgers University in Industrial Engineering (PhD and MS) and Statistics (MS) and from Universidad Nacional Autonoma de Mexico in Actuarial ...Science. His research efforts focus on developing mathematical models for the analysis, computation, and optimization of system performance with

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Development of Mechanistic Reasoning and Multilevel Explanations of Ecology in Third Grade Using Agent-Based Models

ERIC Educational Resources Information Center

Dickes, Amanda Catherine; Sengupta, Pratim; Farris, Amy Voss; Satabdi, Basu

2016-01-01

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects…

Common Grounds for Modelling Mathematics in Educational Software

ERIC Educational Resources Information Center

Neuper, Walther

2010-01-01

Two kinds of software, CAS and DGS, are starting to work towards mutual integration. This paper envisages common grounds for such integration based on principles of computer theorem proving (CTP). Presently, the CTP community seems to lack awareness as to which of their products' features might serve mathematics education from high-school to…

A Constructivist Computational Platform to Support Mathematics Education in Elementary School

ERIC Educational Resources Information Center

Garcia, I.; Pacheco, C.

2013-01-01

Many courses for elementary school are based upon teacher presentation and explanation of basic topics, rather than allowing students to develop their own knowledge. This traditional model may turn elementary-level lessons into an extremely theoretical, boring and non-effective process. In this context, research in mathematics elementary education…

The challenge of computer mathematics.

PubMed

Barendregt, Henk; Wiedijk, Freek

2005-10-15

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

Computer-aided decision making.

Treesearch

Keith M. Reynolds; Daniel L. Schmoldt

2006-01-01

Several major classes of software technologies have been used in decisionmaking for forest management applications over the past few decades. These computer-based technologies include mathematical programming, expert systems, network models, multi-criteria decisionmaking, and integrated systems. Each technology possesses unique advantages and disadvantages, and has...

A Comparative Analysis of a Generalized Lanchester Equation Model and a Stochastic Computer Simulation Model.

DTIC Science & Technology

1987-03-01

model is one in which words or numerical descriptions are used to represent an entity or process. An example of a symbolic model is a mathematical ...are the third type of model used in modeling combat attrition. Analytical models are symbolic models which use mathematical symbols and equations to...simplicity and the ease of tracing through the mathematical computations. In this section I will discuss some of the shortcoming which have been

Numerical Modeling of Nonlinear Thermodynamics in SMA Wires

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

Reynolds, D R; Kloucek, P

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associatedmore » with such materials.« less

CDM: Teaching Discrete Mathematics to Computer Science Majors

ERIC Educational Resources Information Center

Sutner, Klaus

2005-01-01

CDM, for computational discrete mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definition-theorem-proof model, and instead relies heavily on computation as a source of motivation and also for experimentation and illustration. The emphasis on…

Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions.

PubMed

Nehaniv, Chrystopher L; Rhodes, John; Egri-Nagy, Attila; Dini, Paolo; Morris, Eric Rothstein; Horváth, Gábor; Karimi, Fariba; Schreckling, Daniel; Schilstra, Maria J

2015-07-28

Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.

Simulating Microbial Community Patterning Using Biocellion

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

Kang, Seung-Hwa; Kahan, Simon H.; Momeni, Babak

2014-04-17

Mathematical modeling and computer simulation are important tools for understanding complex interactions between cells and their biotic and abiotic environment: similarities and differences between modeled and observed behavior provide the basis for hypothesis forma- tion. Momeni et al. [5] investigated pattern formation in communities of yeast strains engaging in different types of ecological interactions, comparing the predictions of mathematical modeling and simulation to actual patterns observed in wet-lab experiments. However, simu- lations of millions of cells in a three-dimensional community are ex- tremely time-consuming. One simulation run in MATLAB may take a week or longer, inhibiting exploration of the vastmore » space of parameter combinations and assumptions. Improving the speed, scale, and accu- racy of such simulations facilitates hypothesis formation and expedites discovery. Biocellion is a high performance software framework for ac- celerating discrete agent-based simulation of biological systems with millions to trillions of cells. Simulations of comparable scale and accu- racy to those taking a week of computer time using MATLAB require just hours using Biocellion on a multicore workstation. Biocellion fur- ther accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. Biocellion targets computational biologists who have mathematical modeling backgrounds and basic C++ programming skills. This chap- ter describes the necessary steps to adapt the original Momeni et al.'s model to the Biocellion framework as a case study.« less

Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model

NASA Astrophysics Data System (ADS)

Feng, Jinchao; Lansford, Joshua; Mironenko, Alexander; Pourkargar, Davood Babaei; Vlachos, Dionisios G.; Katsoulakis, Markos A.

2018-03-01

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Mathematical Modeling of Diverse Phenomena

NASA Technical Reports Server (NTRS)

Howard, J. C.

1979-01-01

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

Analytical approximation of the InGaZnO thin-film transistors surface potential

NASA Astrophysics Data System (ADS)

Colalongo, Luigi

2016-10-01

Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

Terrestrial implications of mathematical modeling developed for space biomedical research

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology

PubMed Central

Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; dos Santos, Rodrigo Weber; Lobosco, Marcelo

2017-01-01

ABSTRACT New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus. PMID:28027002

Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.

PubMed

Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo

2017-02-01

New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.

Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

NASA Astrophysics Data System (ADS)

Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.

2017-10-01

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.

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

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

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

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

Computational modeling in melanoma for novel drug discovery.

PubMed

Pennisi, Marzio; Russo, Giulia; Di Salvatore, Valentina; Candido, Saverio; Libra, Massimo; Pappalardo, Francesco

2016-06-01

There is a growing body of evidence highlighting the applications of computational modeling in the field of biomedicine. It has recently been applied to the in silico analysis of cancer dynamics. In the era of precision medicine, this analysis may allow the discovery of new molecular targets useful for the design of novel therapies and for overcoming resistance to anticancer drugs. According to its molecular behavior, melanoma represents an interesting tumor model in which computational modeling can be applied. Melanoma is an aggressive tumor of the skin with a poor prognosis for patients with advanced disease as it is resistant to current therapeutic approaches. This review discusses the basics of computational modeling in melanoma drug discovery and development. Discussion includes the in silico discovery of novel molecular drug targets, the optimization of immunotherapies and personalized medicine trials. Mathematical and computational models are gradually being used to help understand biomedical data produced by high-throughput analysis. The use of advanced computer models allowing the simulation of complex biological processes provides hypotheses and supports experimental design. The research in fighting aggressive cancers, such as melanoma, is making great strides. Computational models represent the key component to complement these efforts. Due to the combinatorial complexity of new drug discovery, a systematic approach based only on experimentation is not possible. Computational and mathematical models are necessary for bringing cancer drug discovery into the era of omics, big data and personalized medicine.

Estimating Sobol Sensitivity Indices Using Correlations

EPA Science Inventory

Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol's method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on...

Research on Computers in Mathematics Education, IV. The Use of Computers in Mathematics Education Resource Series.

ERIC Educational Resources Information Center

Kieren, Thomas E.

This last paper in a set of four reviews research on a wide variety of computer applications in the mathematics classroom. It covers computer-based instruction, especially drill-and-practice and tutorial modes; computer-managed instruction; and computer-augmented problem-solving. Analytical comments on the findings and status of the research are…

Differences in the Mathematics-Vocabulary Knowledge of Fifth-Grade Students with and without Learning Difficulties

ERIC Educational Resources Information Center

Forsyth, Suzanne R.; Powell, Sarah R.

2017-01-01

The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of fifth-grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and…

Automation of reliability evaluation procedures through CARE - The computer-aided reliability estimation program.

NASA Technical Reports Server (NTRS)

Mathur, F. P.

1972-01-01

Description of an on-line interactive computer program called CARE (Computer-Aided Reliability Estimation) which can model self-repair and fault-tolerant organizations and perform certain other functions. Essentially CARE consists of a repository of mathematical equations defining the various basic redundancy schemes. These equations, under program control, are then interrelated to generate the desired mathematical model to fit the architecture of the system under evaluation. The mathematical model is then supplied with ground instances of its variables and is then evaluated to generate values for the reliability-theoretic functions applied to the model.

Modellus: Learning Physics with Mathematical Modelling

NASA Astrophysics Data System (ADS)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations--differential equations--are the most important mathematical objects used for modelling Natural phenomena. In traditional approaches, they are introduced only at advanced level, because it takes a long time for students to be introduced to the fundamental principles of Calculus. With the new proposed approach, rates of change can be introduced also at early stages on learning if teachers stress semi-quantitative reasoning and use adequate computer tools. In this thesis, there is also presented Modellus, a computer tool for modelling and experimentation. This computer tool has a user interface that allows students to start doing meaningful conceptual and empirical experiments without the need to learn new syntax, as is usual with established tools. The different steps in the process of constructing and exploring models can be done with Modellus, both from physical points of view and from mathematical points of view. Modellus activities show how mathematics and physics have a unity that is very difficult to see with traditional approaches. Mathematical models are treated as concrete-abstract objects: concrete in the sense that they can be manipulated directly with a computer and abstract in the sense that they are representations of relations between variables. Data gathered from two case studies, one with secondary school students and another with first year undergraduate students support the main ideas of the thesis. Also data gathered from teachers (from college and secondary schools), mainly through an email structured questionnaire, shows that teachers agree on the potential of modelling in the learning of physics (and mathematics) and of the most important aspects of the proposed framework to integrate modelling as an essential component of the curriculum. Schools, as all institutions, change at a very slow rate. There are a multitude of reasons for this. And traditional curricula, where the emphasis is on rote learning of facts, can only be changed if schools have access to new and powerful views of learning and to new tools, that support meaningful conceptual learning and are as common and easy to use as pencil and paper.

An adaptive drug delivery design using neural networks for effective treatment of infectious diseases: a simulation study.

PubMed

Padhi, Radhakant; Bhardhwaj, Jayender R

2009-06-01

An adaptive drug delivery design is presented in this paper using neural networks for effective treatment of infectious diseases. The generic mathematical model used describes the coupled evolution of concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of a damaged organ due to the disease under the influence of external drugs. From a system theoretic point of view, the external drugs can be interpreted as control inputs, which can be designed based on control theoretic concepts. In this study, assuming a set of nominal parameters in the mathematical model, first a nonlinear controller (drug administration) is designed based on the principle of dynamic inversion. This nominal drug administration plan was found to be effective in curing "nominal model patients" (patients whose immunological dynamics conform to the mathematical model used for the control design exactly. However, it was found to be ineffective in curing "realistic model patients" (patients whose immunological dynamics may have off-nominal parameter values and possibly unwanted inputs) in general. Hence, to make the drug delivery dosage design more effective for realistic model patients, a model-following adaptive control design is carried out next by taking the help of neural networks, that are trained online. Simulation studies indicate that the adaptive controller proposed in this paper holds promise in killing the invading pathogens and healing the damaged organ even in the presence of parameter uncertainties and continued pathogen attack. Note that the computational requirements for computing the control are very minimal and all associated computations (including the training of neural networks) can be carried out online. However it assumes that the required diagnosis process can be carried out at a sufficient faster rate so that all the states are available for control computation.

Mathematics Word Problem Solving: An Investigation into Schema-Based Instruction in a Computer-Mediated Setting and a Teacher-Mediated Setting with Mathematically Low-Performing Students

ERIC Educational Resources Information Center

Leh, Jayne

2011-01-01

Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…

Comparison of the Effects of Computer-Based Practice and Conceptual Understanding Interventions on Mathematics Fact Retention and Generalization

ERIC Educational Resources Information Center

Kanive, Rebecca; Nelson, Peter M.; Burns, Matthew K.; Ysseldyke, James

2014-01-01

The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story

ERIC Educational Resources Information Center

Gunbas, N.

2015-01-01

The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

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

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

COMPILATION OF GROUND-WATER MODELS

EPA Science Inventory

Ground-water modeling is a computer-based methodology for mathematical analysis of the mechanisms and controls of ground-water systems for the evaluation of policies, action, and designs that may affect such systems. n addition to satisfying scientific interest in the workings of...

Development of a Model for Some Aspects of University Policy. Technical Report.

ERIC Educational Resources Information Center

Goossens, J. L. M.; And Others

A method to calculate the need for academic staff per faculty, based on educational programs and numbers of students, is described which is based on quantitative relations between programs, student enrollment, and total budget. The model is described schematically and presented in a mathematical form adapted to computer processing. Its application…

Estimating wildfire behavior and effects

Treesearch

Frank A. Albini

1976-01-01

This paper presents a brief survey of the research literature on wildfire behavior and effects and assembles formulae and graphical computation aids based on selected theoretical and empirical models. The uses of mathematical fire behavior models are discussed, and the general capabilities and limitations of currently available models are outlined.

Computer-Game-Based Tutoring of Mathematics

ERIC Educational Resources Information Center

Ke, Fengfeng

2013-01-01

This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…

Metrological traceability in education: A practical online system for measuring and managing middle school mathematics instruction

NASA Astrophysics Data System (ADS)

Torres Irribarra, D.; Freund, R.; Fisher, W.; Wilson, M.

2015-02-01

Computer-based, online assessments modelled, designed, and evaluated for adaptively administered invariant measurement are uniquely suited to defining and maintaining traceability to standardized units in education. An assessment of this kind is embedded in the Assessing Data Modeling and Statistical Reasoning (ADM) middle school mathematics curriculum. Diagnostic information about middle school students' learning of statistics and modeling is provided via computer-based formative assessments for seven constructs that comprise a learning progression for statistics and modeling from late elementary through the middle school grades. The seven constructs are: Data Display, Meta-Representational Competence, Conceptions of Statistics, Chance, Modeling Variability, Theory of Measurement, and Informal Inference. The end product is a web-delivered system built with Ruby on Rails for use by curriculum development teams working with classroom teachers in designing, developing, and delivering formative assessments. The online accessible system allows teachers to accurately diagnose students' unique comprehension and learning needs in a common language of real-time assessment, logging, analysis, feedback, and reporting.

Computational models of the pulmonary circulation: Insights and the move towards clinically directed studies

PubMed Central

Tawhai, Merryn H.; Clark, Alys R.; Burrowes, Kelly S.

2011-01-01

Biophysically-based computational models provide a tool for integrating and explaining experimental data, observations, and hypotheses. Computational models of the pulmonary circulation have evolved from minimal and efficient constructs that have been used to study individual mechanisms that contribute to lung perfusion, to sophisticated multi-scale and -physics structure-based models that predict integrated structure-function relationships within a heterogeneous organ. This review considers the utility of computational models in providing new insights into the function of the pulmonary circulation, and their application in clinically motivated studies. We review mathematical and computational models of the pulmonary circulation based on their application; we begin with models that seek to answer questions in basic science and physiology and progress to models that aim to have clinical application. In looking forward, we discuss the relative merits and clinical relevance of computational models: what important features are still lacking; and how these models may ultimately be applied to further increasing our understanding of the mechanisms occurring in disease of the pulmonary circulation. PMID:22034608

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions.

PubMed

Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji

2018-06-01

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Modeling of Pressure Drop During Refrigerant Condensation in Pipe Minichannels

NASA Astrophysics Data System (ADS)

Sikora, Małgorzata; Bohdal, Tadeusz

2017-12-01

Investigations of refrigerant condensation in pipe minichannels are very challenging and complicated issue. Due to the multitude of influences very important is mathematical and computer modeling. Its allows for performing calculations for many different refrigerants under different flow conditions. A large number of experimental results published in the literature allows for experimental verification of correctness of the models. In this work is presented a mathematical model for calculation of flow resistance during condensation of refrigerants in the pipe minichannel. The model was developed in environment based on conservation equations. The results of calculations were verified by authors own experimental investigations results.

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

Computational models of neuromodulation.

PubMed

Fellous, J M; Linster, C

1998-05-15

Computational modeling of neural substrates provides an excellent theoretical framework for the understanding of the computational roles of neuromodulation. In this review, we illustrate, with a large number of modeling studies, the specific computations performed by neuromodulation in the context of various neural models of invertebrate and vertebrate preparations. We base our characterization of neuromodulations on their computational and functional roles rather than on anatomical or chemical criteria. We review the main framework in which neuromodulation has been studied theoretically (central pattern generation and oscillations, sensory processing, memory and information integration). Finally, we present a detailed mathematical overview of how neuromodulation has been implemented at the single cell and network levels in modeling studies. Overall, neuromodulation is found to increase and control computational complexity.

Using Computation Curriculum-Based Measurement Probes for Error Pattern Analysis

ERIC Educational Resources Information Center

Dennis, Minyi Shih; Calhoon, Mary Beth; Olson, Christopher L.; Williams, Cara

2014-01-01

This article describes how "curriculum-based measurement--computation" (CBM-C) mathematics probes can be used in combination with "error pattern analysis" (EPA) to pinpoint difficulties in basic computation skills for students who struggle with learning mathematics. Both assessment procedures provide ongoing assessment data…

Instructional design in mathematics for undergraduate students based on learning by mistakes approach utilizing scilab assistance

NASA Astrophysics Data System (ADS)

Kartika, H.

2018-03-01

The issue related to making mistake while learning such as negative emotion is found while students learn mathematics with the aid of a computer. When the computer output showed a mistake message, the students considered it as a computer software malfunction. Based on this issue, the writer designs an instructional model based on learning by mistake approach and which is Scilab assisted. The method used in this research is research design involving undergraduate students in matrix algebra courses. The data collected throught survey with questionnaire to gain feedback about the approach implemented. The data analyzed using quantitative descriptive. The instructional design proposed is the student act as a mistake corrector while the teacher acts as a mistake maker. Teacher deliberately makes mistakes with the help of Scilab software. On the other hand, students correct, analyze and explain errors resulting from Scilab software. The result of this research is an ICT based instructional design which is expected to be applicable as an alternative learning in directing students to think positively about mistakes in learning. Furthermore, students are also expected to improve their ability in understanding and thinking critically while solving problems and improving themselves in learning mathematics.

Modeling Flow in Porous Media with Double Porosity/Permeability.

NASA Astrophysics Data System (ADS)

Seyed Joodat, S. H.; Nakshatrala, K. B.; Ballarini, R.

2016-12-01

Although several continuum models are available to study the flow of fluids in porous media with two pore-networks [1], they lack a firm theoretical basis. In this poster presentation, we will present a mathematical model with firm thermodynamic basis and a robust computational framework for studying flow in porous media that exhibit double porosity/permeability. The mathematical model will be derived by appealing to the maximization of rate of dissipation hypothesis, which ensures that the model is in accord with the second law of thermodynamics. We will also present important properties that the solutions under the model satisfy, along with an analytical solution procedure based on the Green's function method. On the computational front, a stabilized mixed finite element formulation will be derived based on the variational multi-scale formalism. The equal-order interpolation, which is computationally the most convenient, is stable under this formulation. The performance of this formulation will be demonstrated using patch tests, numerical convergence study, and representative problems. It will be shown that the pressure and velocity profiles under the double porosity/permeability model are qualitatively and quantitatively different from the corresponding ones under the classical Darcy equations. Finally, it will be illustrated that the surface pore-structure is not sufficient in characterizing the flow through a complex porous medium, which pitches a case for using advanced characterization tools like micro-CT. References [1] G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]," Journal of Applied Mathematics and Mechanics, vol. 24, pp. 1286-1303, 1960.

Automatic computation for optimum height planning of apartment buildings to improve solar access

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

Seong, Yoon-Bok; Kim, Yong-Yee; Seok, Ho-Tae

2011-01-15

The objective of this study is to suggest a mathematical model and an optimal algorithm for determining the height of apartment buildings to satisfy the solar rights of survey buildings or survey housing units. The objective is also to develop an automatic computation model for the optimum height of apartment buildings and then to clarify the performance and expected effects. To accomplish the objective of this study, the following procedures were followed: (1) The necessity of the height planning of obstruction buildings to satisfy the solar rights of survey buildings or survey housing units is demonstrated by analyzing through amore » literature review the recent trend of disputes related to solar rights and to examining the social requirements in terms of solar rights. In addition, the necessity of the automatic computation system for height planning of apartment buildings is demonstrated and a suitable analysis method for this system is chosen by investigating the characteristics of analysis methods for solar rights assessment. (2) A case study on the process of height planning of apartment buildings will be briefly described and the problems occurring in this process will then be examined carefully. (3) To develop an automatic computation model for height planning of apartment buildings, geometrical elements forming apartment buildings are defined by analyzing the geometrical characteristics of apartment buildings. In addition, design factors and regulations required in height planning of apartment buildings are investigated. Based on this knowledge, the methodology and mathematical algorithm to adjust the height of apartment buildings by automatic computation are suggested and probable problems and the ways to resolve these problems are discussed. Finally, the methodology and algorithm for the optimization are suggested. (4) Based on the suggested methodology and mathematical algorithm, the automatic computation model for optimum height of apartment buildings is developed and the developed system is verified through the application of some cases. The effects of the suggested model are then demonstrated quantitatively and qualitatively. (author)« less

Capability of GPGPU for Faster Thermal Analysis Used in Data Assimilation

NASA Astrophysics Data System (ADS)

Takaki, Ryoji; Akita, Takeshi; Shima, Eiji

A thermal mathematical model plays an important role in operations on orbit as well as spacecraft thermal designs. The thermal mathematical model has some uncertain thermal characteristic parameters, such as thermal contact resistances between components, effective emittances of multilayer insulation (MLI) blankets, discouraging make up efficiency and accuracy of the model. A particle filter which is one of successive data assimilation methods has been applied to construct spacecraft thermal mathematical models. This method conducts a lot of ensemble computations, which require large computational power. Recently, General Purpose computing in Graphics Processing Unit (GPGPU) has been attracted attention in high performance computing. Therefore GPGPU is applied to increase the computational speed of thermal analysis used in the particle filter. This paper shows the speed-up results by using GPGPU as well as the application method of GPGPU.

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

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

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

Experiences of Student Mathematics-Teachers in Computer-Based Mathematics Learning Environment

ERIC Educational Resources Information Center

Karatas, Ilhan

2011-01-01

Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving…

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

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

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

PubMed

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

2010-01-01

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

Mathematical learning instruction and teacher motivation factors affecting science technology engineering and math (STEM) major choices in 4-year colleges and universities: Multilevel structural equation modeling

NASA Astrophysics Data System (ADS)

Lee, Ahlam

2011-12-01

Using the Educational Longitudinal Study of 2002/06, this study examined the effects of the selected mathematical learning and teacher motivation factors on graduates' science, technology, engineering, and math (STEM) related major choices in 4-year colleges and universities, as mediated by math performance and math self-efficacy. Using multilevel structural equation modeling, I analyzed: (1) the association between mathematical learning instruction factors (i.e., computer, individual, and lecture-based learning activities in mathematics) and students' STEM major choices in 4-year colleges and universities as mediated by math performance and math self-efficacy and (2) the association between school factor, teacher motivation and students' STEM major choices in 4-year colleges and universities via mediators of math performance and math self-efficacy. The results revealed that among the selected learning experience factors, computer-based learning activities in math classrooms yielded the most positive effects on math self-efficacy, which significantly predicted the increase in the proportion of students' STEM major choice as mediated by math self-efficacy. Further, when controlling for base-year math Item Response Theory (IRT) scores, a positive relationship between individual-based learning activities in math classrooms and the first follow-up math IRT scores emerged, which related to the high proportion of students' STEM major choices. The results also indicated that individual and lecture-based learning activities in math yielded positive effects on math self-efficacy, which related to STEM major choice. Concerning between-school levels, teacher motivation yielded positive effects on the first follow up math IRT score, when controlling for base year IRT score. The results from this study inform educators, parents, and policy makers on how mathematics instruction can improve student math performance and encourage more students to prepare for STEM careers. Students should receive all possible opportunities to use computers to enhance their math self-efficacy, be encouraged to review math materials, and concentrate on listening to math teachers' lectures. While all selected math-learning activities should be embraced in math instruction, computer and individual-based learning activities, which reflect student-driven learning, should be emphasized in the high school instruction. Likewise, students should be encouraged to frequently engage in individual-based learning activities to improve their math performance.

Mathematical modeling and characteristic analysis for over-under turbine based combined cycle engine

NASA Astrophysics Data System (ADS)

Ma, Jingxue; Chang, Juntao; Ma, Jicheng; Bao, Wen; Yu, Daren

2018-07-01

The turbine based combined cycle engine has become the most promising hypersonic airbreathing propulsion system for its superiority of ground self-starting, wide flight envelop and reusability. The simulation model of the turbine based combined cycle engine plays an important role in the research of performance analysis and control system design. In this paper, a turbine based combined cycle engine mathematical model is built on the Simulink platform, including a dual-channel air intake system, a turbojet engine and a ramjet. It should be noted that the model of the air intake system is built based on computational fluid dynamics calculation, which provides valuable raw data for modeling of the turbine based combined cycle engine. The aerodynamic characteristics of turbine based combined cycle engine in turbojet mode, ramjet mode and mode transition process are studied by the mathematical model, and the influence of dominant variables on performance and safety of the turbine based combined cycle engine is analyzed. According to the stability requirement of thrust output and the safety in the working process of turbine based combined cycle engine, a control law is proposed that could guarantee the steady output of thrust by controlling the control variables of the turbine based combined cycle engine in the whole working process.

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-02-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.

The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations.

PubMed

Glaister, Karen

2007-05-01

To determine if the presence of mathematical and computer anxiety in nursing students affects learning of dosage calculations. The quasi-experimental study compared learning outcomes at differing levels of mathematical and computer anxiety when integrative and computer based learning approaches were used. Participants involved a cohort of second year nursing students (n=97). Mathematical anxiety exists in 20% (n=19) of the student nurse population, and 14% (n=13) experienced mathematical testing anxiety. Those students more anxious about mathematics and the testing of mathematics benefited from integrative learning to develop conditional knowledge (F(4,66)=2.52 at p<.05). Computer anxiety was present in 12% (n=11) of participants, with those reporting medium and high levels of computer anxiety performing less well than those with low levels (F(1,81)=3.98 at p<.05). Instructional strategies need to account for the presence of mathematical and computer anxiety when planning an educational program to develop competency in dosage calculations.

Review Of Applied Mathematical Models For Describing The Behaviour Of Aqueous Humor In Eye Structures

NASA Astrophysics Data System (ADS)

Dzierka, M.; Jurczak, P.

2015-12-01

In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.

Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

USGS Publications Warehouse

Iverson, Richard M.; LeVeque, Randall J.

2009-01-01

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

Mathematical and computational aspects of nonuniform frictional slip modeling

NASA Astrophysics Data System (ADS)

Gorbatikh, Larissa

2004-07-01

A mechanics-based model of non-uniform frictional sliding is studied from the mathematical/computational analysis point of view. This problem is of a key importance for a number of applications (particularly geomechanical ones), where materials interfaces undergo partial frictional sliding under compression and shear. We show that the problem is reduced to Dirichlet's problem for monotonic loading and to Riemman's problem for cyclic loading. The problem may look like a traditional crack interaction problem, however, it is confounded by the fact that locations of n sliding intervals are not known. They are to be determined from the condition for the stress intensity factors: KII=0 at the ends of the sliding zones. Computationally, it reduces to solving a system of 2n coupled non-linear algebraic equations involving singular integrals with unknown limits of integration.

ADAM: analysis of discrete models of biological systems using computer algebra.

PubMed

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

A Computer Based Program to Improve Reading and Mathematics Scores for High School Students.

ERIC Educational Resources Information Center

Bond, Carole L.; And Others

A study examined the effect on reading achievement, mathematics achievement, and ACT scores when computer based instruction (CBI) was compressed into a 6-week period of time. In addition, the effects of learning style and receptive language deficits on these scores were studied. Computer based instruction is a primary source of instruction that…

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

PubMed

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.

Method and system for dynamic probabilistic risk assessment

NASA Technical Reports Server (NTRS)

Dugan, Joanne Bechta (Inventor); Xu, Hong (Inventor)

2013-01-01

The DEFT methodology, system and computer readable medium extends the applicability of the PRA (Probabilistic Risk Assessment) methodology to computer-based systems, by allowing DFT (Dynamic Fault Tree) nodes as pivot nodes in the Event Tree (ET) model. DEFT includes a mathematical model and solution algorithm, supports all common PRA analysis functions and cutsets. Additional capabilities enabled by the DFT include modularization, phased mission analysis, sequence dependencies, and imperfect coverage.

Teachers' Use of Computational Tools to Construct and Explore Dynamic Mathematical Models

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2011-01-01

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

Model-Based Design of Biochemical Microreactors

PubMed Central

Elbinger, Tobias; Gahn, Markus; Neuss-Radu, Maria; Hante, Falk M.; Voll, Lars M.; Leugering, Günter; Knabner, Peter

2016-01-01

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphate. PMID:26913283

Computational neuroanatomy: ontology-based representation of neural components and connectivity.

PubMed

Rubin, Daniel L; Talos, Ion-Florin; Halle, Michael; Musen, Mark A; Kikinis, Ron

2009-02-05

A critical challenge in neuroscience is organizing, managing, and accessing the explosion in neuroscientific knowledge, particularly anatomic knowledge. We believe that explicit knowledge-based approaches to make neuroscientific knowledge computationally accessible will be helpful in tackling this challenge and will enable a variety of applications exploiting this knowledge, such as surgical planning. We developed ontology-based models of neuroanatomy to enable symbolic lookup, logical inference and mathematical modeling of neural systems. We built a prototype model of the motor system that integrates descriptive anatomic and qualitative functional neuroanatomical knowledge. In addition to modeling normal neuroanatomy, our approach provides an explicit representation of abnormal neural connectivity in disease states, such as common movement disorders. The ontology-based representation encodes both structural and functional aspects of neuroanatomy. The ontology-based models can be evaluated computationally, enabling development of automated computer reasoning applications. Neuroanatomical knowledge can be represented in machine-accessible format using ontologies. Computational neuroanatomical approaches such as described in this work could become a key tool in translational informatics, leading to decision support applications that inform and guide surgical planning and personalized care for neurological disease in the future.

An evidential reasoning extension to quantitative model-based failure diagnosis

NASA Technical Reports Server (NTRS)

Gertler, Janos J.; Anderson, Kenneth C.

1992-01-01

The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied. A quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system. On the basis of the latter, diagnostic models are derived each of which comprises a set of orthogonal parity equations. To improve the robustness of the algorithm, several models may be used in parallel, providing potentially incomplete and/or conflicting inferences. Dempster's rule of combination is used to integrate evidence from the different models. The basic probability measures are assigned utilizing quantitative information extracted from the mathematical model and from online computation performed therewith.

A preoperative mathematic model for computed tomographic guided microwave ablation treatment of hepatic dome tumors.

PubMed

Gao, Fei; Wang, Guo-Bao; Xiang, Zhan-Wang; Yang, Bin; Xue, Jing-Bing; Mo, Zhi-Qiang; Zhong, Zhi-Hui; Zhang, Tao; Zhang, Fu-Jun; Fan, Wei-Jun

2016-05-03

This study sought to prospectively evaluate the feasibility and safety of a preoperative mathematic model for computed tomographic(CT) guided microwave(MW) ablation treatment of hepatic dome tumors. This mathematic model was a regular cylinder quantifying appropriate puncture routes from the bottom up. A total of 103 patients with hepatic dome tumors were enrolled and randomly divided into 2 groups based on whether this model was used or not: Group A (using the model; n = 43) versus Group B (not using the model; n = 60). All tumors were treated by CT-guided MW ablation and follow-up contrast CT were reviewed. The average number of times for successful puncture, average ablation time, and incidence of right shoulder pain were less in Group A than Group B (1.4 vs. 2.5, P = 0.001; 8.8 vs. 11.1 minutes, P = 0.003; and 4.7% vs. 20%, P = 0.039). The technical success rate was higher in Group A than Group B (97.7% vs. 85.0%, P = 0.032). There were no significant differences between the two groups in primary and secondary technique efficacy rates (97.7% vs. 88.3%, P = 0.081; 90.0% vs. 72.7%, P = 0.314). No major complications occurred in both groups. The mathematic model of regular cylinder is feasible and safe for CT-guided MW ablation in treating hepatic dome tumors.

Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

PubMed

Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

2015-02-01

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

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

He, Xu; Tuo, Rui; Jeff Wu, C. F.

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

DOE PAGES

He, Xu; Tuo, Rui; Jeff Wu, C. F.

2017-01-31

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Variables that Affect Math Teacher Candidates' Intentions to Integrate Computer-Assisted Mathematics Education (CAME)

ERIC Educational Resources Information Center

Erdogan, Ahmet

2010-01-01

Based on Social Cognitive Carier Theory (SCCT) (Lent, Brown, & Hackett, 1994, 2002), this study tested the effects of mathematics teacher candidates' self-efficacy in, outcome expectations from, and interest in CAME on their intentions to integrate Computer-Assisted Mathematics Education (CAME). While mathematics teacher candidates' outcome…

A System Computational Model of Implicit Emotional Learning

PubMed Central

Puviani, Luca; Rama, Sidita

2016-01-01

Nowadays, the experimental study of emotional learning is commonly based on classical conditioning paradigms and models, which have been thoroughly investigated in the last century. Unluckily, models based on classical conditioning are unable to explain or predict important psychophysiological phenomena, such as the failure of the extinction of emotional responses in certain circumstances (for instance, those observed in evaluative conditioning, in post-traumatic stress disorders and in panic attacks). In this manuscript, starting from the experimental results available from the literature, a computational model of implicit emotional learning based both on prediction errors computation and on statistical inference is developed. The model quantitatively predicts (a) the occurrence of evaluative conditioning, (b) the dynamics and the resistance-to-extinction of the traumatic emotional responses, (c) the mathematical relation between classical conditioning and unconditioned stimulus revaluation. Moreover, we discuss how the derived computational model can lead to the development of new animal models for resistant-to-extinction emotional reactions and novel methodologies of emotions modulation. PMID:27378898

A System Computational Model of Implicit Emotional Learning.

PubMed

Puviani, Luca; Rama, Sidita

2016-01-01

Nowadays, the experimental study of emotional learning is commonly based on classical conditioning paradigms and models, which have been thoroughly investigated in the last century. Unluckily, models based on classical conditioning are unable to explain or predict important psychophysiological phenomena, such as the failure of the extinction of emotional responses in certain circumstances (for instance, those observed in evaluative conditioning, in post-traumatic stress disorders and in panic attacks). In this manuscript, starting from the experimental results available from the literature, a computational model of implicit emotional learning based both on prediction errors computation and on statistical inference is developed. The model quantitatively predicts (a) the occurrence of evaluative conditioning, (b) the dynamics and the resistance-to-extinction of the traumatic emotional responses, (c) the mathematical relation between classical conditioning and unconditioned stimulus revaluation. Moreover, we discuss how the derived computational model can lead to the development of new animal models for resistant-to-extinction emotional reactions and novel methodologies of emotions modulation.

BehavePlus fire modeling system, version 5.0: Variables

Treesearch

Patricia L. Andrews

2009-01-01

This publication has been revised to reflect updates to version 4.0 of the BehavePlus software. It was originally published as the BehavePlus fire modeling system, version 4.0: Variables in July, 2008.The BehavePlus fire modeling system is a computer program based on mathematical models that describe wildland fire behavior and effects and the...

Current problems in applied mathematics and mathematical modeling

NASA Astrophysics Data System (ADS)

Alekseev, A. S.

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

Computational model, method, and system for kinetically-tailoring multi-drug chemotherapy for individuals

DOEpatents

Gardner, Shea Nicole

2007-10-23

A method and system for tailoring treatment regimens to individual patients with diseased cells exhibiting evolution of resistance to such treatments. A mathematical model is provided which models rates of population change of proliferating and quiescent diseased cells using cell kinetics and evolution of resistance of the diseased cells, and pharmacokinetic and pharmacodynamic models. Cell kinetic parameters are obtained from an individual patient and applied to the mathematical model to solve for a plurality of treatment regimens, each having a quantitative efficacy value associated therewith. A treatment regimen may then be selected from the plurlaity of treatment options based on the efficacy value.

A neotropical Miocene pollen database employing image-based search and semantic modeling.

PubMed

Han, Jing Ginger; Cao, Hongfei; Barb, Adrian; Punyasena, Surangi W; Jaramillo, Carlos; Shyu, Chi-Ren

2014-08-01

Digital microscopic pollen images are being generated with increasing speed and volume, producing opportunities to develop new computational methods that increase the consistency and efficiency of pollen analysis and provide the palynological community a computational framework for information sharing and knowledge transfer. • Mathematical methods were used to assign trait semantics (abstract morphological representations) of the images of neotropical Miocene pollen and spores. Advanced database-indexing structures were built to compare and retrieve similar images based on their visual content. A Web-based system was developed to provide novel tools for automatic trait semantic annotation and image retrieval by trait semantics and visual content. • Mathematical models that map visual features to trait semantics can be used to annotate images with morphology semantics and to search image databases with improved reliability and productivity. Images can also be searched by visual content, providing users with customized emphases on traits such as color, shape, and texture. • Content- and semantic-based image searches provide a powerful computational platform for pollen and spore identification. The infrastructure outlined provides a framework for building a community-wide palynological resource, streamlining the process of manual identification, analysis, and species discovery.

Projects Using a Computer Algebra System in First-Year Undergraduate Mathematics

ERIC Educational Resources Information Center

Rosenzweig, Martin

2007-01-01

This paper illustrates the use of computer-based projects in two one-semester first-year undergraduate mathematics classes. Developed over a period of years, the approach is one in which the classes are organised into work-groups, with computer-based projects being undertaken periodically to illustrate the class material. These projects are…

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

PubMed

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

2017-11-01

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

Workshop Physics Activity Guide, Module 3: Heat Temperature and Nuclear Radiation, Thermodynamics, Kinetic Theory, Heat Engines, Nuclear Decay, and Random Monitoring (Units 16 - 18 & 28)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research.

Prediction of blood pressure and blood flow in stenosed renal arteries using CFD

NASA Astrophysics Data System (ADS)

Jhunjhunwala, Pooja; Padole, P. M.; Thombre, S. B.; Sane, Atul

2018-04-01

In the present work an attempt is made to develop a diagnostive tool for renal artery stenosis (RAS) which is inexpensive and in-vitro. To analyse the effects of increase in the degree of severity of stenosis on hypertension and blood flow, haemodynamic parameters are studied by performing numerical simulations. A total of 16 stenosed models with varying degree of stenosis severity from 0-97.11% are assessed numerically. Blood is modelled as a shear-thinning, non-Newtonian fluid using the Carreau model. Computational Fluid Dynamics (CFD) analysis is carried out to compute the values of flow parameters like maximum velocity and maximum pressure attained by blood due to stenosis under pulsatile flow. These values are further used to compute the increase in blood pressure and decrease in available blood flow to kidney. The computed available blood flow and secondary hypertension for varying extent of stenosis are mapped by curve fitting technique using MATLAB and a mathematical model is developed. Based on these mathematical models, a quantification tool is developed for tentative prediction of probable availability of blood flow to the kidney and severity of stenosis if secondary hypertension is known.

Mathematical and Computational Modeling in Complex Biological Systems

PubMed Central

Li, Wenyang; Zhu, Xiaoliang

2017-01-01

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology. PMID:28386558

Mathematical and Computational Modeling in Complex Biological Systems.

PubMed

Ji, Zhiwei; Yan, Ke; Li, Wenyang; Hu, Haigen; Zhu, Xiaoliang

2017-01-01

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

Computational Literacy and "The Big Picture" Concerning Computers in Mathematics Education

ERIC Educational Resources Information Center

diSessa, Andrea A.

2018-01-01

This article develops some ideas concerning the "big picture" of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of "computation as a new literacy" in some detail and with concrete examples of sixth grade students…

Software For Computing Reliability Of Other Software

NASA Technical Reports Server (NTRS)

Nikora, Allen; Antczak, Thomas M.; Lyu, Michael

1995-01-01

Computer Aided Software Reliability Estimation (CASRE) computer program developed for use in measuring reliability of other software. Easier for non-specialists in reliability to use than many other currently available programs developed for same purpose. CASRE incorporates mathematical modeling capabilities of public-domain Statistical Modeling and Estimation of Reliability Functions for Software (SMERFS) computer program and runs in Windows software environment. Provides menu-driven command interface; enabling and disabling of menu options guides user through (1) selection of set of failure data, (2) execution of mathematical model, and (3) analysis of results from model. Written in C language.

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

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

Computer Assisted Vocational Math. Written for TRS-80, Model I, Level II, 16K.

ERIC Educational Resources Information Center

Daly, Judith; And Others

This computer-assisted curriculum is intended to be used to enhance a vocational mathematics/applied mathematics course. A total of 32 packets were produced to increase the basic mathematics skills of students in the following vocational programs: automotive trades, beauty culture, building trades, climate control, electrical trades,…

Thinking is believing.

PubMed

Kasturirangan, Rajesh

2008-01-01

Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures.

A Seminar in Mathematical Model-Building.

ERIC Educational Resources Information Center

Smith, David A.

1979-01-01

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

Development and application of unified algorithms for problems in computational science

NASA Technical Reports Server (NTRS)

Shankar, Vijaya; Chakravarthy, Sukumar

1987-01-01

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

The Proposal of a Evolutionary Strategy Generating the Data Structures Based on a Horizontal Tree for the Tests

NASA Astrophysics Data System (ADS)

Żukowicz, Marek; Markiewicz, Michał

2016-09-01

The aim of the article is to present a mathematical definition of the object model, that is known in computer science as TreeList and to show application of this model for design evolutionary algorithm, that purpose is to generate structures based on this object. The first chapter introduces the reader to the problem of presenting data using the TreeList object. The second chapter describes the problem of testing data structures based on TreeList. The third one shows a mathematical model of the object TreeList and the parameters, used in determining the utility of structures created through this model and in evolutionary strategy, that generates these structures for testing purposes. The last chapter provides a brief summary and plans for future research related to the algorithm presented in the article.

The Effect of Advisement and Competition on Transfer, Advisor Use, and Attitude toward Mathematics Using a Computer-Based Simulation Game.

ERIC Educational Resources Information Center

Van Eck, Richard

This study looks at the roles that competition and context of advisement play in transfer, advisor use, attitude toward mathematics, and attitude toward instruction in a computer-based simulation game that required the use of mathematics skills. It is concluded that for transfer training, non-competitive simulation games might be the best choice,…

Applicability of mathematical modeling to problems of environmental physiology

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Identification of metabolic pathways using pathfinding approaches: a systematic review.

PubMed

Abd Algfoor, Zeyad; Shahrizal Sunar, Mohd; Abdullah, Afnizanfaizal; Kolivand, Hoshang

2017-03-01

Metabolic pathways have become increasingly available for various microorganisms. Such pathways have spurred the development of a wide array of computational tools, in particular, mathematical pathfinding approaches. This article can facilitate the understanding of computational analysis of metabolic pathways in genomics. Moreover, stoichiometric and pathfinding approaches in metabolic pathway analysis are discussed. Three major types of studies are elaborated: stoichiometric identification models, pathway-based graph analysis and pathfinding approaches in cellular metabolism. Furthermore, evaluation of the outcomes of the pathways with mathematical benchmarking metrics is provided. This review would lead to better comprehension of metabolism behaviors in living cells, in terms of computed pathfinding approaches. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oup.com.

BIOCOMPUTATION: some history and prospects.

PubMed

Cull, Paul

2013-06-01

At first glance, biology and computer science are diametrically opposed sciences. Biology deals with carbon based life forms shaped by evolution and natural selection. Computer Science deals with electronic machines designed by engineers and guided by mathematical algorithms. In this brief paper, we review biologically inspired computing. We discuss several models of computation which have arisen from various biological studies. We show what these have in common, and conjecture how biology can still suggest answers and models for the next generation of computing problems. We discuss computation and argue that these biologically inspired models do not extend the theoretical limits on computation. We suggest that, in practice, biological models may give more succinct representations of various problems, and we mention a few cases in which biological models have proved useful. We also discuss the reciprocal impact of computer science on biology and cite a few significant contributions to biological science. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

New approach for T-wave peak detection and T-wave end location in 12-lead paced ECG signals based on a mathematical model.

PubMed

Madeiro, João P V; Nicolson, William B; Cortez, Paulo C; Marques, João A L; Vázquez-Seisdedos, Carlos R; Elangovan, Narmadha; Ng, G Andre; Schlindwein, Fernando S

2013-08-01

This paper presents an innovative approach for T-wave peak detection and subsequent T-wave end location in 12-lead paced ECG signals based on a mathematical model of a skewed Gaussian function. Following the stage of QRS segmentation, we establish search windows using a number of the earliest intervals between each QRS offset and subsequent QRS onset. Then, we compute a template based on a Gaussian-function, modified by a mathematical procedure to insert asymmetry, which models the T-wave. Cross-correlation and an approach based on the computation of Trapezium's area are used to locate, respectively, the peak and end point of each T-wave throughout the whole raw ECG signal. For evaluating purposes, we used a database of high resolution 12-lead paced ECG signals, recorded from patients with ischaemic cardiomyopathy (ICM) in the University Hospitals of Leicester NHS Trust, UK, and the well-known QT database. The average T-wave detection rates, sensitivity and positive predictivity, were both equal to 99.12%, for the first database, and, respectively, equal to 99.32% and 99.47%, for QT database. The average time errors computed for T-wave peak and T-wave end locations were, respectively, -0.38±7.12 ms and -3.70±15.46 ms, for the first database, and 1.40±8.99 ms and 2.83±15.27 ms, for QT database. The results demonstrate the accuracy, consistency and robustness of the proposed method for a wide variety of T-wave morphologies studied. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Computer simulation of the metastatic progression.

PubMed

Wedemann, Gero; Bethge, Anja; Haustein, Volker; Schumacher, Udo

2014-01-01

A novel computer model based on a discrete event simulation procedure describes quantitatively the processes underlying the metastatic cascade. Analytical functions describe the size of the primary tumor and the metastases, while a rate function models the intravasation events of the primary tumor and metastases. Events describe the behavior of the malignant cells until the formation of new metastases. The results of the computer simulations are in quantitative agreement with clinical data determined from a patient with hepatocellular carcinoma in the liver. The model provides a more detailed view on the process than a conventional mathematical model. In particular, the implications of interventions on metastasis formation can be calculated.

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

EPR-based material modelling of soils

NASA Astrophysics Data System (ADS)

Faramarzi, Asaad; Alani, Amir M.

2013-04-01

In the past few decades, as a result of the rapid developments in computational software and hardware, alternative computer aided pattern recognition approaches have been introduced to modelling many engineering problems, including constitutive modelling of materials. The main idea behind pattern recognition systems is that they learn adaptively from experience and extract various discriminants, each appropriate for its purpose. In this work an approach is presented for developing material models for soils based on evolutionary polynomial regression (EPR). EPR is a recently developed hybrid data mining technique that searches for structured mathematical equations (representing the behaviour of a system) using genetic algorithm and the least squares method. Stress-strain data from triaxial tests are used to train and develop EPR-based material models for soil. The developed models are compared with some of the well-known conventional material models and it is shown that EPR-based models can provide a better prediction for the behaviour of soils. The main benefits of using EPR-based material models are that it provides a unified approach to constitutive modelling of all materials (i.e., all aspects of material behaviour can be implemented within a unified environment of an EPR model); it does not require any arbitrary choice of constitutive (mathematical) models. In EPR-based material models there are no material parameters to be identified. As the model is trained directly from experimental data therefore, EPR-based material models are the shortest route from experimental research (data) to numerical modelling. Another advantage of EPR-based constitutive model is that as more experimental data become available, the quality of the EPR prediction can be improved by learning from the additional data, and therefore, the EPR model can become more effective and robust. The developed EPR-based material models can be incorporated in finite element (FE) analysis.

Computer-Aided Air-Traffic Control In The Terminal Area

NASA Technical Reports Server (NTRS)

Erzberger, Heinz

1995-01-01

Developmental computer-aided system for automated management and control of arrival traffic at large airport includes three integrated subsystems. One subsystem, called Traffic Management Advisor, another subsystem, called Descent Advisor, and third subsystem, called Final Approach Spacing Tool. Data base that includes current wind measurements and mathematical models of performances of types of aircraft contributes to effective operation of system.

Collective Properties of Neural Systems and Their Relation to Other Physical Models

DTIC Science & Technology

1988-08-05

been computed explicitly. This has been achieved algorithmically by utilizing methods introduced earlier. It should be emphasized that in addition to...Research Institute for Mathematical Sciences. K’oto Universin. K roto 606. .apan and E. BAROUCH Department of Mathematics and Computer Sciene. Clarkon...Mathematics and Computer Science, Clarkson University, where this work was collaborated. References I. IBabu, S. V. and Barouch E., An exact soIlution for the

Dynamic Analyses Including Joints Of Truss Structures

NASA Technical Reports Server (NTRS)

Belvin, W. Keith

1991-01-01

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

Traditional vs. Innovative Uses of Computers among Mathematics Pre-Service Teachers in Serbia

ERIC Educational Resources Information Center

Teo, Timothy; Milutinovic, Verica; Zhou, Mingming; Bankovic, Dragic

2017-01-01

This study examined pre-service teachers' intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers' experience with computers and their technological pedagogical content knowledge (TPCK).…

Optimization of Cooling Water Flow Rate in Nuclear and Thermal Power Plants Based on a Mathematical Model of Cooling Systems{sup 1}

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

Murav’ev, V. P., E-mail: murval1@mail.ru; Kochetkov, A. V.; Glazova, E. G.

A mathematical model and algorithms are proposed for automatic calculation of the optimum flow rate of cooling water in nuclear and thermal power plants with cooling systems of arbitrary complexity. An unlimited number of configuration and design variants are assumed with the possibility of obtaining a result for any computational time interval, from monthly to hourly. The structural solutions corresponding to an optimum cooling water flow rate can be used for subsequent engineering-economic evaluation of the best cooling system variant. The computerized mathematical model and algorithms make it possible to determine the availability and degree of structural changes for themore » cooling system in all stages of the life cycle of a plant.« less

Review and verification of CARE 3 mathematical model and code

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

PubMed Central

Zenker, Sven; Rubin, Jonathan; Clermont, Gilles

2007-01-01

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information. PMID:17997590

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Mathematical modelling of the human cardiovascular system in the presence of stenosis

NASA Technical Reports Server (NTRS)

Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

1993-01-01

This paper reports a theoretical study on the distribution of blood flow in the human cardiovascular system when one or more blood vessels are affected by stenosis. The analysis employs a mathematical model of the entire system based on the finite element method. The arterial-venous network is represented by a large number of interconnected segments in the model. Values for the model parameters are based upon the published data on the physiological and rheological properties of blood. Computational results show how blood flow through various parts of the cardiovascular system is affected by stenosis in different blood vessels. No significant changes in the flow parameters of the cardiovascular system were found to occur when the reduction in the lumen diameter of the stenosed vessels was less than 65%.

Models of Individual Trajectories in Computer-Assisted Instruction for Deaf Students. Technical Report No. 214.

ERIC Educational Resources Information Center

Suppes, P.; And Others

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

An approach to the mathematical modelling of a controlled ecological life support system

NASA Technical Reports Server (NTRS)

Averner, M. M.

1981-01-01

An approach to the design of a computer based model of a closed ecological life-support system suitable for use in extraterrestrial habitats is presented. The model is based on elemental mass balance and contains representations of the metabolic activities of biological components. The model can be used as a tool in evaluating preliminary designs for closed regenerative life support systems and as a method for predicting the behavior of such systems.

A preoperative mathematic model for computed tomographic guided microwave ablation treatment of hepatic dome tumors

PubMed Central

Yang, Bin; Xue, Jing-Bing; Mo, Zhi-Qiang; Zhong, Zhi-Hui; Zhang, Tao; Zhang, Fu-Jun; Fan, Wei-Jun

2016-01-01

Purpose This study sought to prospectively evaluate the feasibility and safety of a preoperative mathematic model for computed tomographic(CT) guided microwave(MW) ablation treatment of hepatic dome tumors. Methods This mathematic model was a regular cylinder quantifying appropriate puncture routes from the bottom up. A total of 103 patients with hepatic dome tumors were enrolled and randomly divided into 2 groups based on whether this model was used or not: Group A (using the model; n = 43) versus Group B (not using the model; n = 60). All tumors were treated by CT-guided MW ablation and follow-up contrast CT were reviewed. Results The average number of times for successful puncture, average ablation time, and incidence of right shoulder pain were less in Group A than Group B (1.4 vs. 2.5, P = 0.001; 8.8 vs. 11.1 minutes, P = 0.003; and 4.7% vs. 20%, P = 0.039). The technical success rate was higher in Group A than Group B (97.7% vs. 85.0%, P = 0.032). There were no significant differences between the two groups in primary and secondary technique efficacy rates (97.7% vs. 88.3%, P = 0.081; 90.0% vs. 72.7%, P = 0.314). No major complications occurred in both groups. Conclusion The mathematic model of regular cylinder is feasible and safe for CT-guided MW ablation in treating hepatic dome tumors. PMID:27028994

The Influence of Test Mode and Visuospatial Ability on Mathematics Assessment Performance

ERIC Educational Resources Information Center

Logan, Tracy

2015-01-01

Mathematics assessment and testing are increasingly situated within digital environments with international tests moving to computer-based testing in the near future. This paper reports on a secondary data analysis which explored the influence the mode of assessment--computer-based (CBT) and pencil-and-paper based (PPT)--and visuospatial ability…

Physically based modeling in catchment hydrology at 50: Survey and outlook

NASA Astrophysics Data System (ADS)

Paniconi, Claudio; Putti, Mario

2015-09-01

Integrated, process-based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection-dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science.

Computational neuroanatomy: ontology-based representation of neural components and connectivity

PubMed Central

Rubin, Daniel L; Talos, Ion-Florin; Halle, Michael; Musen, Mark A; Kikinis, Ron

2009-01-01

Background A critical challenge in neuroscience is organizing, managing, and accessing the explosion in neuroscientific knowledge, particularly anatomic knowledge. We believe that explicit knowledge-based approaches to make neuroscientific knowledge computationally accessible will be helpful in tackling this challenge and will enable a variety of applications exploiting this knowledge, such as surgical planning. Results We developed ontology-based models of neuroanatomy to enable symbolic lookup, logical inference and mathematical modeling of neural systems. We built a prototype model of the motor system that integrates descriptive anatomic and qualitative functional neuroanatomical knowledge. In addition to modeling normal neuroanatomy, our approach provides an explicit representation of abnormal neural connectivity in disease states, such as common movement disorders. The ontology-based representation encodes both structural and functional aspects of neuroanatomy. The ontology-based models can be evaluated computationally, enabling development of automated computer reasoning applications. Conclusion Neuroanatomical knowledge can be represented in machine-accessible format using ontologies. Computational neuroanatomical approaches such as described in this work could become a key tool in translational informatics, leading to decision support applications that inform and guide surgical planning and personalized care for neurological disease in the future. PMID:19208191

Discrete Mathematics Course Supported by CAS MATHEMATICA

ERIC Educational Resources Information Center

Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

2017-01-01

In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…

Explorations in Elementary Mathematical Modeling

ERIC Educational Resources Information Center

Shahin, Mazen

2010-01-01

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

Application of mathematical models and computation in plant metabolomics

USDA-ARS?s Scientific Manuscript database

The investigation and reporting of plants’ chemical constituents has greatly evolved over the centuries of natural products and phytochemical research. Starting from the extraction and identification of plant-based bioactive components, such as historical salicin or more recent paclitaxel, phytochem...

Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes

NASA Technical Reports Server (NTRS)

Bittker, D. A.

1993-01-01

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

Mathematical description of complex chemical kinetics and application to CFD modeling codes

NASA Technical Reports Server (NTRS)

Bittker, D. A.

1993-01-01

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers.

PubMed

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

Mathematical model of rolling an elastic wheel over deformable support base

NASA Astrophysics Data System (ADS)

Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.

2018-02-01

One of the main direction of economic growth in Russia remains to be a speedy development of north and northeast regions that are the constituents of the 60 percent of the country territory. The further development of these territories requires new methods and technologies for solving transport and technological problems when off-road transportation of cargoes and people is conducting. One of the fundamental methods of patency prediction is imitation modeling of wheeled vehicles movement in different operating conditions. Both deformable properties of tires and physical and mechanical properties of the ground: normal tire deflection and gauge depth; variation of contact patch area depending on the load and pressure of air in the tire; existence of hysteresis losses in the tire material which are influencing on the rolling resistance due to friction processes between tire and ground in the contact patch; existence of the tangential reaction from the ground by entire contact area influence on the tractive patency. Nowadays there are two main trends in theoretical research of interaction wheeled propulsion device with ground: analytical method involving mathematical description of explored process and finite element method based on computational modeling. Mathematical models of interaction tire with the ground are used both in processes of interaction individual wheeled propulsion device with ground and researches of mobile vehicle dynamical models operated in specific road and climate conditions. One of the most significant imperfection of these models is the description of interaction wheel with flat deformable support base whereas profile of real support base surface has essential height of unevenness which is commensurate with radius of the wheel. The description of processes taking place in the ground under influence of the wheeled propulsion device using the finite element method is relatively new but most applicable lately. The application of this method allows to provide the most accurate description of the interaction process of a wheeled propulsion devices and the ground, also this method allows to define tension in the ground, deformation of the ground and the tire and ground’s compression. However, the high laboriousness of computations is essential shortcoming of that method therefore it’s hard to use these models as part of the general motion model of multi-axis wheeled vehicles. The purpose of this research is the elaboration of mathematical model of elastic wheel rolling over deformable rough support base taking into account the contact patch deformation. The mathematical model of rectilinear rolling an elastic wheel over rough deformable support base, taking into account variation of contact patch area and variation in the direction of the radial and tangential reactions also load bearing capacity of the ground, is developed. The efficiency of developed mathematical model of rectilinear rolling an elastic wheel over rough deformable support base is proved by the simulation methods.

SURE reliability analysis: Program and mathematics

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; White, Allan L.

1988-01-01

The SURE program is a new reliability analysis tool for ultrareliable computer system architectures. The computational methods on which the program is based provide an efficient means for computing accurate upper and lower bounds for the death state probabilities of a large class of semi-Markov models. Once a semi-Markov model is described using a simple input language, the SURE program automatically computes the upper and lower bounds on the probability of system failure. A parameter of the model can be specified as a variable over a range of values directing the SURE program to perform a sensitivity analysis automatically. This feature, along with the speed of the program, makes it especially useful as a design tool.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

PubMed

Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen

2018-05-01

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli. We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

The YAV-8B simulation and modeling. Volume 2: Program listing

NASA Technical Reports Server (NTRS)

1983-01-01

Detailed mathematical models of varying complexity representative of the YAV-8B aircraft are defined and documented. These models are used in parameter estimation and in linear analysis computer programs while investigating YAV-8B aircraft handling qualities. Both a six degree of freedom nonlinear model and a linearized three degree of freedom longitudinal and lateral directional model were developed. The nonlinear model is based on the mathematical model used on the MCAIR YAV-8B manned flight simulator. This simulator model has undergone periodic updating based on the results of approximately 360 YAV-8B flights and 8000 hours of wind tunnel testing. Qualified YAV-8B flight test pilots have commented that the handling qualities characteristics of the simulator are quite representative of the real aircraft. These comments are validated herein by comparing data from both static and dynamic flight test maneuvers to the same obtained using the nonlinear program.

Effectiveness of Computer Animation and Geometrical Instructional Model on Mathematics Achievement and Retention among Junior Secondary School Students

ERIC Educational Resources Information Center

Gambari, A. I.; Falode, C. O.; Adegbenro, D. A.

2014-01-01

This study investigated the effectiveness of computer animation and geometry instructional model on mathematics achievement and retention on Junior Secondary School Students in Minna, Nigeria. It also examined the influence of gender on students' achievement and retention. The research was a pre-test post-test experimental and control group…

Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Khramushin, Vasily

2016-02-01

The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

Concentrator optical characterization using computer mathematical modelling and point source testing

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Manual of phosphoric acid fuel cell stack three-dimensional model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

A detailed distributed mathematical model of phosphoric acid fuel cell stack have been developed, with the FORTRAN computer program, for analyzing the temperature distribution in the stack and the associated current density distribution on the cell plates. Energy, mass, and electrochemical analyses in the stack were combined to develop the model. Several reasonable assumptions were made to solve this mathematical model by means of the finite differences numerical method.

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

PubMed Central

2011-01-01

Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics. PMID:21774817

Automated information system for analysis and prediction of production situations in blast furnace plant

NASA Astrophysics Data System (ADS)

Lavrov, V. V.; Spirin, N. A.

2016-09-01

Advances in modern science and technology are inherently connected with the development, implementation, and widespread use of computer systems based on mathematical modeling. Algorithms and computer systems are gaining practical significance solving a range of process tasks in metallurgy of MES-level (Manufacturing Execution Systems - systems controlling industrial process) of modern automated information systems at the largest iron and steel enterprises in Russia. This fact determines the necessity to develop information-modeling systems based on mathematical models that will take into account the physics of the process, the basics of heat and mass exchange, the laws of energy conservation, and also the peculiarities of the impact of technological and standard characteristics of raw materials on the manufacturing process data. Special attention in this set of operations for metallurgic production is devoted to blast-furnace production, as it consumes the greatest amount of energy, up to 50% of the fuel used in ferrous metallurgy. The paper deals with the requirements, structure and architecture of BF Process Engineer's Automated Workstation (AWS), a computer decision support system of MES Level implemented in the ICS of the Blast Furnace Plant at Magnitogorsk Iron and Steel Works. It presents a brief description of main model subsystems as well as assumptions made in the process of mathematical modelling. Application of the developed system allows the engineering and process staff to analyze online production situations in the blast furnace plant, to solve a number of process tasks related to control of heat, gas dynamics and slag conditions of blast-furnace smelting as well as to calculate the optimal composition of blast-furnace slag, which eventually results in increasing technical and economic performance of blast-furnace production.

A Novel Approach to Develop the Lower Order Model of Multi-Input Multi-Output System

NASA Astrophysics Data System (ADS)

Rajalakshmy, P.; Dharmalingam, S.; Jayakumar, J.

2017-10-01

A mathematical model is a virtual entity that uses mathematical language to describe the behavior of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines like physics, biology, and electrical engineering as well as in the social sciences like economics, sociology and political science. Physicists, Engineers, Computer scientists, and Economists use mathematical models most extensively. With the advent of high performance processors and advanced mathematical computations, it is possible to develop high performing simulators for complicated Multi Input Multi Ouptut (MIMO) systems like Quadruple tank systems, Aircrafts, Boilers etc. This paper presents the development of the mathematical model of a 500 MW utility boiler which is a highly complex system. A synergistic combination of operational experience, system identification and lower order modeling philosophy has been effectively used to develop a simplified but accurate model of a circulation system of a utility boiler which is a MIMO system. The results obtained are found to be in good agreement with the physics of the process and with the results obtained through design procedure. The model obtained can be directly used for control system studies and to realize hardware simulators for boiler testing and operator training.

BehavePlus fire modeling system, version 5.0: Design and Features

Treesearch

Faith Ann Heinsch; Patricia L. Andrews

2010-01-01

The BehavePlus fire modeling system is a computer program that is based on mathematical models that describe wildland fire behavior and effects and the fire environment. It is a flexible system that produces tables, graphs, and simple diagrams. It can be used for a host of fire management applications, including projecting the behavior of an ongoing fire, planning...

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

PubMed

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

1990-01-01

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

Output Devices, Computation, and the Future of Mathematical Crafts.

ERIC Educational Resources Information Center

Eisenberg, Michael

2002-01-01

The advent of powerful, affordable output devices offers the potential for a vastly expanded landscape of computationally-enriched mathematical craft activities in education. Craft activities have both intellectual and emotional affordances that are relatively lacking in "traditional" computer-based education. Describes three software applications…

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

Assessment of traffic noise levels in urban areas using different soft computing techniques.

PubMed

Tomić, J; Bogojević, N; Pljakić, M; Šumarac-Pavlović, D

2016-10-01

Available traffic noise prediction models are usually based on regression analysis of experimental data, and this paper presents the application of soft computing techniques in traffic noise prediction. Two mathematical models are proposed and their predictions are compared to data collected by traffic noise monitoring in urban areas, as well as to predictions of commonly used traffic noise models. The results show that application of evolutionary algorithms and neural networks may improve process of development, as well as accuracy of traffic noise prediction.

Partnership in Being a Specialist Mathematics and Computing College--Who Gains What, How and Why?

ERIC Educational Resources Information Center

Sinkinson, Anne J.

2007-01-01

The research took place in a mathematics and computing specialist school. The article reports on part of a case study of the mathematics department's experience of being a major contributor to the requirements of being a specialist school. This article aims to explore and describe one model of partnership within the "community" remit of…

Evolutionary game theory using agent-based methods.

PubMed

Adami, Christoph; Schossau, Jory; Hintze, Arend

2016-12-01

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright © 2016 Elsevier B.V. All rights reserved.

Optimum load distribution between heat sources based on the Cournot model

NASA Astrophysics Data System (ADS)

Penkovskii, A. V.; Stennikov, V. A.; Khamisov, O. V.

2015-08-01

One of the widespread models of the heat supply of consumers, which is represented in the "Single buyer" format, is considered. The methodological base proposed for its description and investigation presents the use of principles of the theory of games, basic propositions of microeconomics, and models and methods of the theory of hydraulic circuits. The original mathematical model of the heat supply system operating under conditions of the "Single buyer" organizational structure provides the derivation of a solution satisfying the market Nash equilibrium. The distinctive feature of the developed mathematical model is that, along with problems solved traditionally within the bounds of bilateral relations of heat energy sources-heat consumer, it considers a network component with its inherent physicotechnical properties of the heat network and business factors connected with costs of the production and transportation of heat energy. This approach gives the possibility to determine optimum levels of load of heat energy sources. These levels provide the given heat energy demand of consumers subject to the maximum profit earning of heat energy sources and the fulfillment of conditions for formation of minimum heat network costs for a specified time. The practical realization of the search of market equilibrium is considered by the example of a heat supply system with two heat energy sources operating on integrated heat networks. The mathematical approach to the solution search is represented in the graphical form and illustrates computations based on the stepwise iteration procedure for optimization of levels of loading of heat energy sources (groping procedure by Cournot) with the corresponding computation of the heat energy price for consumers.

Traffic Flow Density Distribution Based on FEM

NASA Astrophysics Data System (ADS)

Ma, Jing; Cui, Jianming

In analysis of normal traffic flow, it usually uses the static or dynamic model to numerical analyze based on fluid mechanics. However, in such handling process, the problem of massive modeling and data handling exist, and the accuracy is not high. Finite Element Method (FEM) is a production which is developed from the combination of a modern mathematics, mathematics and computer technology, and it has been widely applied in various domain such as engineering. Based on existing theory of traffic flow, ITS and the development of FEM, a simulation theory of the FEM that solves the problems existing in traffic flow is put forward. Based on this theory, using the existing Finite Element Analysis (FEA) software, the traffic flow is simulated analyzed with fluid mechanics and the dynamics. Massive data processing problem of manually modeling and numerical analysis is solved, and the authenticity of simulation is enhanced.

Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.

ERIC Educational Resources Information Center

Natour, Denise M.

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Students' Use of Electronic Support Tools in Mathematics

ERIC Educational Resources Information Center

Crawford, Lindy; Higgins, Kristina N.; Huscroft-D'Angelo, Jacqueline N.; Hall, Lindsay

2016-01-01

This study investigated students' use of electronic support tools within a computer-based mathematics program. Electronic support tools are tools, such as hyperlinks or calculators, available within many computer-based instructional programs. A convenience sample of 73 students in grades 4-6 was selected to participate in the study. Students…

Development of an Intelligent Instruction System for Mathematical Computation

ERIC Educational Resources Information Center

Kim, Du Gyu; Lee, Jaemu

2013-01-01

In this paper, we propose the development of a web-based, intelligent instruction system to help elementary school students for mathematical computation. We concentrate on the intelligence facilities which support diagnosis and advice. The existing web-based instruction systems merely give information on whether the learners' replies are…

A Computer Based Education (CBE) Program for Middle School Mathematics Intervention

ERIC Educational Resources Information Center

Gulley, Bill

2009-01-01

A Computer Based Education (CBE) program for intervention mathematics was developed, used, and modified over a period of three years in a computer lab at an Arizona Title I middle school. The program is described along with a rationale for the need, design, and use of such a program. Data was collected in the third year and results of the program…

A neotropical Miocene pollen database employing image-based search and semantic modeling1

PubMed Central

Han, Jing Ginger; Cao, Hongfei; Barb, Adrian; Punyasena, Surangi W.; Jaramillo, Carlos; Shyu, Chi-Ren

2014-01-01

• Premise of the study: Digital microscopic pollen images are being generated with increasing speed and volume, producing opportunities to develop new computational methods that increase the consistency and efficiency of pollen analysis and provide the palynological community a computational framework for information sharing and knowledge transfer. • Methods: Mathematical methods were used to assign trait semantics (abstract morphological representations) of the images of neotropical Miocene pollen and spores. Advanced database-indexing structures were built to compare and retrieve similar images based on their visual content. A Web-based system was developed to provide novel tools for automatic trait semantic annotation and image retrieval by trait semantics and visual content. • Results: Mathematical models that map visual features to trait semantics can be used to annotate images with morphology semantics and to search image databases with improved reliability and productivity. Images can also be searched by visual content, providing users with customized emphases on traits such as color, shape, and texture. • Discussion: Content- and semantic-based image searches provide a powerful computational platform for pollen and spore identification. The infrastructure outlined provides a framework for building a community-wide palynological resource, streamlining the process of manual identification, analysis, and species discovery. PMID:25202648

Visual Modeling as a Motivation for Studying Mathematics and Art

ERIC Educational Resources Information Center

Sendova, Evgenia; Grkovska, Slavica

2005-01-01

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

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Design and construction of miniature artificial ecosystem based on dynamic response optimization

NASA Astrophysics Data System (ADS)

Hu, Dawei; Liu, Hong; Tong, Ling; Li, Ming; Hu, Enzhu

The miniature artificial ecosystem (MAES) is a combination of man, silkworm, salad and mi-croalgae to partially regenerate O2 , sanitary water and food, simultaneously dispose CO2 and wastes, therefore it have a fundamental life support function. In order to enhance the safety and reliability of MAES and eliminate the influences of internal variations and external dis-turbances, it was necessary to configure MAES as a closed-loop control system, and it could be considered as a prototype for future bioregenerative life support system. However, MAES is a complex system possessing large numbers of parameters, intricate nonlinearities, time-varying factors as well as uncertainties, hence it is difficult to perfectly design and construct a prototype through merely conducting experiments by trial and error method. Our research presented an effective way to resolve preceding problem by use of dynamic response optimiza-tion. Firstly the mathematical model of MAES with first-order nonlinear ordinary differential equations including parameters was developed based on relevant mechanisms and experimental data, secondly simulation model of MAES was derived on the platform of MatLab/Simulink to perform model validation and further digital simulations, thirdly reference trajectories of de-sired dynamic response of system outputs were specified according to prescribed requirements, and finally optimization for initial values, tuned parameter and independent parameters was carried out using the genetic algorithm, the advanced direct search method along with parallel computing methods through computer simulations. The result showed that all parameters and configurations of MAES were determined after a series of computer experiments, and its tran-sient response performances and steady characteristics closely matched the reference curves. Since the prototype is a physical system that represents the mathematical model with reason-able accuracy, so the process of designing and constructing a prototype of MAES is the reverse of mathematical modeling, and must have prerequisite assists from these results of computer simulation.

Basic research for the geodynamics program

NASA Technical Reports Server (NTRS)

1991-01-01

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Structure, function, and behaviour of computational models in systems biology

PubMed Central

2013-01-01

Background Systems Biology develops computational models in order to understand biological phenomena. The increasing number and complexity of such “bio-models” necessitate computer support for the overall modelling task. Computer-aided modelling has to be based on a formal semantic description of bio-models. But, even if computational bio-models themselves are represented precisely in terms of mathematical expressions their full meaning is not yet formally specified and only described in natural language. Results We present a conceptual framework – the meaning facets – which can be used to rigorously specify the semantics of bio-models. A bio-model has a dual interpretation: On the one hand it is a mathematical expression which can be used in computational simulations (intrinsic meaning). On the other hand the model is related to the biological reality (extrinsic meaning). We show that in both cases this interpretation should be performed from three perspectives: the meaning of the model’s components (structure), the meaning of the model’s intended use (function), and the meaning of the model’s dynamics (behaviour). In order to demonstrate the strengths of the meaning facets framework we apply it to two semantically related models of the cell cycle. Thereby, we make use of existing approaches for computer representation of bio-models as much as possible and sketch the missing pieces. Conclusions The meaning facets framework provides a systematic in-depth approach to the semantics of bio-models. It can serve two important purposes: First, it specifies and structures the information which biologists have to take into account if they build, use and exchange models. Secondly, because it can be formalised, the framework is a solid foundation for any sort of computer support in bio-modelling. The proposed conceptual framework establishes a new methodology for modelling in Systems Biology and constitutes a basis for computer-aided collaborative research. PMID:23721297

Turbine Engine Mathematical Model Validation

DTIC Science & Technology

1976-12-01

AEDC-TR-76-90 ~Ec i ? Z985 TURBINE ENGINE MATHEMATICAL MODEL VALIDATION ENGINE TEST FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE...i f n e c e s e a ~ ~ d i den t i f y by b l ock number) YJI01-GE-100 engine turbine engines mathematical models computations mathematical...report presents and discusses the results of an investigation to develop a rationale and technique for the validation of turbine engine steady-state

Temporal Subtraction of Digital Breast Tomosynthesis Images for Improved Mass Detection

DTIC Science & Technology

2008-10-01

K. Fishman and B. M. W. Tsui, "Development of a computer-generated model for the coronary arterial tree based on multislice CT and morphometric data...mathematical models based on geometric primitives8-22. Bakic et al created synthetic x-ray mammograms using a 3D simulated breast tissue model consisting of...utilized a combination of voxel matrices and geometric primitives to create a breast phantom that includes the breast surface, the duct system, and

A new parallel DNA algorithm to solve the task scheduling problem based on inspired computational model.

PubMed

Wang, Zhaocai; Ji, Zuwen; Wang, Xiaoming; Wu, Tunhua; Huang, Wei

2017-12-01

As a promising approach to solve the computationally intractable problem, the method based on DNA computing is an emerging research area including mathematics, computer science and molecular biology. The task scheduling problem, as a well-known NP-complete problem, arranges n jobs to m individuals and finds the minimum execution time of last finished individual. In this paper, we use a biologically inspired computational model and describe a new parallel algorithm to solve the task scheduling problem by basic DNA molecular operations. In turn, we skillfully design flexible length DNA strands to represent elements of the allocation matrix, take appropriate biological experiment operations and get solutions of the task scheduling problem in proper length range with less than O(n 2 ) time complexity. Copyright © 2017. Published by Elsevier B.V.

A critical review of the field application of a mathematical model of malaria eradication

PubMed Central

Nájera, J. A.

1974-01-01

A malaria control field research trial in northern Nigeria was planned with the aid of a computer simulation based on Macdonald's mathematical model of malaria epidemiology. Antimalaria attack was based on a combination of mass drug administration (chloroquine and pyrimethamine) and DDT house spraying. The observed results were at great variance with the predictions of the model. The causes of these discrepancies included inadequate estimation of the model's basic variables, and overestimation, in planning the simulation, of the effects of the attack measures and of the degree of perfection attainable by their application. The discrepancies were to a great extent also due to deficiencies in the model. An analysis is made of those considered to be the most important. It is concluded that research efforts should be encouraged to increase our knowledge of the basic epidemiological factors, their variation and correlations, and to formulate more realistic and useful theoretical models. PMID:4156197

Teaching Subtraction and Multiplication with Regrouping Using the Concrete-Representational-Abstract Sequence and Strategic Instruction Model

ERIC Educational Resources Information Center

Flores, Margaret M.; Hinton, Vanessa; Strozier, Shaunita D.

2014-01-01

Based on Common Core Standards (2010), mathematics interventions should emphasize conceptual understanding of numbers and operations as well as fluency. For students at risk for failure, the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) have been shown effective in teaching computation with an emphasis…

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

An Examination of the Relationship between Computation, Problem Solving, and Reading

ERIC Educational Resources Information Center

Cormier, Damien C.; Yeo, Seungsoo; Christ, Theodore J.; Offrey, Laura D.; Pratt, Katherine

2016-01-01

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

Promise of new imaging technologies for assessing ovarian function.

PubMed

Singh, Jaswant; Adams, Gregg P; Pierson, Roger A

2003-10-15

Advancements in imaging technologies over the last two decades have ushered a quiet revolution in research approaches to the study of ovarian structure and function. The most significant changes in our understanding of the ovary have resulted from the use of ultrasonography which has enabled sequential analyses in live animals. Computer-assisted image analysis and mathematical modeling of the dynamic changes within the ovary has permitted exciting new avenues of research with readily quantifiable endpoints. Spectral, color-flow and power Doppler imaging now facilitate physiologic interpretations of vascular dynamics over time. Similarly, magnetic resonance imaging (MRI) is emerging as a research tool in ovarian imaging. New technologies, such as three-dimensional ultrasonography and MRI, ultrasound-based biomicroscopy and synchrotron-based techniques each have the potential to enhance our real-time picture of ovarian function to the near-cellular level. Collectively, information available in ultrasonography, MRI, computer-assisted image analysis and mathematical modeling heralds a new era in our understanding of the basic processes of female and male reproduction.

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration.

PubMed

Hossain, Md Shakhawath; Bergstrom, D J; Chen, X B

2015-11-01

The in vitro chondrocyte cell culture process in a perfusion bioreactor provides enhanced nutrient supply as well as the flow-induced shear stress that may have a positive influence on the cell growth. Mathematical and computational modelling of such a culture process, by solving the coupled flow, mass transfer and cell growth equations simultaneously, can provide important insight into the biomechanical environment of a bioreactor and the related cell growth process. To do this, a two-way coupling between the local flow field and cell growth is required. Notably, most of the computational and mathematical models to date have not taken into account the influence of the cell growth on the local flow field and nutrient concentration. The present research aimed at developing a mathematical model and performing a numerical simulation using the lattice Boltzmann method to predict the chondrocyte cell growth without a scaffold on a flat plate placed inside a perfusion bioreactor. The model considers the two-way coupling between the cell growth and local flow field, and the simulation has been performed for 174 culture days. To incorporate the cell growth into the model, a control-volume-based surface growth modelling approach has been adopted. The simulation results show the variation of local fluid velocity, shear stress and concentration distribution during the culture period due to the growth of the cell phase and also illustrate that the shear stress can increase the cell volume fraction to a certain extent.

Computers in mathematics: teacher-inservice training at a distance

NASA Astrophysics Data System (ADS)

Friedman, Edward A.; Jurkat, M. P.

1993-01-01

While research and experience show many advantages for incorporation of computer technology into secondary school mathematics instruction, less than 5 percent of the nation's teachers are actively using computers in their classrooms. This is the case even though mathematics teachers in grades 7 - 12 are often familiar with computer technology and have computers available to them in their schools. The implementation bottleneck is in-service teacher training and there are few models of effective implementation available for teachers to emulate. Stevens Institute of Technology has been active since 1988 in research and development efforts to incorporate computers into classroom use. We have found that teachers need to see examples of classroom experience with hardware and software and they need to have assistance as they experiment with applications of software and the development of lesson plans. High-band width technology can greatly facilitate teacher training in this area through transmission of video documentaries, software discussions, teleconferencing, peer interactions, classroom observations, etc. We discuss the experience that Stevens has had with face-to-face teacher training as well as with satellite-based teleconferencing using one-way video and two- way audio. Included are reviews of analyses of this project by researchers from Educational Testing Service, Princeton University, and Bank Street School of Education.

Examining the Use of Computer Algebra Systems in University-Level Mathematics Teaching

ERIC Educational Resources Information Center

Lavicza, Zsolt

2009-01-01

The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…

Smart sensors and virtual physiology human approach as a basis of personalized therapies in diabetes mellitus.

PubMed

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient's information to the models.A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies.

Smart Sensors and Virtual Physiology Human Approach as a Basis of Personalized Therapies in Diabetes Mellitus

PubMed Central

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient’s information to the models. A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies. PMID:21625646

Spline Laplacian estimate of EEG potentials over a realistic magnetic resonance-constructed scalp surface model.

PubMed

Babiloni, F; Babiloni, C; Carducci, F; Fattorini, L; Onorati, P; Urbano, A

1996-04-01

This paper presents a realistic Laplacian (RL) estimator based on a tensorial formulation of the surface Laplacian (SL) that uses the 2-D thin plate spline function to obtain a mathematical description of a realistic scalp surface. Because of this tensorial formulation, the RL does not need an orthogonal reference frame placed on the realistic scalp surface. In simulation experiments the RL was estimated with an increasing number of "electrodes" (up to 256) on a mathematical scalp model, the analytic Laplacian being used as a reference. Second and third order spherical spline Laplacian estimates were examined for comparison. Noise of increasing magnitude and spatial frequency was added to the simulated potential distributions. Movement-related potentials and somatosensory evoked potentials sampled with 128 electrodes were used to estimate the RL on a realistically shaped, MR-constructed model of the subject's scalp surface. The RL was also estimated on a mathematical spherical scalp model computed from the real scalp surface. Simulation experiments showed that the performances of the RL estimator were similar to those of the second and third order spherical spline Laplacians. Furthermore, the information content of scalp-recorded potentials was clearly better when the RL estimator computed the SL of the potential on an MR-constructed scalp surface model.

ITEMS Project: An online sequence for teaching mathematics and astronomy

NASA Astrophysics Data System (ADS)

Martínez, Bernat; Pérez, Josep

2010-10-01

This work describes an elearning sequence for teaching geometry and astronomy in lower secondary school created inside the ITEMS (Improving Teacher Education in Mathematics and Science) project. It is based on results from the astronomy education research about studentsŠ difficulties in understanding elementary astronomical observations and models. The sequence consists of a set of computer animations embedded in an elearning environment aimed at supporting students in learning about astronomy ideas that require the use of geometrical concepts and visual-spatial reasoning.

Numerical simulations of the flow with the prescribed displacement of the airfoil and comparison with experiment

NASA Astrophysics Data System (ADS)

Řidký, V.; Šidlof, P.; Vlček, V.

2013-04-01

The work is devoted to comparing measured data with the results of numerical simulations. As mathematical model was used mathematical model whitout turbulence for incompressible flow In the experiment was observed the behavior of designed NACA0015 airfoil in airflow. For the numerical solution was used OpenFOAM computational package, this is open-source software based on finite volume method. In the numerical solution is prescribed displacement of the airfoil, which corresponds to the experiment. The velocity at a point close to the airfoil surface is compared with the experimental data obtained from interferographic measurements of the velocity field. Numerical solution is computed on a 3D mesh composed of about 1 million ortogonal hexahedron elements. The time step is limited by the Courant number. Parallel computations are run on supercomputers of the CIV at Technical University in Prague (HAL and FOX) and on a computer cluster of the Faculty of Mechatronics of Liberec (HYDRA). Run time is fixed at five periods, the results from the fifth periods and average value for all periods are then be compared with experiment.

Incorporating individual health-protective decisions into disease transmission models: a mathematical framework.

PubMed

Durham, David P; Casman, Elizabeth A

2012-03-07

It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak.

Incorporating individual health-protective decisions into disease transmission models: a mathematical framework

PubMed Central

Durham, David P.; Casman, Elizabeth A.

2012-01-01

It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak. PMID:21775324

Verifiable fault tolerance in measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Hayashi, Masahito

2017-09-01

Quantum systems, in general, cannot be simulated efficiently by a classical computer, and hence are useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately, that verification of the output of the quantum systems is not so trivial, since predicting the output is exponentially hard. As another problem, the quantum system is very delicate for noise and thus needs an error correction. Here, we propose a framework for verification of the output of fault-tolerant quantum computation in a measurement-based model. In contrast to existing analyses on fault tolerance, we do not assume any noise model on the resource state, but an arbitrary resource state is tested by using only single-qubit measurements to verify whether or not the output of measurement-based quantum computation on it is correct. Verifiability is equipped by a constant time repetition of the original measurement-based quantum computation in appropriate measurement bases. Since full characterization of quantum noise is exponentially hard for large-scale quantum computing systems, our framework provides an efficient way to practically verify the experimental quantum error correction.

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

PubMed Central

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation. PMID:28824513

Computational Evaluation of the Traceback Method

ERIC Educational Resources Information Center

Kol, Sheli; Nir, Bracha; Wintner, Shuly

2014-01-01

Several models of language acquisition have emerged in recent years that rely on computational algorithms for simulation and evaluation. Computational models are formal and precise, and can thus provide mathematically well-motivated insights into the process of language acquisition. Such models are amenable to robust computational evaluation,…

Integrating interactive computational modeling in biology curricula.

PubMed

Helikar, Tomáš; Cutucache, Christine E; Dahlquist, Lauren M; Herek, Tyler A; Larson, Joshua J; Rogers, Jim A

2015-03-01

While the use of computer tools to simulate complex processes such as computer circuits is normal practice in fields like engineering, the majority of life sciences/biological sciences courses continue to rely on the traditional textbook and memorization approach. To address this issue, we explored the use of the Cell Collective platform as a novel, interactive, and evolving pedagogical tool to foster student engagement, creativity, and higher-level thinking. Cell Collective is a Web-based platform used to create and simulate dynamical models of various biological processes. Students can create models of cells, diseases, or pathways themselves or explore existing models. This technology was implemented in both undergraduate and graduate courses as a pilot study to determine the feasibility of such software at the university level. First, a new (In Silico Biology) class was developed to enable students to learn biology by "building and breaking it" via computer models and their simulations. This class and technology also provide a non-intimidating way to incorporate mathematical and computational concepts into a class with students who have a limited mathematical background. Second, we used the technology to mediate the use of simulations and modeling modules as a learning tool for traditional biological concepts, such as T cell differentiation or cell cycle regulation, in existing biology courses. Results of this pilot application suggest that there is promise in the use of computational modeling and software tools such as Cell Collective to provide new teaching methods in biology and contribute to the implementation of the "Vision and Change" call to action in undergraduate biology education by providing a hands-on approach to biology.

An evaluation of Computational Fluid dynamics model for flood risk analysis

NASA Astrophysics Data System (ADS)

Di Francesco, Silvia; Biscarini, Chiara; Montesarchio, Valeria

2014-05-01

This work presents an analysis of the hydrological-hydraulic engineering requisites for Risk evaluation and efficient flood damage reduction plans. Most of the research efforts have been dedicated to the scientific and technical aspects of risk assessment, providing estimates of possible alternatives and of the risk associated. In the decision making process for mitigation plan, the contribute of scientist is crucial, due to the fact that Risk-Damage analysis is based on evaluation of flow field ,of Hydraulic Risk and on economical and societal considerations. The present paper will focus on the first part of process, the mathematical modelling of flood events which is the base for all further considerations. The evaluation of potential catastrophic damage consequent to a flood event and in particular to dam failure requires modelling of the flood with sufficient detail so to capture the spatial and temporal evolutions of the event, as well of the velocity field. Thus, the selection of an appropriate mathematical model to correctly simulate flood routing is an essential step. In this work we present the application of two 3D Computational fluid dynamics models to a synthetic and real case study in order to evaluate the correct evolution of flow field and the associated flood Risk . The first model is based on a opensource CFD platform called openFoam. Water flow is schematized with a classical continuum approach based on Navier-Stokes equation coupled with Volume of fluid (VOF) method to take in account the multiphase character of river bottom-water- air systems. The second model instead is based on the Lattice Boltzmann method, an innovative numerical fluid dynamics scheme based on Boltzmann's kinetic equation that represents the flow dynamics at the macroscopic level by incorporating a microscopic kinetic approach. Fluid is seen as composed by particles that can move and collide among them. Simulation results from both models are promising and congruent to experimental results available in literature, thought the LBM model requires less computational effort respect to the NS one.

Internationalizing the Mathematical Finance Course

ERIC Educational Resources Information Center

Okonkwo, Zephyrinus C.

2017-01-01

About the year 2000, the Department of Mathematics and Computer Science, Albany State University (ASU), Albany, Georgia, USA envisioned the need to have a comprehensive curriculum revision based on recommendations of the Conference Boards of The Mathematical Sciences, the American Mathematical Society, the Mathematical Association of American, and…

A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor.

PubMed

Shakhawath Hossain, Md; Bergstrom, D J; Chen, X B

2015-12-01

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process. © 2015 Wiley Periodicals, Inc.

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Tan, H. Q.; Dong, X.

1989-01-01

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Development of guidelines for the definition of the relavant information content in data classes

NASA Technical Reports Server (NTRS)

Schmitt, E.

1973-01-01

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Development of a model and computer code to describe solar grade silicon production processes

NASA Technical Reports Server (NTRS)

Srivastava, R.; Gould, R. K.

1979-01-01

Mathematical models, and computer codes based on these models were developed which allow prediction of the product distribution in chemical reactors in which gaseous silicon compounds are converted to condensed phase silicon. The reactors to be modeled are flow reactors in which silane or one of the halogenated silanes is thermally decomposed or reacted with an alkali metal, H2 or H atoms. Because the product of interest is particulate silicon, processes which must be modeled, in addition to mixing and reaction of gas-phase reactants, include the nucleation and growth of condensed Si via coagulation, condensation, and heterogeneous reaction.

Satellite orbit computation methods

NASA Technical Reports Server (NTRS)

1977-01-01

Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

Computer Courseware Evaluations. A Series of Reports Compiled by the Clearinghouse Computer Technology Project.

ERIC Educational Resources Information Center

Alberta Dept. of Education, Edmonton.

This report reviews Apple computer courseware in business education, library skills, mathematics, science, special education, and word processing based on the curricular requirements of Alberta, Canada. It provides detailed evaluations of 23 authorized titles in business education (2), mathematics (20), and science (1); 3 of the math titles are…

Enhancing Student Writing and Computer Programming with LATEX and MATLAB in Multivariable Calculus

ERIC Educational Resources Information Center

Sullivan, Eric; Melvin, Timothy

2016-01-01

Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…

ILS Glide Slope Performance Prediction. Volume B

DTIC Science & Technology

1974-09-01

figures are identical in both volumes. 󈧔. Abottec A mathematical model for predicting the performance of ILS glide slope arrays in the presence of...irregularities on the performance of ILS Glide Slope antenna systems, a mathematical -electromagnetic scattering computer model has been developed. This work was...Antenna ........... 4-4 9. Test Case Results ..................................... r-3 ix PART I. IEO -j 1.INTRODUCTION IA mathematical model has been

The Material Supply Adjustment Process in RAMF-SM, Step 2

DTIC Science & Technology

2016-06-01

contain. The Risk Assessment and Mitigation Framework for Strategic Materials (RAMF-SM) is a suite of mathematical models and databases that has been...Risk Assessment and Mitigation Framework for Strategic Materials (RAMF-SM) is a suite of mathematical models and databases used to support the...and computes material shortfalls.1 Several mathematical models and dozens of databases, encompassing thousands of data items, support the

A Computer-Based Game That Promotes Mathematics Learning More than a Conventional Approach

ERIC Educational Resources Information Center

McLaren, Bruce M.; Adams, Deanne M.; Mayer, Richard E.; Forlizzi, Jodi

2017-01-01

Excitement about learning from computer-based games has been papable in recent years and has led to the development of many educational games. However, there are relatively few sound empirical studies in the scientific literature that have shown the benefits of learning mathematics from games as opposed to more traditional approaches. The…

Comparing Computer Adaptive and Curriculum-Based Measures of Math in Progress Monitoring

ERIC Educational Resources Information Center

Shapiro, Edward S.; Dennis, Minyi Shih; Fu, Qiong

2015-01-01

The purpose of the study was to compare the use of a Computer Adaptive Test and Curriculum-Based Measurement in the assessment of mathematics. This study also investigated the degree to which slope or rate of change predicted student outcomes on the annual state assessment of mathematics above and beyond scores of single point screening…

The Development of an Individualized Instructional Program in Beginning College Mathematics Utilizing Computer Based Resource Units. Final Report.

ERIC Educational Resources Information Center

Rockhill, Theron D.

Reported is an attempt to develop and evaluate an individualized instructional program in pre-calculus college mathematics. Four computer based resource units were developed in the areas of set theory, relations and function, algebra, trigonometry, and analytic geometry. Objectives were determined by experienced calculus teachers, and…

Creating a Supportive Environment to Enhance Computer Based Learning for Underrepresented Minorities in College Algebra Classrooms

ERIC Educational Resources Information Center

Kendricks, Kimberly D.

2011-01-01

Significant research in K-12 education has shown that computer based learning in mathematics positively impacts students' attitudes toward mathematics and greatly increases academic performance. Little research has shown, however, how this success can be replicated in a postsecondary classroom for minority students. This paper is a case study that…

Computing maximum-likelihood estimates for parameters of the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

Donato, David I.

2012-01-01

This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

2003-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Students’ Spatial Ability through Open-Ended Approach Aided by Cabri 3D

NASA Astrophysics Data System (ADS)

Priatna, N.

2017-09-01

The use of computer software such as Cabri 3D for learning activities is very unlimited. Students can adjust their learning speed according to their level of ability. Open-ended approach strongly supports the use of computer software in learning, because the goal of open-ended learning is to help developing creative activities and mathematical mindset of students through problem solving simultaneously. In other words, creative activities and mathematical mindset of students should be developed as much as possible in accordance with the ability of spatial ability of each student. Spatial ability is the ability of students in constructing and representing geometry models. This study aims to determine the improvement of spatial ability of junior high school students who obtained learning with open-ended approach aided by Cabri 3D. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2×3 factorial model. The instrument of the study is spatial ability test. Based on analysis of the data, it is found that the improvement of spatial ability of students who received open-ended learning aided by Cabri 3D was greater than students who received expository learning, both as a whole and based on the categories of students’ initial mathematical ability.

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

On the Shoulders of Giants: New Approaches to Numeracy.

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

Forces created by the proliferation of computer hardware and software, by innovative methods of mathematical modelling and applications, by broader demographic considerations, and by schools themselves are profoundly changing the way mathematics is practiced, the way mathematics is taught, and the way mathematics is learned. In this volume, a…

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

PubMed

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

2017-04-01

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

A Modular Approach to Teaching Mathematical Modeling in Biotechnology in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Larripa, Kamila R.; Mazzag, Borbala

2016-01-01

Our paper describes a solution we found to a still existing need to develop mathematical modeling courses for undergraduate biology majors. Some challenges of such courses are: (i) relatively limited exposure of biology students to higher-level mathematical and computational concepts; (ii) availability of texts that can give a flavor of how…

An Innovative Learning Model for Computation in First Year Mathematics

ERIC Educational Resources Information Center

Tonkes, E. J.; Loch, B. I.; Stace, A. W.

2005-01-01

MATLAB is a sophisticated software tool for numerical analysis and visualization. The University of Queensland has adopted Matlab as its official teaching package across large first year mathematics courses. In the past, the package has met severe resistance from students who have not appreciated their computational experience. Several main…

Modeling the dynamics of multipartite quantum systems created departing from two-level systems using general local and non-local interactions

NASA Astrophysics Data System (ADS)

Delgado, Francisco

2017-12-01

Quantum information is an emergent area merging physics, mathematics, computer science and engineering. To reach its technological goals, it is requiring adequate approaches to understand how to combine physical restrictions, computational approaches and technological requirements to get functional universal quantum information processing. This work presents the modeling and the analysis of certain general type of Hamiltonian representing several physical systems used in quantum information and establishing a dynamics reduction in a natural grammar for bipartite processing based on entangled states.

Utility of computer simulations in landscape genetics

Treesearch

Bryan K. Epperson; Brad H. McRae; Kim Scribner; Samuel A. Cushman; Michael S. Rosenberg; Marie-Josee Fortin; Patrick M. A. James; Melanie Murphy; Stephanie Manel; Pierre Legendre; Mark R. T. Dale

2010-01-01

Population genetics theory is primarily based on mathematical models in which spatial complexity and temporal variability are largely ignored. In contrast, the field of landscape genetics expressly focuses on how population genetic processes are affected by complex spatial and temporal environmental heterogeneity. It is spatially explicit and relates patterns to...

Effect of section shape on frequencies of natural oscillations of tubular springs

NASA Astrophysics Data System (ADS)

Pirogov, S. P.; Chuba, A. Yu; Cherentsov, D. A.

2018-05-01

The necessity of determining the frequencies of natural oscillations of manometric tubular springs is substantiated. Based on the mathematical model and computer program, numerical experiments were performed that allowed us to reveal the effect of geometric parameters on the frequencies of free oscillations of manometric tubular springs.

Dynamic Modeling of Cell-Free Biochemical Networks Using Effective Kinetic Models

DTIC Science & Technology

2015-03-16

sensitivity value was the maximum uncertainty in that value estimated by the Sobol method. 2.4. Global Sensitivity Analysis of the Reduced Order Coagulation...sensitivity analysis, using the variance-based method of Sobol , to estimate which parameters controlled the performance of the reduced order model [69]. We...Environment. Comput. Sci. Eng. 2007, 9, 90–95. 69. Sobol , I. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

The study of heat penetration of kimchi soup on stationary and rotary retorts.

PubMed

Cho, Won-Il; Park, Eun-Ji; Cheon, Hee Soon; Chung, Myong-Soo

2015-03-01

The aim of this study was to determine the heat-penetration characteristics using stationary and rotary retorts to manufacture Kimchi soup. Both heat-penetration tests and computer simulation based on mathematical modeling were performed. The sterility was measured at five different positions in the pouch. The results revealed only a small deviation of F 0 among the different positions, and the rate of heat transfer was increased by rotation of the retort. The thermal processing of retort-pouched Kimchi soup was analyzed mathematically using a finite-element model, and optimum models for predicting the time course of the temperature and F 0 were developed. The mathematical models could accurately predict the actual heat penetration of retort-pouched Kimchi soup. The average deviation of the temperature between the experimental and mathematical predicted model was 2.46% (R(2)=0.975). The changes in nodal temperature and F 0 caused by microbial inactivation in the finite-element model predicted using the NISA program were very similar to that of the experimental data of for the retorted Kimchi soup during sterilization with rotary retorts. The correlation coefficient between the simulation using the NISA program and the experimental data was very high, at 99%.

The Study of Heat Penetration of Kimchi Soup on Stationary and Rotary Retorts

PubMed Central

Cho, Won-Il; Park, Eun-Ji; Cheon, Hee Soon; Chung, Myong-Soo

2015-01-01

The aim of this study was to determine the heat-penetration characteristics using stationary and rotary retorts to manufacture Kimchi soup. Both heat-penetration tests and computer simulation based on mathematical modeling were performed. The sterility was measured at five different positions in the pouch. The results revealed only a small deviation of F0 among the different positions, and the rate of heat transfer was increased by rotation of the retort. The thermal processing of retort-pouched Kimchi soup was analyzed mathematically using a finite-element model, and optimum models for predicting the time course of the temperature and F0 were developed. The mathematical models could accurately predict the actual heat penetration of retort-pouched Kimchi soup. The average deviation of the temperature between the experimental and mathematical predicted model was 2.46% (R2=0.975). The changes in nodal temperature and F0 caused by microbial inactivation in the finite-element model predicted using the NISA program were very similar to that of the experimental data of for the retorted Kimchi soup during sterilization with rotary retorts. The correlation coefficient between the simulation using the NISA program and the experimental data was very high, at 99%. PMID:25866751

Probabilistic assessment methodology for continuous-type petroleum accumulations

USGS Publications Warehouse

Crovelli, R.A.

2003-01-01

The analytic resource assessment method, called ACCESS (Analytic Cell-based Continuous Energy Spreadsheet System), was developed to calculate estimates of petroleum resources for the geologic assessment model, called FORSPAN, in continuous-type petroleum accumulations. The ACCESS method is based upon mathematical equations derived from probability theory in the form of a computer spreadsheet system. ?? 2003 Elsevier B.V. All rights reserved.

Electrical Wave Propagation in a Minimally Realistic Fiber Architecture Model of the Left Ventricle

NASA Astrophysics Data System (ADS)

Song, Xianfeng; Setayeshgar, Sima

2006-03-01

Experimental results indicate a nested, layered geometry for the fiber surfaces of the left ventricle, where fiber directions are approximately aligned in each surface and gradually rotate through the thickness of the ventricle. Numerical and analytical results have highlighted the importance of this rotating anisotropy and its possible destabilizing role on the dynamics of scroll waves in excitable media with application to the heart. Based on the work of Peskin[1] and Peskin and McQueen[2], we present a minimally realistic model of the left ventricle that adequately captures the geometry and anisotropic properties of the heart as a conducting medium while being easily parallelizable, and computationally more tractable than fully realistic anatomical models. Complementary to fully realistic and anatomically-based computational approaches, studies using such a minimal model with the addition of successively realistic features, such as excitation-contraction coupling, should provide unique insight into the basic mechanisms of formation and obliteration of electrical wave instabilities. We describe our construction, implementation and validation of this model. [1] C. S. Peskin, Communications on Pure and Applied Mathematics 42, 79 (1989). [2] C. S. Peskin and D. M. McQueen, in Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, 309(1996)

Building new computational models to support health behavior change and maintenance: new opportunities in behavioral research.

PubMed

Spruijt-Metz, Donna; Hekler, Eric; Saranummi, Niilo; Intille, Stephen; Korhonen, Ilkka; Nilsen, Wendy; Rivera, Daniel E; Spring, Bonnie; Michie, Susan; Asch, David A; Sanna, Alberto; Salcedo, Vicente Traver; Kukakfa, Rita; Pavel, Misha

2015-09-01

Adverse and suboptimal health behaviors and habits are responsible for approximately 40 % of preventable deaths, in addition to their unfavorable effects on quality of life and economics. Our current understanding of human behavior is largely based on static "snapshots" of human behavior, rather than ongoing, dynamic feedback loops of behavior in response to ever-changing biological, social, personal, and environmental states. This paper first discusses how new technologies (i.e., mobile sensors, smartphones, ubiquitous computing, and cloud-enabled processing/computing) and emerging systems modeling techniques enable the development of new, dynamic, and empirical models of human behavior that could facilitate just-in-time adaptive, scalable interventions. The paper then describes concrete steps to the creation of robust dynamic mathematical models of behavior including: (1) establishing "gold standard" measures, (2) the creation of a behavioral ontology for shared language and understanding tools that both enable dynamic theorizing across disciplines, (3) the development of data sharing resources, and (4) facilitating improved sharing of mathematical models and tools to support rapid aggregation of the models. We conclude with the discussion of what might be incorporated into a "knowledge commons," which could help to bring together these disparate activities into a unified system and structure for organizing knowledge about behavior.

Application of Mathematical and Three-Dimensional Computer Modeling Tools in the Planning of Processes of Fuel and Energy Complexes

NASA Astrophysics Data System (ADS)

Aksenova, Olesya; Nikolaeva, Evgenia; Cehlár, Michal

2017-11-01

This work aims to investigate the effectiveness of mathematical and three-dimensional computer modeling tools in the planning of processes of fuel and energy complexes at the planning and design phase of a thermal power plant (TPP). A solution for purification of gas emissions at the design development phase of waste treatment systems is proposed employing mathematical and three-dimensional computer modeling - using the E-nets apparatus and the development of a 3D model of the future gas emission purification system. Which allows to visualize the designed result, to select and scientifically prove economically feasible technology, as well as to ensure the high environmental and social effect of the developed waste treatment system. The authors present results of a treatment of planned technological processes and the system for purifying gas emissions in terms of E-nets. using mathematical modeling in the Simulink application. What allowed to create a model of a device from the library of standard blocks and to perform calculations. A three-dimensional model of a system for purifying gas emissions has been constructed. It allows to visualize technological processes and compare them with the theoretical calculations at the design phase of a TPP and. if necessary, make adjustments.

Towards An Engineering Discipline of Computational Security

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

Mili, Ali; Sheldon, Frederick T; Jilani, Lamia Labed

2007-01-01

George Boole ushered the era of modern logic by arguing that logical reasoning does not fall in the realm of philosophy, as it was considered up to his time, but in the realm of mathematics. As such, logical propositions and logical arguments are modeled using algebraic structures. Likewise, we submit that security attributes must be modeled as formal mathematical propositions that are subject to mathematical analysis. In this paper, we approach this problem by attempting to model security attributes in a refinement-like framework that has traditionally been used to represent reliability and safety claims. Keywords: Computable security attributes, survivability, integrity,more » dependability, reliability, safety, security, verification, testing, fault tolerance.« less

Integrating Intracellular Dynamics Using CompuCell3D and Bionetsolver: Applications to Multiscale Modelling of Cancer Cell Growth and Invasion

PubMed Central

Andasari, Vivi; Roper, Ryan T.; Swat, Maciej H.; Chaplain, Mark A. J.

2012-01-01

In this paper we present a multiscale, individual-based simulation environment that integrates CompuCell3D for lattice-based modelling on the cellular level and Bionetsolver for intracellular modelling. CompuCell3D or CC3D provides an implementation of the lattice-based Cellular Potts Model or CPM (also known as the Glazier-Graner-Hogeweg or GGH model) and a Monte Carlo method based on the metropolis algorithm for system evolution. The integration of CC3D for cellular systems with Bionetsolver for subcellular systems enables us to develop a multiscale mathematical model and to study the evolution of cell behaviour due to the dynamics inside of the cells, capturing aspects of cell behaviour and interaction that is not possible using continuum approaches. We then apply this multiscale modelling technique to a model of cancer growth and invasion, based on a previously published model of Ramis-Conde et al. (2008) where individual cell behaviour is driven by a molecular network describing the dynamics of E-cadherin and -catenin. In this model, which we refer to as the centre-based model, an alternative individual-based modelling technique was used, namely, a lattice-free approach. In many respects, the GGH or CPM methodology and the approach of the centre-based model have the same overall goal, that is to mimic behaviours and interactions of biological cells. Although the mathematical foundations and computational implementations of the two approaches are very different, the results of the presented simulations are compatible with each other, suggesting that by using individual-based approaches we can formulate a natural way of describing complex multi-cell, multiscale models. The ability to easily reproduce results of one modelling approach using an alternative approach is also essential from a model cross-validation standpoint and also helps to identify any modelling artefacts specific to a given computational approach. PMID:22461894

Summary of mathematical models for a conventional and vertical junction photoconverter

NASA Technical Reports Server (NTRS)

Heinbockel, J. H.

1986-01-01

The geometry and computer programming for mathematical models of a one-dimensional conventional photoconverter, a one-dimensional vertical junction photoconverter, a three-dimensional conventinal photoconverter, and a three-dimensional vertical junction solar cell are discussed.

Mathematical model for steady state, simple ampholyte isoelectric focusing: Development, computer simulation and implementation

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.

1979-01-01

The elimination of Ampholine from the system by establishing the pH gradient with simple ampholytes is proposed. A mathematical model was exercised at the level of the two-component system by using values for mobilities, diffusion coefficients, and dissociation constants representative of glutamic acid and histidine. The constants assumed in the calculations are reported. The predictions of the model and computer simulation of isoelectric focusing experiments are in direct importance to obtain Ampholine-free, stable pH gradients.

College Preparatory Mathematics: Change from Within.

ERIC Educational Resources Information Center

Kysh, Judith M.

1995-01-01

The College Preparatory Mathematics: Change from Within Project (CPM) was created to develop a rich, integrated mathematics curriculum, based on the best current wisdom of how people learn and the mathematics needed in an era of computers, and involving teachers in materials development. (MKR)

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

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1991-01-01

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

The brian simulator.

PubMed

Goodman, Dan F M; Brette, Romain

2009-09-01

"Brian" is a simulator for spiking neural networks (http://www.briansimulator.org). The focus is on making the writing of simulation code as quick and easy as possible for the user, and on flexibility: new and non-standard models are no more difficult to define than standard ones. This allows scientists to spend more time on the details of their models, and less on their implementation. Neuron models are defined by writing differential equations in standard mathematical notation, facilitating scientific communication. Brian is written in the Python programming language, and uses vector-based computation to allow for efficient simulations. It is particularly useful for neuroscientific modelling at the systems level, and for teaching computational neuroscience.

Eddy Viscosity for Variable Density Coflowing Streams,

DTIC Science & Technology

EDDY CURRENTS, *JET MIXING FLOW, *VISCOSITY, *AIR FLOW, MATHEMATICAL MODELS, INCOMPRESSIBLE FLOW, AXISYMMETRIC FLOW, MATHEMATICAL PREDICTION, THRUST AUGMENTATION , EJECTORS , COMPUTER PROGRAMMING, SECONDARY FLOW, DENSITY, MODIFICATION.

The Identification, Implementation, and Evaluation of Critical User Interface Design Features of Computer-Assisted Instruction Programs in Mathematics for Students with Learning Disabilities

ERIC Educational Resources Information Center

Seo, You-Jin; Woo, Honguk

2010-01-01

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, "Math Explorer", which delivers…

Encouraging More Women into Computer Science: Initiating a Single-Sex Intervention Program in Sweden.

ERIC Educational Resources Information Center

Brandell, Gerd; Carlsson, Svante; Eklbom, Hakan; Nord, Ann-Charlotte

1997-01-01

Describes the process of starting a new program in computer science and engineering that is heavily based on applied mathematics and only open to women. Emphasizes that success requires considerable interest in mathematics and curiosity about computer science among female students at the secondary level and the acceptance of the single-sex program…

Investigating Student Use of Electronic Support Tools and Mathematical Reasoning

ERIC Educational Resources Information Center

Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark

2016-01-01

Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…

A Formal Valuation Framework for Emotions and Their Control.

PubMed

Huys, Quentin J M; Renz, Daniel

2017-09-15

Computational psychiatry aims to apply mathematical and computational techniques to help improve psychiatric care. To achieve this, the phenomena under scrutiny should be within the scope of formal methods. As emotions play an important role across many psychiatric disorders, such computational methods must encompass emotions. Here, we consider formal valuation accounts of emotions. We focus on the fact that the flexibility of emotional responses and the nature of appraisals suggest the need for a model-based valuation framework for emotions. However, resource limitations make plain model-based valuation impossible and require metareasoning strategies to apportion cognitive resources adaptively. We argue that emotions may implement such metareasoning approximations by restricting the range of behaviors and states considered. We consider the processes that guide the deployment of the approximations, discerning between innate, model-free, heuristic, and model-based controllers. A formal valuation and metareasoning framework may thus provide a principled approach to examining emotions. Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Computational Model of Population Dynamics Based on the Cell Cycle and Local Interactions

NASA Astrophysics Data System (ADS)

Oprisan, Sorinel Adrian; Oprisan, Ana

2005-03-01

Our study bridges cellular (mesoscopic) level interactions and global population (macroscopic) dynamics of carcinoma. The morphological differences and transitions between well and smooth defined benign tumors and tentacular malignat tumors suggest a theoretical analysis of tumor invasion based on the development of mathematical models exhibiting bifurcations of spatial patterns in the density of tumor cells. Our computational model views the most representative and clinically relevant features of oncogenesis as a fight between two distinct sub-systems: the immune system of the host and the neoplastic system. We implemented the neoplastic sub-system using a three-stage cell cycle: active, dormant, and necrosis. The second considered sub-system consists of cytotoxic active (effector) cells — EC, with a very broad phenotype ranging from NK cells to CTL cells, macrophages, etc. Based on extensive numerical simulations, we correlated the fractal dimensions for carcinoma, which could be obtained from tumor imaging, with the malignat stage. Our computational model was able to also simulate the effects of surgical, chemotherapeutical, and radiotherapeutical treatments.

Use of the computational-informational web-GIS system for the development of climatology students' skills in modeling and understanding climate change

NASA Astrophysics Data System (ADS)

Gordova, Yulia; Martynova, Yulia; Shulgina, Tamara

2015-04-01

The current situation with the training of specialists in environmental sciences is complicated by the fact that the very scientific field is experiencing a period of rapid development. Global change has caused the development of measurement techniques and modeling of environmental characteristics, accompanied by the expansion of the conceptual and mathematical apparatus. Understanding and forecasting processes in the Earth system requires extensive use of mathematical modeling and advanced computing technologies. As a rule, available training programs in the environmental sciences disciplines do not have time to adapt to such rapid changes in the domain content. As a result, graduates of faculties do not understand processes and mechanisms of the global change, have only superficial knowledge of mathematical modeling of processes in the environment. They do not have the required skills in numerical modeling, data processing and analysis of observations and computation outputs and are not prepared to work with the meteorological data. For adequate training of future specialists in environmental sciences we propose the following approach, which reflects the new "research" paradigm in education. We believe that the training of such specialists should be done not in an artificial learning environment, but based on actual operating information-computational systems used in environment studies, in the so-called virtual research environment via development of virtual research and learning laboratories. In the report the results of the use of computational-informational web-GIS system "Climate" (http://climate.scert.ru/) as a prototype of such laboratory are discussed. The approach is realized at Tomsk State University to prepare bachelors in meteorology. Student survey shows that their knowledge has become deeper and more systemic after undergoing training in virtual learning laboratory. The scientific team plans to assist any educators to utilize the system in earth science education. This work is partially supported by SB RAS project VIII.80.2.1, RFBR grants 13-05-12034 and 14-05-00502.

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

Mathematical and computational modeling simulation of solar drying Systems

USDA-ARS?s Scientific Manuscript database

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...

Applying mathematical modeling to create job rotation schedules for minimizing occupational noise exposure.

PubMed

Tharmmaphornphilas, Wipawee; Green, Benjamin; Carnahan, Brian J; Norman, Bryan A

2003-01-01

This research developed worker schedules by using administrative controls and a computer programming model to reduce the likelihood of worker hearing loss. By rotating the workers through different jobs during the day it was possible to reduce their exposure to hazardous noise levels. Computer simulations were made based on data collected in a real setting. Worker schedules currently used at the site are compared with proposed worker schedules from the computer simulations. For the worker assignment plans found by the computer model, the authors calculate a significant decrease in time-weighted average (TWA) sound level exposure. The maximum daily dose that any worker is exposed to is reduced by 58.8%, and the maximum TWA value for the workers is reduced by 3.8 dB from the current schedule.

A flexible computer aid for conceptual design based on constraint propagation and component-modeling. [of aircraft in three dimensions

NASA Technical Reports Server (NTRS)

Kolb, Mark A.

1988-01-01

The Rubber Airplane program, which combines two symbolic processing techniques with a component-based database of design knowledge, is proposed as a computer aid for conceptual design. Using object-oriented programming, programs are organized around the objects and behavior to be simulated, and using constraint propagation, declarative statements designate mathematical relationships among all the equation variables. It is found that the additional level of organizational structure resulting from the arrangement of the design information in terms of design components provides greater flexibility and convenience.

NOTE: Acceleration of Monte Carlo-based scatter compensation for cardiac SPECT

NASA Astrophysics Data System (ADS)

Sohlberg, A.; Watabe, H.; Iida, H.

2008-07-01

Single proton emission computed tomography (SPECT) images are degraded by photon scatter making scatter compensation essential for accurate reconstruction. Reconstruction-based scatter compensation with Monte Carlo (MC) modelling of scatter shows promise for accurate scatter correction, but it is normally hampered by long computation times. The aim of this work was to accelerate the MC-based scatter compensation using coarse grid and intermittent scatter modelling. The acceleration methods were compared to un-accelerated implementation using MC-simulated projection data of the mathematical cardiac torso (MCAT) phantom modelling 99mTc uptake and clinical myocardial perfusion studies. The results showed that when combined the acceleration methods reduced the reconstruction time for 10 ordered subset expectation maximization (OS-EM) iterations from 56 to 11 min without a significant reduction in image quality indicating that the coarse grid and intermittent scatter modelling are suitable for MC-based scatter compensation in cardiac SPECT.

Promoting Transfer of Mathematics Skills through the Use of a Computer-Based Instructional Simulation Game and Advisement.

ERIC Educational Resources Information Center

Van Eck, Richard

This study looked at the effect of contextual advisement and competition on transfer of mathematics skills in a computer-based instructional simulation game and simulation in which game participants helped their "aunt and uncle" fix up a house. Competition referred to whether or not the participant was playing against a computer…

n-D shape/texture optimal synthetic description and modeling by GEOGINE

NASA Astrophysics Data System (ADS)

Fiorini, Rodolfo A.; Dacquino, Gianfranco F.

2004-12-01

GEOGINE(GEOmetrical enGINE), a state-of-the-art OMG (Ontological Model Generator) based on n-D Tensor Invariants for multidimensional shape/texture optimal synthetic description and learning, is presented. Usually elementary geometric shape robust characterization, subjected to geometric transformation, on a rigorous mathematical level is a key problem in many computer applications in different interest areas. The past four decades have seen solutions almost based on the use of n-Dimensional Moment and Fourier descriptor invariants. The present paper introduces a new approach for automatic model generation based on n -Dimensional Tensor Invariants as formal dictionary. An ontological model is the kernel used for specifying ontologies so that how close an ontology can be from the real world depends on the possibilities offered by the ontological model. By this approach even chromatic information content can be easily and reliably decoupled from target geometric information and computed into robus colour shape parameter attributes. Main GEOGINEoperational advantages over previous approaches are: 1) Automated Model Generation, 2) Invariant Minimal Complete Set for computational efficiency, 3) Arbitrary Model Precision for robust object description.

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

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

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

Computational ecology as an emerging science

PubMed Central

Petrovskii, Sergei; Petrovskaya, Natalia

2012-01-01

It has long been recognized that numerical modelling and computer simulations can be used as a powerful research tool to understand, and sometimes to predict, the tendencies and peculiarities in the dynamics of populations and ecosystems. It has been, however, much less appreciated that the context of modelling and simulations in ecology is essentially different from those that normally exist in other natural sciences. In our paper, we review the computational challenges arising in modern ecology in the spirit of computational mathematics, i.e. with our main focus on the choice and use of adequate numerical methods. Somewhat paradoxically, the complexity of ecological problems does not always require the use of complex computational methods. This paradox, however, can be easily resolved if we recall that application of sophisticated computational methods usually requires clear and unambiguous mathematical problem statement as well as clearly defined benchmark information for model validation. At the same time, many ecological problems still do not have mathematically accurate and unambiguous description, and available field data are often very noisy, and hence it can be hard to understand how the results of computations should be interpreted from the ecological viewpoint. In this scientific context, computational ecology has to deal with a new paradigm: conventional issues of numerical modelling such as convergence and stability become less important than the qualitative analysis that can be provided with the help of computational techniques. We discuss this paradigm by considering computational challenges arising in several specific ecological applications. PMID:23565336

A Mathematical Model for the Middle Ear Ventilation

NASA Astrophysics Data System (ADS)

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

2008-09-01

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

Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom?

ERIC Educational Resources Information Center

Newton, Douglas P.; Newton, Lynn D.

2007-01-01

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and…

Manycore Performance-Portability: Kokkos Multidimensional Array Library

DOE PAGES

Edwards, H. Carter; Sunderland, Daniel; Porter, Vicki; ...

2012-01-01

Large, complex scientific and engineering application code have a significant investment in computational kernels to implement their mathematical models. Porting these computational kernels to the collection of modern manycore accelerator devices is a major challenge in that these devices have diverse programming models, application programming interfaces (APIs), and performance requirements. The Kokkos Array programming model provides library-based approach to implement computational kernels that are performance-portable to CPU-multicore and GPGPU accelerator devices. This programming model is based upon three fundamental concepts: (1) manycore compute devices each with its own memory space, (2) data parallel kernels and (3) multidimensional arrays. Kernel executionmore » performance is, especially for NVIDIA® devices, extremely dependent on data access patterns. Optimal data access pattern can be different for different manycore devices – potentially leading to different implementations of computational kernels specialized for different devices. The Kokkos Array programming model supports performance-portable kernels by (1) separating data access patterns from computational kernels through a multidimensional array API and (2) introduce device-specific data access mappings when a kernel is compiled. An implementation of Kokkos Array is available through Trilinos [Trilinos website, http://trilinos.sandia.gov/, August 2011].« less

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

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

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

The Effects of Pedagogical Agents on Mathematics Anxiety and Mathematics Learning

ERIC Educational Resources Information Center

Wei, Quan

2010-01-01

The purpose of this study was to investigate the impact of the mathematics anxiety treatment messages in a computer-based environment on ninth-grade students' mathematics anxiety and mathematics learning. The study also examined whether the impact of the treatment messages would be differentiated by learner's gender and by learner's prior…

Software development and its description for Geoid determination based on Spherical-Cap-Harmonics Modelling using digital-zenith camera and gravimetric measurements hybrid data

NASA Astrophysics Data System (ADS)

Morozova, K.; Jaeger, R.; Balodis, J.; Kaminskis, J.

2017-10-01

Over several years the Institute of Geodesy and Geoinformatics (GGI) was engaged in the design and development of a digital zenith camera. At the moment the camera developments are finished and tests by field measurements are done. In order to check these data and to use them for geoid model determination DFHRS (Digital Finite element Height reference surface (HRS)) v4.3. software is used. It is based on parametric modelling of the HRS as a continous polynomial surface. The HRS, providing the local Geoid height N, is a necessary geodetic infrastructure for a GNSS-based determination of physcial heights H from ellipsoidal GNSS heights h, by H=h-N. The research and this publication is dealing with the inclusion of the data of observed vertical deflections from digital zenith camera into the mathematical model of the DFHRS approach and software v4.3. A first target was to test out and validate the mathematical model and software, using additionally real data of the above mentioned zenith camera observations of deflections of the vertical. A second concern of the research was to analyze the results and the improvement of the Latvian quasi-geoid computation compared to the previous version HRS computed without zenith camera based deflections of the vertical. The further development of the mathematical model and software concerns the use of spherical-cap-harmonics as the designed carrier function for the DFHRS v.5. It enables - in the sense of the strict integrated geodesy approach, holding also for geodetic network adjustment - both a full gravity field and a geoid and quasi-geoid determination. In addition, it allows the inclusion of gravimetric measurements, together with deflections of the vertical from digital-zenith cameras, and all other types of observations. The theoretical description of the updated version of DFHRS software and methods are discussed in this publication.

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

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Breast tumor malignancy modelling using evolutionary neural logic networks.

PubMed

Tsakonas, Athanasios; Dounias, Georgios; Panagi, Georgia; Panourgias, Evangelia

2006-01-01

The present work proposes a computer assisted methodology for the effective modelling of the diagnostic decision for breast tumor malignancy. The suggested approach is based on innovative hybrid computational intelligence algorithms properly applied in related cytological data contained in past medical records. The experimental data used in this study were gathered in the early 1990s in the University of Wisconsin, based in post diagnostic cytological observations performed by expert medical staff. Data were properly encoded in a computer database and accordingly, various alternative modelling techniques were applied on them, in an attempt to form diagnostic models. Previous methods included standard optimisation techniques, as well as artificial intelligence approaches, in a way that a variety of related publications exists in modern literature on the subject. In this report, a hybrid computational intelligence approach is suggested, which effectively combines modern mathematical logic principles, neural computation and genetic programming in an effective manner. The approach proves promising either in terms of diagnostic accuracy and generalization capabilities, or in terms of comprehensibility and practical importance for the related medical staff.

Mathematical model of the current density for the 30-cm engineering model thruster

NASA Technical Reports Server (NTRS)

Cuffel, R. F.

1975-01-01

Mathematical models are presented for both the singly and doubly charged ion current densities downstream of the 30-cm engineering model thruster with 0.5% compensated dished grids. These models are based on the experimental measurements of Vahrenkamp at a 2-amp ion beam operating condition. The cylindrically symmetric beam of constant velocity ions is modeled with continuous radial source and focusing functions across 'plane' grids with similar angular distribution functions. A computer program is used to evaluate the double integral for current densities in the near field and to obtain a far field approximation beyond 10 grid radii. The utility of the model is demonstrated for (1) calculating the directed thrust and (2) determining the impingement levels on various spacecraft surfaces from a two-axis gimballed, 2 x 3 thruster array.

Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

PubMed Central

Liao, David; Tlsty, Thea D.

2014-01-01

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

Artificial Intelligence, Computational Thinking, and Mathematics Education

ERIC Educational Resources Information Center

Gadanidis, George

2017-01-01

Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

Computational Modeling and Mathematics Applied to the Physical Sciences.

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC.

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

Python as a federation tool for GENESIS 3.0.

PubMed

Cornelis, Hugo; Rodriguez, Armando L; Coop, Allan D; Bower, James M

2012-01-01

The GENESIS simulation platform was one of the first broad-scale modeling systems in computational biology to encourage modelers to develop and share model features and components. Supported by a large developer community, it participated in innovative simulator technologies such as benchmarking, parallelization, and declarative model specification and was the first neural simulator to define bindings for the Python scripting language. An important feature of the latest version of GENESIS is that it decomposes into self-contained software components complying with the Computational Biology Initiative federated software architecture. This architecture allows separate scripting bindings to be defined for different necessary components of the simulator, e.g., the mathematical solvers and graphical user interface. Python is a scripting language that provides rich sets of freely available open source libraries. With clean dynamic object-oriented designs, they produce highly readable code and are widely employed in specialized areas of software component integration. We employ a simplified wrapper and interface generator to examine an application programming interface and make it available to a given scripting language. This allows independent software components to be 'glued' together and connected to external libraries and applications from user-defined Python or Perl scripts. We illustrate our approach with three examples of Python scripting. (1) Generate and run a simple single-compartment model neuron connected to a stand-alone mathematical solver. (2) Interface a mathematical solver with GENESIS 3.0 to explore a neuron morphology from either an interactive command-line or graphical user interface. (3) Apply scripting bindings to connect the GENESIS 3.0 simulator to external graphical libraries and an open source three dimensional content creation suite that supports visualization of models based on electron microscopy and their conversion to computational models. Employed in this way, the stand-alone software components of the GENESIS 3.0 simulator provide a framework for progressive federated software development in computational neuroscience.

Python as a Federation Tool for GENESIS 3.0

PubMed Central

Cornelis, Hugo; Rodriguez, Armando L.; Coop, Allan D.; Bower, James M.

2012-01-01

The GENESIS simulation platform was one of the first broad-scale modeling systems in computational biology to encourage modelers to develop and share model features and components. Supported by a large developer community, it participated in innovative simulator technologies such as benchmarking, parallelization, and declarative model specification and was the first neural simulator to define bindings for the Python scripting language. An important feature of the latest version of GENESIS is that it decomposes into self-contained software components complying with the Computational Biology Initiative federated software architecture. This architecture allows separate scripting bindings to be defined for different necessary components of the simulator, e.g., the mathematical solvers and graphical user interface. Python is a scripting language that provides rich sets of freely available open source libraries. With clean dynamic object-oriented designs, they produce highly readable code and are widely employed in specialized areas of software component integration. We employ a simplified wrapper and interface generator to examine an application programming interface and make it available to a given scripting language. This allows independent software components to be ‘glued’ together and connected to external libraries and applications from user-defined Python or Perl scripts. We illustrate our approach with three examples of Python scripting. (1) Generate and run a simple single-compartment model neuron connected to a stand-alone mathematical solver. (2) Interface a mathematical solver with GENESIS 3.0 to explore a neuron morphology from either an interactive command-line or graphical user interface. (3) Apply scripting bindings to connect the GENESIS 3.0 simulator to external graphical libraries and an open source three dimensional content creation suite that supports visualization of models based on electron microscopy and their conversion to computational models. Employed in this way, the stand-alone software components of the GENESIS 3.0 simulator provide a framework for progressive federated software development in computational neuroscience. PMID:22276101

Calculating degree-based topological indices of dominating David derived networks

NASA Astrophysics Data System (ADS)

Ahmad, Muhammad Saeed; Nazeer, Waqas; Kang, Shin Min; Imran, Muhammad; Gao, Wei

2017-12-01

An important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the dominating David derived networks [1, 2, 3, 4, 5].

Case Study Projects for College Mathematics Courses Based on a Particular Function of Two Variables

ERIC Educational Resources Information Center

Shi, Y.

2007-01-01

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, "Mathematics and Computer Education," 39(3), 198-205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry,…

Computing Linear Mathematical Models Of Aircraft

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1991-01-01

Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

Parallel multiscale simulations of a brain aneurysm

PubMed Central

Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em

2012-01-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκ αr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκ αr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work. PMID:23734066

Parallel multiscale simulations of a brain aneurysm.

PubMed

Grinberg, Leopold; Fedosov, Dmitry A; Karniadakis, George Em

2013-07-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκ αr . The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκ αr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.

Parallel multiscale simulations of a brain aneurysm

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

Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2013-07-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm.more » The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.« less

Integrating First-Year Technology and Finite Mathematics Courses

ERIC Educational Resources Information Center

Shafii-Mousavi, Morteza; Kochanowski, Paul

2006-01-01

This paper describes an interdisciplinary project-based mathematics course linked to a computer technology course. The linkage encourages an appreciation of mathematics and technology as students see an immediate use for these skills in completing actual real-world projects. Linking mathematics and technology integrates subjects taught in…

Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

ERIC Educational Resources Information Center

Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

2014-01-01

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

Computer-Aided Geometry Modeling

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

SELECTED ANNOTATED BIBLIOGRAPHY ON SYSTEMS OF THEORETICAL DEVICES,

DTIC Science & Technology

BIONICS, BIBLIOGRAPHIES), (*BIBLIOGRAPHIES, BIONICS), (*CYBERNETICS, BIBLIOGRAPHIES), MATHEMATICS, COMPUTER LOGIC, NETWORKS, NERVOUS SYSTEM , THEORY , SEQUENCE SWITCHES, SWITCHING CIRCUITS, REDUNDANT COMPONENTS, LEARNING, MATHEMATICAL MODELS, BEHAVIOR, NERVES, SIMULATION, NERVE CELLS

Computational Control of Flexible Aerospace Systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

An electromagnetism-like metaheuristic for open-shop problems with no buffer

NASA Astrophysics Data System (ADS)

Naderi, Bahman; Najafi, Esmaeil; Yazdani, Mehdi

2012-12-01

This paper considers open-shop scheduling with no intermediate buffer to minimize total tardiness. This problem occurs in many production settings, in the plastic molding, chemical, and food processing industries. The paper mathematically formulates the problem by a mixed integer linear program. The problem can be optimally solved by the model. The paper also develops a novel metaheuristic based on an electromagnetism algorithm to solve the large-sized problems. The paper conducts two computational experiments. The first includes small-sized instances by which the mathematical model and general performance of the proposed metaheuristic are evaluated. The second evaluates the metaheuristic for its performance to solve some large-sized instances. The results show that the model and algorithm are effective to deal with the problem.

10 CFR 431.17 - Determination of efficiency.

Code of Federal Regulations, 2010 CFR

2010-01-01

... method or methods used; the mathematical model, the engineering or statistical analysis, computer... accordance with § 431.16 of this subpart, or by application of an alternative efficiency determination method... must be: (i) Derived from a mathematical model that represents the mechanical and electrical...

Cross-Age Peer Tutoring and Fluency-Based Instruction to Achieve Fluency with Mathematics Computation Skills: A Randomized Controlled Trial

ERIC Educational Resources Information Center

Greene, Irene; Mc Tiernan, Aoife; Holloway, Jennifer

2018-01-01

The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say…

Intelligent Tutoring Systems: Formalization as Automata and Interface Design Using Neural Networks

ERIC Educational Resources Information Center

Curilem, S. Gloria; Barbosa, Andrea R.; de Azevedo, Fernando M.

2007-01-01

This article proposes a mathematical model of Intelligent Tutoring Systems (ITS), based on observations of the behaviour of these systems. One of the most important problems of pedagogical software is to establish a common language between the knowledge areas involved in their development, basically pedagogical, computing and domain areas. A…

Analysis of contour images using optics of spiral beams

NASA Astrophysics Data System (ADS)

Volostnikov, V. G.; Kishkin, S. A.; Kotova, S. P.

2018-03-01

An approach is outlined to the recognition of contour images using computer technology based on coherent optics principles. A mathematical description of the recognition process algorithm and the results of numerical modelling are presented. The developed approach to the recognition of contour images using optics of spiral beams is described and justified.

Computer Language For Optimization Of Design

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.; Lucas, Stephen H.

1991-01-01

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

Model of Fluidized Bed Containing Reacting Solids and Gases

NASA Technical Reports Server (NTRS)

Bellan, Josette; Lathouwers, Danny

2003-01-01

A mathematical model has been developed for describing the thermofluid dynamics of a dense, chemically reacting mixture of solid particles and gases. As used here, "dense" signifies having a large volume fraction of particles, as for example in a bubbling fluidized bed. The model is intended especially for application to fluidized beds that contain mixtures of carrier gases, biomass undergoing pyrolysis, and sand. So far, the design of fluidized beds and other gas/solid industrial processing equipment has been based on empirical correlations derived from laboratory- and pilot-scale units. The present mathematical model is a product of continuing efforts to develop a computational capability for optimizing the designs of fluidized beds and related equipment on the basis of first principles. Such a capability could eliminate the need for expensive, time-consuming predesign testing.

Trajectory-based morphological operators: a model for efficient image processing.

PubMed

Jimeno-Morenilla, Antonio; Pujol, Francisco A; Molina-Carmona, Rafael; Sánchez-Romero, José L; Pujol, Mar

2014-01-01

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images.

Interactivity of Visual Mathematical Representations: Factors Affecting Learning and Cognitive Processes

ERIC Educational Resources Information Center

Sedig, Kamran; Liang, Hai-Ning

2006-01-01

Computer-based mathematical cognitive tools (MCTs) are a category of external aids intended to support and enhance learning and cognitive processes of learners. MCTs often contain interactive visual mathematical representations (VMRs), where VMRs are graphical representations that encode properties and relationships of mathematical concepts. In…

Models of neuromodulation for computational psychiatry.

PubMed

Iglesias, Sandra; Tomiello, Sara; Schneebeli, Maya; Stephan, Klaas E

2017-05-01

Psychiatry faces fundamental challenges: based on a syndrome-based nosology, it presently lacks clinical tests to infer on disease processes that cause symptoms of individual patients and must resort to trial-and-error treatment strategies. These challenges have fueled the recent emergence of a novel field-computational psychiatry-that strives for mathematical models of disease processes at physiological and computational (information processing) levels. This review is motivated by one particular goal of computational psychiatry: the development of 'computational assays' that can be applied to behavioral or neuroimaging data from individual patients and support differential diagnosis and guiding patient-specific treatment. Because the majority of available pharmacotherapeutic approaches in psychiatry target neuromodulatory transmitters, models that infer (patho)physiological and (patho)computational actions of different neuromodulatory transmitters are of central interest for computational psychiatry. This article reviews the (many) outstanding questions on the computational roles of neuromodulators (dopamine, acetylcholine, serotonin, and noradrenaline), outlines available evidence, and discusses promises and pitfalls in translating these findings to clinical applications. WIREs Cogn Sci 2017, 8:e1420. doi: 10.1002/wcs.1420 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

Computational assessment of model-based wave separation using a database of virtual subjects.

PubMed

Hametner, Bernhard; Schneider, Magdalena; Parragh, Stephanie; Wassertheurer, Siegfried

2017-11-07

The quantification of arterial wave reflection is an important area of interest in arterial pulse wave analysis. It can be achieved by wave separation analysis (WSA) if both the aortic pressure waveform and the aortic flow waveform are known. For better applicability, several mathematical models have been established to estimate aortic flow solely based on pressure waveforms. The aim of this study is to investigate and verify the model-based wave separation of the ARCSolver method on virtual pulse wave measurements. The study is based on an open access virtual database generated via simulations. Seven cardiac and arterial parameters were varied within physiological healthy ranges, leading to a total of 3325 virtual healthy subjects. For assessing the model-based ARCSolver method computationally, this method was used to perform WSA based on the aortic root pressure waveforms of the virtual patients. Asa reference, the values of WSA using both the pressure and flow waveforms provided by the virtual database were taken. The investigated parameters showed a good overall agreement between the model-based method and the reference. Mean differences and standard deviations were -0.05±0.02AU for characteristic impedance, -3.93±1.79mmHg for forward pressure amplitude, 1.37±1.56mmHg for backward pressure amplitude and 12.42±4.88% for reflection magnitude. The results indicate that the mathematical blood flow model of the ARCSolver method is a feasible surrogate for a measured flow waveform and provides a reasonable way to assess arterial wave reflection non-invasively in healthy subjects. Copyright © 2017 Elsevier Ltd. All rights reserved.

On 3-D inelastic analysis methods for hot section components (base program)

NASA Technical Reports Server (NTRS)

Wilson, R. B.; Bak, M. J.; Nakazawa, S.; Banerjee, P. K.

1986-01-01

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report.

Discrete-time model reduction in limited frequency ranges

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Program Helps Generate Boundary-Element Mathematical Models

NASA Technical Reports Server (NTRS)

Goldberg, R. K.

1995-01-01

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

Connecting Expectations and Values: Students' Perceptions of Developmental Mathematics in a Computer-Based Learning Environment

ERIC Educational Resources Information Center

Jackson, Karen Latrice Terrell

2014-01-01

Students' perceptions influence their expectations and values. According to Expectations and Values Theory of Achievement Motivation (EVT-AM), students' expectations and values impact their behaviors (Eccles & Wigfield, 2002). This study seeks to find students' perceptions of developmental mathematics in a mastery learning computer-based…

The World According to Malthus and Volterra: The Mathematical Theory of the Struggle for Existence.

ERIC Educational Resources Information Center

Bogdanov, Constantine

1992-01-01

Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

NASA Technical Reports Server (NTRS)

Austin, F.; Markowitz, J.; Goldenberg, S.; Zetkov, G. A.

1973-01-01

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.

Comparing computer adaptive and curriculum-based measures of math in progress monitoring.

PubMed

Shapiro, Edward S; Dennis, Minyi Shih; Fu, Qiong

2015-12-01

The purpose of the study was to compare the use of a Computer Adaptive Test and Curriculum-Based Measurement in the assessment of mathematics. This study also investigated the degree to which slope or rate of change predicted student outcomes on the annual state assessment of mathematics above and beyond scores of single point screening assessments (i.e., the computer adaptive test or the CBM assessment just before the administration of the state assessment). Repeated measurement of mathematics once per month across a 7-month period using a Computer Adaptive Test (STAR-Math) and Curriculum-Based Measurement (CBM, AIMSweb Math Computation, AIMSweb Math Concepts/Applications) was collected for a maximum total of 250 third, fourth, and fifth grade students. Results showed STAR-Math in all 3 grades and AIMSweb Math Concepts/Applications in the third and fifth grades had primarily linear growth patterns in mathematics. AIMSweb Math Computation in all grades and AIMSweb Math Concepts/Applications in Grade 4 had decelerating positive trends. Predictive validity evidence showed the strongest relationships were between STAR-Math and outcomes for third and fourth grade students. The blockwise multiple regression by grade revealed that slopes accounted for only a very small proportion of additional variance above and beyond what was explained by the scores obtained on a single point of assessment just prior to the administration of the state assessment. (c) 2015 APA, all rights reserved).

Network-based stochastic semisupervised learning.

PubMed

Silva, Thiago Christiano; Zhao, Liang

2012-03-01

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Mathematical and Computational Aspects of Multiscale Materials Modeling, Mathematics-Numerical analysis, Section II.A.a.3.4, Conference and symposia organization II.A.2.a

DTIC Science & Technology

2015-02-04

dislocation dynamics models ( DDD ), continuum representations). Coupling of these models is difficult. Coupling of atomistics and DDD models has been...explored to some extent, but the coupling between DDD and continuum models of the evolution of large populations of dislocations is essentially unexplored

Great Lakes modeling: Are the mathematics outpacing the data and our understanding of the system?

EPA Science Inventory

Mathematical modeling in the Great Lakes has come a long way from the pioneering work done by Manhattan College in the 1970s, when the models operated on coarse computational grids (often lake-wide) and used simple eutrophication formulations. Moving forward 40 years, we are now...

Hybrid model based unified scheme for endoscopic Cerenkov and radio-luminescence tomography: Simulation demonstration

NASA Astrophysics Data System (ADS)

Wang, Lin; Cao, Xin; Ren, Qingyun; Chen, Xueli; He, Xiaowei

2018-05-01

Cerenkov luminescence imaging (CLI) is an imaging method that uses an optical imaging scheme to probe a radioactive tracer. Application of CLI with clinically approved radioactive tracers has opened an opportunity for translating optical imaging from preclinical to clinical applications. Such translation was further improved by developing an endoscopic CLI system. However, two-dimensional endoscopic imaging cannot identify accurate depth and obtain quantitative information. Here, we present an imaging scheme to retrieve the depth and quantitative information from endoscopic Cerenkov luminescence tomography, which can also be applied for endoscopic radio-luminescence tomography. In the scheme, we first constructed a physical model for image collection, and then a mathematical model for characterizing the luminescent light propagation from tracer to the endoscopic detector. The mathematical model is a hybrid light transport model combined with the 3rd order simplified spherical harmonics approximation, diffusion, and radiosity equations to warrant accuracy and speed. The mathematical model integrates finite element discretization, regularization, and primal-dual interior-point optimization to retrieve the depth and the quantitative information of the tracer. A heterogeneous-geometry-based numerical simulation was used to explore the feasibility of the unified scheme, which demonstrated that it can provide a satisfactory balance between imaging accuracy and computational burden.

Mathematical Model of the One-stage Magneto-optical Sensor Based on Faraday Effect

NASA Astrophysics Data System (ADS)

Babaev, O. G.; Paranin, V. D.; Sinitsin, L. I.

2018-01-01

The aim of this work is to refine a model of magneto-optical sensors based on Faraday’s longitudinal magneto-optical effect. The tasks of the study include computer modeling and analysis of the transfer characteristic of a single-stage magneto-optical sensor for various polarization of the input beam and non-ideal optical components. The proposed mathematical model and software make it possible to take into account the non-ideal characteristics of film polaroids observed in operation in the near infrared region and at increased temperatures. On the basis of the results of the model analysis it was found that the dependence of normalized transmission T(γ2) has periodic nature. Choosing the angle (γ 2-γ 1) makes it possible to shift the initial operation point and change the sensitivity dT/dγ 2. The influence of the input beam polarization increases with the increase of polaroid parameter deviation from ideal and shows itself as reduction of modulation depth and angular shift of the sensor conversion response.

A nonlinear bi-level programming approach for product portfolio management.

PubMed

Ma, Shuang

2016-01-01

Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

Agent-Based Phytoplankton Models of Cellular and Population Processes: Fostering Individual-Based Learning in Undergraduate Research

NASA Astrophysics Data System (ADS)

Berges, J. A.; Raphael, T.; Rafa Todd, C. S.; Bate, T. C.; Hellweger, F. L.

2016-02-01

Engaging undergraduate students in research projects that require expertise in multiple disciplines (e.g. cell biology, population ecology, and mathematical modeling) can be challenging because they have often not developed the expertise that allows them to participate at a satisfying level. Use of agent-based modeling can allow exploration of concepts at more intuitive levels, and encourage experimentation that emphasizes processes over computational skills. Over the past several years, we have involved undergraduate students in projects examining both ecological and cell biological aspects of aquatic microbial biology, using the freely-downloadable, agent-based modeling environment NetLogo (https://ccl.northwestern.edu/netlogo/). In Netlogo, actions of large numbers of individuals can be simulated, leading to complex systems with emergent behavior. The interface features appealing graphics, monitors, and control structures. In one example, a group of sophomores in a BioMathematics program developed an agent-based model of phytoplankton population dynamics in a pond ecosystem, motivated by observed macroscopic changes in cell numbers (due to growth and death), and driven by responses to irradiance, temperature and a limiting nutrient. In a second example, junior and senior undergraduates conducting Independent Studies created a model of the intracellular processes governing stress and cell death for individual phytoplankton cells (based on parameters derived from experiments using single-cell culturing and flow cytometry), and then this model was embedded in the agents in the pond ecosystem model. In our experience, students with a range of mathematical abilities learned to code quickly and could use the software with varying degrees of sophistication, for example, creation of spatially-explicit two and three-dimensional models. Skills developed quickly and transferred readily to other platforms (e.g. Matlab).

Improving Odometric Accuracy for an Autonomous Electric Cart.

PubMed

Toledo, Jonay; Piñeiro, Jose D; Arnay, Rafael; Acosta, Daniel; Acosta, Leopoldo

2018-01-12

In this paper, a study of the odometric system for the autonomous cart Verdino, which is an electric vehicle based on a golf cart, is presented. A mathematical model of the odometric system is derived from cart movement equations, and is used to compute the vehicle position and orientation. The inputs of the system are the odometry encoders, and the model uses the wheels diameter and distance between wheels as parameters. With this model, a least square minimization is made in order to get the nominal best parameters. This model is updated, including a real time wheel diameter measurement improving the accuracy of the results. A neural network model is used in order to learn the odometric model from data. Tests are made using this neural network in several configurations and the results are compared to the mathematical model, showing that the neural network can outperform the first proposed model.

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

Lai, Jih-Sheng

This paper introduces control system design based softwares, SIMNON and MATLAB/SIMULINK, for power electronics system simulation. A complete power electronics system typically consists of a rectifier bridge along with its smoothing capacitor, an inverter, and a motor. The system components, featuring discrete or continuous, linear or nonlinear, are modeled in mathematical equations. Inverter control methods,such as pulse-width-modulation and hysteresis current control, are expressed in either computer algorithms or digital circuits. After describing component models and control methods, computer programs are then developed for complete systems simulation. Simulation results are mainly used for studying system performances, such as input and outputmore » current harmonics, torque ripples, and speed responses. Key computer programs and simulation results are demonstrated for educational purposes.« less

Computer modeling of heat pipe performance

NASA Technical Reports Server (NTRS)

Peterson, G. P.

1983-01-01

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

Computational method for analysis of polyethylene biodegradation

NASA Astrophysics Data System (ADS)

Watanabe, Masaji; Kawai, Fusako; Shibata, Masaru; Yokoyama, Shigeo; Sudate, Yasuhiro

2003-12-01

In a previous study concerning the biodegradation of polyethylene, we proposed a mathematical model based on two primary factors: the direct consumption or absorption of small molecules and the successive weight loss of large molecules due to β-oxidation. Our model is an initial value problem consisting of a differential equation whose independent variable is time. Its unknown variable represents the total weight of all the polyethylene molecules that belong to a molecular-weight class specified by a parameter. In this paper, we describe a numerical technique to introduce experimental results into analysis of our model. We first establish its mathematical foundation in order to guarantee its validity, by showing that the initial value problem associated with the differential equation has a unique solution. Our computational technique is based on a linear system of differential equations derived from the original problem. We introduce some numerical results to illustrate our technique as a practical application of the linear approximation. In particular, we show how to solve the inverse problem to determine the consumption rate and the β-oxidation rate numerically, and illustrate our numerical technique by analyzing the GPC patterns of polyethylene wax obtained before and after 5 weeks cultivation of a fungus, Aspergillus sp. AK-3. A numerical simulation based on these degradation rates confirms that the primary factors of the polyethylene biodegradation posed in modeling are indeed appropriate.

Accurate evaluation of sensitivity for calibration between a LiDAR and a panoramic camera used for remote sensing

NASA Astrophysics Data System (ADS)

García-Moreno, Angel-Iván; González-Barbosa, José-Joel; Ramírez-Pedraza, Alfonso; Hurtado-Ramos, Juan B.; Ornelas-Rodriguez, Francisco-Javier

2016-04-01

Computer-based reconstruction models can be used to approximate urban environments. These models are usually based on several mathematical approximations and the usage of different sensors, which implies dependency on many variables. The sensitivity analysis presented in this paper is used to weigh the relative importance of each uncertainty contributor into the calibration of a panoramic camera-LiDAR system. Both sensors are used for three-dimensional urban reconstruction. Simulated and experimental tests were conducted. For the simulated tests we analyze and compare the calibration parameters using the Monte Carlo and Latin hypercube sampling techniques. Sensitivity analysis for each variable involved into the calibration was computed by the Sobol method, which is based on the analysis of the variance breakdown, and the Fourier amplitude sensitivity test method, which is based on Fourier's analysis. Sensitivity analysis is an essential tool in simulation modeling and for performing error propagation assessments.

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

PubMed Central

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

2013-01-01

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

From Play to Thoughtful Learning: A Design Strategy to Engage Children with Mathematical Representations

ERIC Educational Resources Information Center

Sedig, Kamran

2008-01-01

Many children do not like learning mathematics. They do not find mathematics fun, motivating, and engaging, and they think it is difficult to learn. Computer-based games have the potential and possibility of addressing this problem. This paper proposes a strategy for designing game-based learning environments that takes advantage of the…

An interdisciplinary collaboration between computer engineering and mathematics/bilingual education to develop a curriculum for underrepresented middle school students

NASA Astrophysics Data System (ADS)

Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel

2013-12-01

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.

Modeling the Cloud to Enhance Capabilities for Crises and Catastrophe Management

DTIC Science & Technology

2016-11-16

order for cloud computing infrastructures to be successfully deployed in real world scenarios as tools for crisis and catastrophe management, where...Statement of the Problem Studied As cloud computing becomes the dominant computational infrastructure[1] and cloud technologies make a transition to hosting...1. Formulate rigorous mathematical models representing technological capabilities and resources in cloud computing for performance modeling and

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

PubMed

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

2018-06-19

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

The Brian Simulator

PubMed Central

Goodman, Dan F. M.; Brette, Romain

2009-01-01

“Brian” is a simulator for spiking neural networks (http://www.briansimulator.org). The focus is on making the writing of simulation code as quick and easy as possible for the user, and on flexibility: new and non-standard models are no more difficult to define than standard ones. This allows scientists to spend more time on the details of their models, and less on their implementation. Neuron models are defined by writing differential equations in standard mathematical notation, facilitating scientific communication. Brian is written in the Python programming language, and uses vector-based computation to allow for efficient simulations. It is particularly useful for neuroscientific modelling at the systems level, and for teaching computational neuroscience. PMID:20011141

Computational technique for stepwise quantitative assessment of equation correctness

NASA Astrophysics Data System (ADS)

Othman, Nuru'l Izzah; Bakar, Zainab Abu

2017-04-01

Many of the computer-aided mathematics assessment systems that are available today possess the capability to implement stepwise correctness checking of a working scheme for solving equations. The computational technique for assessing the correctness of each response in the scheme mainly involves checking the mathematical equivalence and providing qualitative feedback. This paper presents a technique, known as the Stepwise Correctness Checking and Scoring (SCCS) technique that checks the correctness of each equation in terms of structural equivalence and provides quantitative feedback. The technique, which is based on the Multiset framework, adapts certain techniques from textual information retrieval involving tokenization, document modelling and similarity evaluation. The performance of the SCCS technique was tested using worked solutions on solving linear algebraic equations in one variable. 350 working schemes comprising of 1385 responses were collected using a marking engine prototype, which has been developed based on the technique. The results show that both the automated analytical scores and the automated overall scores generated by the marking engine exhibit high percent agreement, high correlation and high degree of agreement with manual scores with small average absolute and mixed errors.

Computer-aided mathematical analysis of probability of intercept for ground-based communication intercept system

NASA Astrophysics Data System (ADS)

Park, Sang Chul

1989-09-01

We develop a mathematical analysis model to calculate the probability of intercept (POI) for the ground-based communication intercept (COMINT) system. The POI is a measure of the effectiveness of the intercept system. We define the POI as the product of the probability of detection and the probability of coincidence. The probability of detection is a measure of the receiver's capability to detect a signal in the presence of noise. The probability of coincidence is the probability that an intercept system is available, actively listening in the proper frequency band, in the right direction and at the same time that the signal is received. We investigate the behavior of the POI with respect to the observation time, the separation distance, antenna elevations, the frequency of the signal, and the receiver bandwidths. We observe that the coincidence characteristic between the receiver scanning parameters and the signal parameters is the key factor to determine the time to obtain a given POI. This model can be used to find the optimal parameter combination to maximize the POI in a given scenario. We expand this model to a multiple system. This analysis is conducted on a personal computer to provide the portability. The model is also flexible and can be easily implemented under different situations.

Study of the stability of a SEIRS model for computer worm propagation

NASA Astrophysics Data System (ADS)

Hernández Guillén, J. D.; Martín del Rey, A.; Hernández Encinas, L.

2017-08-01

Nowadays, malware is the most important threat to information security. In this sense, several mathematical models to simulate malware spreading have appeared. They are compartmental models where the population of devices is classified into different compartments: susceptible, exposed, infectious, recovered, etc. The main goal of this work is to propose an improved SEIRS (Susceptible-Exposed-Infectious-Recovered-Susceptible) mathematical model to simulate computer worm propagation. It is a continuous model whose dynamic is ruled by means of a system of ordinary differential equations. It considers more realistic parameters related to the propagation; in fact, a modified incidence rate has been used. Moreover, the equilibrium points are computed and their local and global stability analyses are studied. From the explicit expression of the basic reproductive number, efficient control measures are also obtained.

The Routine Fitting of Kinetic Data to Models

PubMed Central

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

1962-01-01

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

Minimal time spiking in various ChR2-controlled neuron models.

PubMed

Renault, Vincent; Thieullen, Michèle; Trélat, Emmanuel

2018-02-01

We use conductance based neuron models, and the mathematical modeling of optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals, and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls.

The Computer Student Worksheet Based Mathematical Literacy for Statistics

NASA Astrophysics Data System (ADS)

Manoy, J. T.; Indarasati, N. A.

2018-01-01

The student worksheet is one of media teaching which is able to improve teaching an activity in the classroom. Indicators in mathematical literacy were included in a student worksheet is able to help the students for applying the concept in daily life. Then, the use of computers in learning can create learning with environment-friendly. This research used developmental research which was Thiagarajan (Four-D) development design. There are 4 stages in the Four-D, define, design, develop, and disseminate. However, this research was finish until the third stage, develop stage. The computer student worksheet based mathematical literacy for statistics executed good quality. This student worksheet is achieving the criteria if able to achieve three aspects, validity, practicality, and effectiveness. The subject in this research was the students at The 1st State Senior High School of Driyorejo, Gresik, grade eleven of The 5th Mathematics and Natural Sciences. The computer student worksheet products based mathematical literacy for statistics executed good quality, while it achieved the aspects for validity, practical, and effectiveness. This student worksheet achieved the validity aspects with an average of 3.79 (94.72%), and practical aspects with an average of 2.85 (71.43%). Besides, it achieved the effectiveness aspects with a percentage of the classical complete students of 94.74% and a percentage of the student positive response of 75%.

A rapid radiative transfer model for reflection of solar radiation

NASA Technical Reports Server (NTRS)

Xiang, X.; Smith, E. A.; Justus, C. G.

1994-01-01

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

The Effect of Contextual Pedagogical Advisement and Competition on Middle-School Students' Attitude toward Mathematics and Mathematics Instruction Using a Computer-Based Simulation Game

ERIC Educational Resources Information Center

Van Eck, Richard

2006-01-01

Many students enter mathematics courses with a poor attitude toward mathematics (Gal & Ginsburg, 1994), making attitude as important a consideration as achievement in mathematics (Cognition and Technology Group at Vanderbilt (CTGV), 1992; Marsh, Cairns, Relich, Barnes, & Debus, 1984; Sedighian & Sedighian, 1996). Pedagogical agents are often…

Polyhedral Sculpture: The Path from Computational Artifact to Real-World Mathematical Object.

ERIC Educational Resources Information Center

Eisenberg, Michael; Nishioka, Ann

Mathematics educators often despair at math's austere, "abstract" reputation. This paper describes recent work in developing an application named "HyperGami," which is designed to integrate both the abstract and"real-world" aspects of mathematics by allowing children to design and construct polyhedral models and…

A mathematical model for computer image tracking.

PubMed

Legters, G R; Young, T Y

1982-06-01

A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.

Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

NASA Astrophysics Data System (ADS)

Melezhik, Vladimir S.

2018-02-01

We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.

Agent-Based Modeling in Molecular Systems Biology.

PubMed

Soheilypour, Mohammad; Mofrad, Mohammad R K

2018-07-01

Molecular systems orchestrating the biology of the cell typically involve a complex web of interactions among various components and span a vast range of spatial and temporal scales. Computational methods have advanced our understanding of the behavior of molecular systems by enabling us to test assumptions and hypotheses, explore the effect of different parameters on the outcome, and eventually guide experiments. While several different mathematical and computational methods are developed to study molecular systems at different spatiotemporal scales, there is still a need for methods that bridge the gap between spatially-detailed and computationally-efficient approaches. In this review, we summarize the capabilities of agent-based modeling (ABM) as an emerging molecular systems biology technique that provides researchers with a new tool in exploring the dynamics of molecular systems/pathways in health and disease. © 2018 WILEY Periodicals, Inc.

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

NASA Technical Reports Server (NTRS)

Bekey, G. A.

1971-01-01

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

Computational Toxicology (S)

EPA Science Inventory

The emerging field of computational toxicology applies mathematical and computer models and molecular biological and chemical approaches to explore both qualitative and quantitative relationships between sources of environmental pollutant exposure and adverse health outcomes. Th...

Mathematics, the Computer, and the Impact on Mathematics Education.

ERIC Educational Resources Information Center

Tooke, D. James

2001-01-01

Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

Finite-Element Methods for Real-Time Simulation of Surgery

NASA Technical Reports Server (NTRS)

Basdogan, Cagatay

2003-01-01

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

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

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

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

Discrete mathematics course supported by CAS MATHEMATICA

NASA Astrophysics Data System (ADS)

Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

2017-08-01

In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our approach, we conducted an anonymous survey. The results of the survey provide evidence that our approach contributes to high outcomes and aligns with the course aims and objectives.

Improving the Fraction Word Problem Solving of Students with Mathematics Learning Disabilities: Interactive Computer Application

ERIC Educational Resources Information Center

Shin, Mikyung; Bryant, Diane P.

2017-01-01

Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

Developing a TI-92 Manual Generator Based on Computer Algebra Systems

ERIC Educational Resources Information Center

Jun, Youngcook

2004-01-01

The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…

Water-discharge determinations for the tidal reach of the Willamette River from Ross Island Bridge to Mile 10.3, Portland, Oregon

USGS Publications Warehouse

Dempster, G.R.; Lutz, Gale A.

1968-01-01

Water-discharge, velocity, and slope variations for a 3.7-mile-Iong tidal reach of the Willamette River at Portland, Oreg., were defined from discharge measurements and river stage data collected between July 1962 and January 1965. Observed water discharge during tide-affected flows, during floods, and during backwater from the Columbia River and recorded stages at each end of the river reach were used to determine water discharge from two mathematical models. These models use a finite-difference method to solve the equations of moderately unsteady open-channel streamflow, and discharges are computed by an electronic digital computer. Discharges computed by using the mathematical models compare satisfactorily with observed discharges, except during the period of backwater from the annual flood of the Columbia River. The flow resistance coefficients used in the models vary with discharge; for one model, the coefficients for discharges above 30,000 cfs (cubic feet per second) are 12 and 24 percent less than the coefficient used for discharges below 30,000 cfs. Daily mean discharges were determined by use of one mathematical model for approximately two-thirds of the water year, October 1963 through September 1964. Agreement of computed with routed daily mean discharges is fair; above 30,000 cfs, average differences between the two discharges are about 10 percent, and below 30,000 cfs, computed daily discharges are consistently greater (by as much as 25 percent) than routed discharges. The other model was used to compute discharges for the unusually high flood flows of December 1964.

Using Computational and Mechanical Models to Study Animal Locomotion

PubMed Central

Miller, Laura A.; Goldman, Daniel I.; Hedrick, Tyson L.; Tytell, Eric D.; Wang, Z. Jane; Yen, Jeannette; Alben, Silas

2012-01-01

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.” PMID:22988026

10 CFR 431.197 - Manufacturer's determination of efficiency for distribution transformers.

Code of Federal Regulations, 2010 CFR

2010-01-01

... methods used; the mathematical model, the engineering or statistical analysis, computer simulation or... (b)(3) of this section, or by application of an alternative efficiency determination method (AEDM... section only if: (i) The AEDM has been derived from a mathematical model that represents the electrical...

Characterizing Interaction with Visual Mathematical Representations

ERIC Educational Resources Information Center

Sedig, Kamran; Sumner, Mark

2006-01-01

This paper presents a characterization of computer-based interactions by which learners can explore and investigate visual mathematical representations (VMRs). VMRs (e.g., geometric structures, graphs, and diagrams) refer to graphical representations that visually encode properties and relationships of mathematical structures and concepts.…

The Layer-Oriented Approach to Declarative Languages for Biological Modeling

PubMed Central

Raikov, Ivan; De Schutter, Erik

2012-01-01

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language. PMID:22615554

The layer-oriented approach to declarative languages for biological modeling.

PubMed

Raikov, Ivan; De Schutter, Erik

2012-01-01

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.

A dynamic subgrid scale model for Large Eddy Simulations based on the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric J.; Duraisamy, Karthik

2017-11-01

The development of reduced models for complex multiscale problems remains one of the principal challenges in computational physics. The optimal prediction framework of Chorin et al. [1], which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived reduced models of dynamical systems. Several promising models have emerged from the optimal prediction community and have found application in molecular dynamics and turbulent flows. In this work, a new M-Z-based closure model that addresses some of the deficiencies of existing methods is developed. The model is constructed by exploiting similarities between two levels of coarse-graining via the Germano identity of fluid mechanics and by assuming that memory effects have a finite temporal support. The appeal of the proposed model, which will be referred to as the 'dynamic-MZ-τ' model, is that it is parameter-free and has a structural form imposed by the mathematics of the coarse-graining process (rather than the phenomenological assumptions made by the modeler, such as in classical subgrid scale models). To promote the applicability of M-Z models in general, two procedures are presented to compute the resulting model form, helping to bypass the tedious error-prone algebra that has proven to be a hindrance to the construction of M-Z-based models for complex dynamical systems. While the new formulation is applicable to the solution of general partial differential equations, demonstrations are presented in the context of Large Eddy Simulation closures for the Burgers equation, decaying homogeneous turbulence, and turbulent channel flow. The performance of the model and validity of the underlying assumptions are investigated in detail.

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

DTIC Science & Technology

2011-03-21

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

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Biocellion: accelerating computer simulation of multicellular biological system models

PubMed Central

Kang, Seunghwa; Kahan, Simon; McDermott, Jason; Flann, Nicholas; Shmulevich, Ilya

2014-01-01

Motivation: Biological system behaviors are often the outcome of complex interactions among a large number of cells and their biotic and abiotic environment. Computational biologists attempt to understand, predict and manipulate biological system behavior through mathematical modeling and computer simulation. Discrete agent-based modeling (in combination with high-resolution grids to model the extracellular environment) is a popular approach for building biological system models. However, the computational complexity of this approach forces computational biologists to resort to coarser resolution approaches to simulate large biological systems. High-performance parallel computers have the potential to address the computing challenge, but writing efficient software for parallel computers is difficult and time-consuming. Results: We have developed Biocellion, a high-performance software framework, to solve this computing challenge using parallel computers. To support a wide range of multicellular biological system models, Biocellion asks users to provide their model specifics by filling the function body of pre-defined model routines. Using Biocellion, modelers without parallel computing expertise can efficiently exploit parallel computers with less effort than writing sequential programs from scratch. We simulate cell sorting, microbial patterning and a bacterial system in soil aggregate as case studies. Availability and implementation: Biocellion runs on x86 compatible systems with the 64 bit Linux operating system and is freely available for academic use. Visit http://biocellion.com for additional information. Contact: seunghwa.kang@pnnl.gov PMID:25064572

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

Plechac, Petr

2016-03-01

The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

Early Career Teachers' Ability to Focus on Typical Students Errors in Relation to the Complexity of a Mathematical Topic

ERIC Educational Resources Information Center

Pankow, Lena; Kaiser, Gabriele; Busse, Andreas; König, Johannes; Blömeke, Sigrid; Hoth, Jessica; Döhrmann, Martina

2016-01-01

The paper presents results from a computer-based assessment in which 171 early career mathematics teachers from Germany were asked to anticipate typical student errors on a given mathematical topic and identify them under time constraints. Fast and accurate perception and knowledge-based judgments are widely accepted characteristics of teacher…

Applications of a Sequence of Points in Teaching Linear Algebra, Numerical Methods and Discrete Mathematics

ERIC Educational Resources Information Center

Shi, Yixun

2009-01-01

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

Modeling and simulation in biomedicine.

PubMed Central

Aarts, J.; Möller, D.; van Wijk van Brievingh, R.

1991-01-01

A group of researchers and educators in The Netherlands, Germany and Czechoslovakia have developed and adapted mathematical computer models of phenomena in the field of physiology and biomedicine for use in higher education. The models are graphical and highly interactive, and are all written in TurboPascal or the mathematical simulation language PSI. An educational shell has been developed to launch the models. The shell allows students to interact with the models and teachers to edit the models, to add new models and to monitor the achievements of the students. The models and the shell have been implemented on a MS-DOS personal computer. This paper describes the features of the modeling package and presents the modeling and simulation of the heart muscle as an example. PMID:1807745

Risk Assessment for Toxic Air Pollutants: A Citizen's Guide

MedlinePlus

... from the source(s). Engineers use either monitors or computer models to estimate the amount of pollutant released ... measure how much of the pollutant is present. Computer models use mathematical equations that represent the processes ...

Girls back off mathematics again: the views and experiences of girls in computer-based mathematics

NASA Astrophysics Data System (ADS)

Vale, Colleen

2002-12-01

The views and experiences of girls in two co-educational mathematics classrooms in which computers were regularly used were researched. Data were collected by observation and videotaping of lessons, questionnaire, and interviews of students and the teachers. In this paper case studies of six girls are presented. Their `stories' reveal a diversity of experiences and views and multiple gender identities. High achieving girls persisted as "outsiders within," other girls "backed off", and exceptional girls challenged gender stereotypes. Implications for social justice in mathematics in the age of the super highway are discussed.

[Advancements of computer chemistry in separation of Chinese medicine].

PubMed

Li, Lingjuan; Hong, Hong; Xu, Xuesong; Guo, Liwei

2011-12-01

Separating technique of Chinese medicine is not only a key technique in the field of Chinese medicine' s research and development, but also a significant step in the modernization of Chinese medicinal preparation. Computer chemistry can build model and look for the regulations from Chinese medicine system which is full of complicated data. This paper analyzed the applicability, key technology, basic mode and common algorithm of computer chemistry applied in the separation of Chinese medicine, introduced the mathematic mode and the setting methods of Extraction kinetics, investigated several problems which based on traditional Chinese medicine membrane procession, and forecasted the application prospect.

Module-based multiscale simulation of angiogenesis in skeletal muscle

PubMed Central

2011-01-01

Background Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem. Results We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis. Conclusions This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions. PMID:21463529

Prototype Biology-Based Radiation Risk Module Project

NASA Technical Reports Server (NTRS)

Terrier, Douglas; Clayton, Ronald G.; Patel, Zarana; Hu, Shaowen; Huff, Janice

2015-01-01

Biological effects of space radiation and risk mitigation are strategic knowledge gaps for the Evolvable Mars Campaign. The current epidemiology-based NASA Space Cancer Risk (NSCR) model contains large uncertainties (HAT #6.5a) due to lack of information on the radiobiology of galactic cosmic rays (GCR) and lack of human data. The use of experimental models that most accurately replicate the response of human tissues is critical for precision in risk projections. Our proposed study will compare DNA damage, histological, and cell kinetic parameters after irradiation in normal 2D human cells versus 3D tissue models, and it will use a multi-scale computational model (CHASTE) to investigate various biological processes that may contribute to carcinogenesis, including radiation-induced cellular signaling pathways. This cross-disciplinary work, with biological validation of an evolvable mathematical computational model, will help reduce uncertainties within NSCR and aid risk mitigation for radiation-induced carcinogenesis.

The Effect of a Math Emporium Course Redesign in Developmental and Introductory Mathematics Courses on Student Achievement and Students' Attitudes toward Mathematics at a Two-Year College

ERIC Educational Resources Information Center

Bishop, Amy Renee

2010-01-01

The purpose of this research was to determine the effect of computer-based instruction on student mathematics achievement and students' attitudes toward mathematics in developmental and introductory mathematics courses, namely Elementary Algebra, Intermediate Algebra, and College Algebra, at a community college. The researcher also examined the…

Forecasting runout of rock and debris avalanches

USGS Publications Warehouse

Iverson, Richard M.; Evans, S.G.; Mugnozza, G.S.; Strom, A.; Hermanns, R.L.

2006-01-01

Physically based mathematical models and statistically based empirical equations each may provide useful means of forecasting runout of rock and debris avalanches. This paper compares the foundations, strengths, and limitations of a physically based model and a statistically based forecasting method, both of which were developed to predict runout across three-dimensional topography. The chief advantage of the physically based model results from its ties to physical conservation laws and well-tested axioms of soil and rock mechanics, such as the Coulomb friction rule and effective-stress principle. The output of this model provides detailed information about the dynamics of avalanche runout, at the expense of high demands for accurate input data, numerical computation, and experimental testing. In comparison, the statistical method requires relatively modest computation and no input data except identification of prospective avalanche source areas and a range of postulated avalanche volumes. Like the physically based model, the statistical method yields maps of predicted runout, but it provides no information on runout dynamics. Although the two methods differ significantly in their structure and objectives, insights gained from one method can aid refinement of the other.

A novel model for DNA sequence similarity analysis based on graph theory.

PubMed

Qi, Xingqin; Wu, Qin; Zhang, Yusen; Fuller, Eddie; Zhang, Cun-Quan

2011-01-01

Determination of sequence similarity is one of the major steps in computational phylogenetic studies. As we know, during evolutionary history, not only DNA mutations for individual nucleotide but also subsequent rearrangements occurred. It has been one of major tasks of computational biologists to develop novel mathematical descriptors for similarity analysis such that various mutation phenomena information would be involved simultaneously. In this paper, different from traditional methods (eg, nucleotide frequency, geometric representations) as bases for construction of mathematical descriptors, we construct novel mathematical descriptors based on graph theory. In particular, for each DNA sequence, we will set up a weighted directed graph. The adjacency matrix of the directed graph will be used to induce a representative vector for DNA sequence. This new approach measures similarity based on both ordering and frequency of nucleotides so that much more information is involved. As an application, the method is tested on a set of 0.9-kb mtDNA sequences of twelve different primate species. All output phylogenetic trees with various distance estimations have the same topology, and are generally consistent with the reported results from early studies, which proves the new method's efficiency; we also test the new method on a simulated data set, which shows our new method performs better than traditional global alignment method when subsequent rearrangements happen frequently during evolutionary history.

Modelling the human immunodeficiency virus (HIV) epidemic: A review of the substance and role of models in South Africa

PubMed Central

2018-01-01

We review key mathematical models of the South African human immunodeficiency virus (HIV) epidemic from the early 1990s onwards. In our descriptions, we sometimes differentiate between the concepts of a model world and its mathematical or computational implementation. The model world is the conceptual realm in which we explicitly declare the rules – usually some simplification of ‘real world’ processes as we understand them. Computing details of informative scenarios in these model worlds is a task requiring specialist knowledge, but all other aspects of the modelling process, from describing the model world to identifying the scenarios and interpreting model outputs, should be understandable to anyone with an interest in the epidemic. PMID:29568647

Actually, What Is an Actuary?

ERIC Educational Resources Information Center

Oudshoorn, Susan; Finkelstein, Gary

1991-01-01

The actuarial profession is described to provide secondary school mathematics teachers insights into how actuaries use mathematics in solving real life problems. Examples are provided involving compound interest, the probability of dying, and inflation with computer modeling. (MDH)

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

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

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

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Finite element techniques in computational time series analysis of turbulent flows

NASA Astrophysics Data System (ADS)

Horenko, I.

2009-04-01

In recent years there has been considerable increase of interest in the mathematical modeling and analysis of complex systems that undergo transitions between several phases or regimes. Such systems can be found, e.g., in weather forecast (transitions between weather conditions), climate research (ice and warm ages), computational drug design (conformational transitions) and in econometrics (e.g., transitions between different phases of the market). In all cases, the accumulation of sufficiently detailed time series has led to the formation of huge databases, containing enormous but still undiscovered treasures of information. However, the extraction of essential dynamics and identification of the phases is usually hindered by the multidimensional nature of the signal, i.e., the information is "hidden" in the time series. The standard filtering approaches (like f.~e. wavelets-based spectral methods) have in general unfeasible numerical complexity in high-dimensions, other standard methods (like f.~e. Kalman-filter, MVAR, ARCH/GARCH etc.) impose some strong assumptions about the type of the underlying dynamics. Approach based on optimization of the specially constructed regularized functional (describing the quality of data description in terms of the certain amount of specified models) will be introduced. Based on this approach, several new adaptive mathematical methods for simultaneous EOF/SSA-like data-based dimension reduction and identification of hidden phases in high-dimensional time series will be presented. The methods exploit the topological structure of the analysed data an do not impose severe assumptions on the underlying dynamics. Special emphasis will be done on the mathematical assumptions and numerical cost of the constructed methods. The application of the presented methods will be first demonstrated on a toy example and the results will be compared with the ones obtained by standard approaches. The importance of accounting for the mathematical assumptions used in the analysis will be pointed up in this example. Finally, applications to analysis of meteorological and climate data will be presented.

Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

NASA Technical Reports Server (NTRS)

Hsia, Wei Shen

1989-01-01

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

A model to estimate the relative position of sites for ligands in serum albumins

NASA Astrophysics Data System (ADS)

Motta, Art Adriel Emidio de Araújo; Grassini, Maria Carolina Vilela; Cortez, Célia Martins; Silva, Dilson

2017-11-01

In this work, we present a mathematical-computational model developed to estimate the relative position of ligand binding sites in HSA and BSA, based on the theory of fluorescence quenching, considering the molecular and spectrofluorimetric differences and similarities between these two albumins. Albumin is the largest and the most abundant serum protein in vertebrates. The ability to bind xenobiotics makes albumin important to the bioavailability and effectiveness of drugs.

Development of computer-aided design system of elastic sensitive elements of automatic metering devices

NASA Astrophysics Data System (ADS)

Kalinkina, M. E.; Kozlov, A. S.; Labkovskaia, R. I.; Pirozhnikova, O. I.; Tkalich, V. L.; Shmakov, N. A.

2018-05-01

The object of research is the element base of devices of control and automation systems, including in its composition annular elastic sensitive elements, methods of their modeling, calculation algorithms and software complexes for automation of their design processes. The article is devoted to the development of the computer-aided design system of elastic sensitive elements used in weight- and force-measuring automation devices. Based on the mathematical modeling of deformation processes in a solid, as well as the results of static and dynamic analysis, the calculation of elastic elements is given using the capabilities of modern software systems based on numerical simulation. In the course of the simulation, the model was a divided hexagonal grid of finite elements with a maximum size not exceeding 2.5 mm. The results of modal and dynamic analysis are presented in this article.

Identifying parameter regions for multistationarity

PubMed Central

Conradi, Carsten; Mincheva, Maya; Wiuf, Carsten

2017-01-01

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity. PMID:28972969

Cartographic Modeling: Computer-assisted Analysis of Spatially Defined Neighborhoods

NASA Technical Reports Server (NTRS)

Berry, J. K.; Tomlin, C. D.

1982-01-01

Cartographic models addressing a wide variety of applications are composed of fundamental map processing operations. These primitive operations are neither data base nor application-specific. By organizing the set of operations into a mathematical-like structure, the basis for a generalized cartographic modeling framework can be developed. Among the major classes of primitive operations are those associated with reclassifying map categories, overlaying maps, determining distance and connectivity, and characterizing cartographic neighborhoods. The conceptual framework of cartographic modeling is established and techniques for characterizing neighborhoods are used as a means of demonstrating some of the more sophisticated procedures of computer-assisted map analysis. A cartographic model for assessing effective roundwood supply is briefly described as an example of a computer analysis. Most of the techniques described have been implemented as part of the map analysis package developed at the Yale School of Forestry and Environmental Studies.

Digital computer simulation of inductor-energy-storage dc-to-dc converters with closed-loop regulators

NASA Technical Reports Server (NTRS)

Ohri, A. K.; Owen, H. A.; Wilson, T. G.; Rodriguez, G. E.

1974-01-01

The simulation of converter-controller combinations by means of a flexible digital computer program which produces output to a graphic display is discussed. The procedure is an alternative to mathematical analysis of converter systems. The types of computer programming involved in the simulation are described. Schematic diagrams, state equations, and output equations are displayed for four basic forms of inductor-energy-storage dc to dc converters. Mathematical models are developed to show the relationship of the parameters.

Dynamic regulation of erythropoiesis: A computer model of general applicability

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1979-01-01

A mathematical model for the control of erythropoiesis was developed based on the balance between oxygen supply and demand at a renal oxygen detector which controls erythropoietin release and red cell production. Feedback regulation of tissue oxygen tension is accomplished by adjustments of hemoglobin levels resulting from the output of a renal-bone marrow controller. Special consideration was given to the determinants of tissue oxygenation including evaluation of the influence of blood flow, capillary diffusivity, oxygen uptake and oxygen-hemoglobin affinity. A theoretical analysis of the overall control system is presented. Computer simulations of altitude hypoxia, red cell infusion hyperoxia, and homolytic anemia demonstrate validity of the model for general human application in health and disease.

Numerical Simulations of Plasma Based Flow Control Applications

NASA Technical Reports Server (NTRS)

Suzen, Y. B.; Huang, P. G.; Jacob, J. D.; Ashpis, D. E.

2005-01-01

A mathematical model was developed to simulate flow control applications using plasma actuators. The effects of the plasma actuators on the external flow are incorporated into Navier Stokes computations as a body force vector. In order to compute this body force vector, the model solves two additional equations: one for the electric field due to the applied AC voltage at the electrodes and the other for the charge density representing the ionized air. The model is calibrated against an experiment having plasma-driven flow in a quiescent environment and is then applied to simulate a low pressure turbine flow with large flow separation. The effects of the plasma actuator on control of flow separation are demonstrated numerically.

Rapid Design and Testing of Novel Gas/liquid Contacting Devices for Post-Combustion CO 2 Capture via 3D Printing - Phase II Final Technical Report

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

Panaccione, Charles; Staab, Greg; Meuleman, Erik

ION has developed a mathematically driven model for a contacting device incorporating mass transfer, heat transfer, and computational fluid dynamics. This model is based upon a parametric structure for purposes of future commercialization. The most promising design from modeling was 3D printed and tested in a bench scale CO 2 capture unit and compared to commercially available structured packing tested in the same unit.

Optimized planning methodologies of ASON implementation

NASA Astrophysics Data System (ADS)

Zhou, Michael M.; Tamil, Lakshman S.

2005-02-01

Advanced network planning concerns effective network-resource allocation for dynamic and open business environment. Planning methodologies of ASON implementation based on qualitative analysis and mathematical modeling are presented in this paper. The methodology includes method of rationalizing technology and architecture, building network and nodal models, and developing dynamic programming for multi-period deployment. The multi-layered nodal architecture proposed here can accommodate various nodal configurations for a multi-plane optical network and the network modeling presented here computes the required network elements for optimizing resource allocation.

Computer-Generated Feedback on Student Writing

ERIC Educational Resources Information Center

Ware, Paige

2011-01-01

A distinction must be made between "computer-generated scoring" and "computer-generated feedback". Computer-generated scoring refers to the provision of automated scores derived from mathematical models built on organizational, syntactic, and mechanical aspects of writing. In contrast, computer-generated feedback, the focus of this article, refers…

An optimization model for metabolic pathways.

PubMed

Planes, F J; Beasley, J E

2009-10-15

Different mathematical methods have emerged in the post-genomic era to determine metabolic pathways. These methods can be divided into stoichiometric methods and path finding methods. In this paper we detail a novel optimization model, based upon integer linear programming, to determine metabolic pathways. Our model links reaction stoichiometry with path finding in a single approach. We test the ability of our model to determine 40 annotated Escherichia coli metabolic pathways. We show that our model is able to determine 36 of these 40 pathways in a computationally effective manner.

13C-based metabolic flux analysis: fundamentals and practice.

PubMed

Yang, Tae Hoon

2013-01-01

Isotope-based metabolic flux analysis is one of the emerging technologies applied to system level metabolic phenotype characterization in metabolic engineering. Among the developed approaches, (13)C-based metabolic flux analysis has been established as a standard tool and has been widely applied to quantitative pathway characterization of diverse biological systems. To implement (13)C-based metabolic flux analysis in practice, comprehending the underlying mathematical and computational modeling fundamentals is of importance along with carefully conducted experiments and analytical measurements. Such knowledge is also crucial when designing (13)C-labeling experiments and properly acquiring key data sets essential for in vivo flux analysis implementation. In this regard, the modeling fundamentals of (13)C-labeling systems and analytical data processing are the main topics we will deal with in this chapter. Along with this, the relevant numerical optimization techniques are addressed to help implementation of the entire computational procedures aiming at (13)C-based metabolic flux analysis in vivo.

Software Validation via Model Animation

NASA Technical Reports Server (NTRS)

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

2015-01-01

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

REVEAL: An Extensible Reduced Order Model Builder for Simulation and Modeling

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

Agarwal, Khushbu; Sharma, Poorva; Ma, Jinliang

2013-04-30

Many science domains need to build computationally efficient and accurate representations of high fidelity, computationally expensive simulations. These computationally efficient versions are known as reduced-order models. This paper presents the design and implementation of a novel reduced-order model (ROM) builder, the REVEAL toolset. This toolset generates ROMs based on science- and engineering-domain specific simulations executed on high performance computing (HPC) platforms. The toolset encompasses a range of sampling and regression methods that can be used to generate a ROM, automatically quantifies the ROM accuracy, and provides support for an iterative approach to improve ROM accuracy. REVEAL is designed to bemore » extensible in order to utilize the core functionality with any simulator that has published input and output formats. It also defines programmatic interfaces to include new sampling and regression techniques so that users can ‘mix and match’ mathematical techniques to best suit the characteristics of their model. In this paper, we describe the architecture of REVEAL and demonstrate its usage with a computational fluid dynamics model used in carbon capture.« less

Mathematical modeling of spinning elastic bodies for modal analysis.

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.; Baddeley, V.

1973-01-01

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Research and the Personal Computer.

ERIC Educational Resources Information Center

Blackburn, D. A.

1989-01-01

Discussed is the history and elements of the personal computer. Its uses as a laboratory assistant and generic toolkit for mathematical analysis and modeling are included. The future of the personal computer in research is addressed. (KR)

An Evaluation into the Views of Candidate Mathematics Teachers over "Tablet Computers" to be Applied in Secondary Schools

ERIC Educational Resources Information Center

Aksu, Hasan Hüseyin

2014-01-01

This study aims to investigate, in terms of different variables, the views of prospective Mathematics teachers on tablet computers to be used in schools as an outcome of the Fatih Project, which was initiated by the Ministry of National Education. In the study, scanning model, one of the quantitative research methods, was used. In the population…

Efficient simulation and model reformulation of two-dimensional electrochemical thermal behavior of lithium-ion batteries

DOE PAGES

Northrop, Paul W. C.; Pathak, Manan; Rife, Derek; ...

2015-03-09

Lithium-ion batteries are an important technology to facilitate efficient energy storage and enable a shift from petroleum based energy to more environmentally benign sources. Such systems can be utilized most efficiently if good understanding of performance can be achieved for a range of operating conditions. Mathematical models can be useful to predict battery behavior to allow for optimization of design and control. An analytical solution is ideally preferred to solve the equations of a mathematical model, as it eliminates the error that arises when using numerical techniques and is usually computationally cheap. An analytical solution provides insight into the behaviormore » of the system and also explicitly shows the effects of different parameters on the behavior. However, most engineering models, including the majority of battery models, cannot be solved analytically due to non-linearities in the equations and state dependent transport and kinetic parameters. The numerical method used to solve the system of equations describing a battery operation can have a significant impact on the computational cost of the simulation. In this paper, a model reformulation of the porous electrode pseudo three dimensional (P3D) which significantly reduces the computational cost of lithium ion battery simulation, while maintaining high accuracy, is discussed. This reformulation enables the use of the P3D model into applications that would otherwise be too computationally expensive to justify its use, such as online control, optimization, and parameter estimation. Furthermore, the P3D model has proven to be robust enough to allow for the inclusion of additional physical phenomena as understanding improves. In this study, the reformulated model is used to allow for more complicated physical phenomena to be considered for study, including thermal effects.« less

Assessment of Situated Learning Using Computer Environments.

ERIC Educational Resources Information Center

Young, Michael

1995-01-01

Suggests that, based on a theory of situated learning, assessment must emphasize process as much as product. Several assessment examples are given, including a computer-based planning assistant for a mathematics and science video, suggestions for computer-based portfolio assessment, and speculations about embedded assessment of virtual situations.…

A Pilot Meta-Analysis of Computer-Based Scaffolding in STEM Education

ERIC Educational Resources Information Center

Belland, Brian R.; Walker, Andrew E.; Olsen, Megan Whitney; Leary, Heather

2015-01-01

This paper employs meta-analysis to determine the influence of computer-based scaffolding characteristics and study and test score quality on cognitive outcomes in science, technology, engineering, and mathematics education at the secondary, college, graduate, and adult levels. Results indicate that (a) computer-based scaffolding positively…

Structural Stability of Mathematical Models of National Economy

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar A.; Sultanov, Bahyt T.; Borovskiy, Yuriy V.; Adilov, Zheksenbek M.; Ashimov, Askar A.

2011-12-01

In the paper we test robustness of particular dynamic systems in a compact regions of a plane and a weak structural stability of one dynamic system of high order in a compact region of its phase space. The test was carried out based on the fundamental theory of dynamical systems on a plane and based on the conditions for weak structural stability of high order dynamic systems. A numerical algorithm for testing the weak structural stability of high order dynamic systems has been proposed. Based on this algorithm we assess the weak structural stability of one computable general equilibrium model.

Mathematical analysis of frontal affinity chromatography in particle and membrane configurations.

PubMed

Tejeda-Mansir, A; Montesinos, R M; Guzmán, R

2001-10-30

The scaleup and optimization of large-scale affinity-chromatographic operations in the recovery, separation and purification of biochemical components is of major industrial importance. The development of mathematical models to describe affinity-chromatographic processes, and the use of these models in computer programs to predict column performance is an engineering approach that can help to attain these bioprocess engineering tasks successfully. Most affinity-chromatographic separations are operated in the frontal mode, using fixed-bed columns. Purely diffusive and perfusion particles and membrane-based affinity chromatography are among the main commercially available technologies for these separations. For a particular application, a basic understanding of the main similarities and differences between particle and membrane frontal affinity chromatography and how these characteristics are reflected in the transport models is of fundamental relevance. This review presents the basic theoretical considerations used in the development of particle and membrane affinity chromatography models that can be applied in the design and operation of large-scale affinity separations in fixed-bed columns. A transport model for column affinity chromatography that considers column dispersion, particle internal convection, external film resistance, finite kinetic rate, plus macropore and micropore resistances is analyzed as a framework for exploring further the mathematical analysis. Such models provide a general realistic description of almost all practical systems. Specific mathematical models that take into account geometric considerations and transport effects have been developed for both particle and membrane affinity chromatography systems. Some of the most common simplified models, based on linear driving-force (LDF) and equilibrium assumptions, are emphasized. Analytical solutions of the corresponding simplified dimensionless affinity models are presented. Particular methods for estimating the parameters that characterize the mass-transfer and adsorption mechanisms in affinity systems are described.

Monitoring temperatures in coal conversion and combustion processes via ultrasound

NASA Astrophysics Data System (ADS)

Gopalsami, N.; Raptis, A. C.; Mulcahey, T. P.

1980-02-01

The state of the art of instrumentation for monitoring temperatures in coal conversion and combustion systems is examined. The instrumentation types studied include thermocouples, radiation pyrometers, and acoustical thermometers. The capabilities and limitations of each type are reviewed. A feasibility study of the ultrasonic thermometry is described. A mathematical model of a pulse-echo ultrasonic temperature measurement system is developed using linear system theory. The mathematical model lends itself to the adaptation of generalized correlation techniques for the estimation of propagation delays. Computer simulations are made to test the efficacy of the signal processing techniques for noise-free as well as noisy signals. Based on the theoretical study, acoustic techniques to measure temperature in reactors and combustors are feasible.

The intrinsic combinatorial organization and information theoretic content of a sequence are correlated to the DNA encoded nucleosome organization of eukaryotic genomes.

PubMed

Utro, Filippo; Di Benedetto, Valeria; Corona, Davide F V; Giancarlo, Raffaele

2016-03-15

Thanks to research spanning nearly 30 years, two major models have emerged that account for nucleosome organization in chromatin: statistical and sequence specific. The first is based on elegant, easy to compute, closed-form mathematical formulas that make no assumptions of the physical and chemical properties of the underlying DNA sequence. Moreover, they need no training on the data for their computation. The latter is based on some sequence regularities but, as opposed to the statistical model, it lacks the same type of closed-form formulas that, in this case, should be based on the DNA sequence only. We contribute to close this important methodological gap between the two models by providing three very simple formulas for the sequence specific one. They are all based on well-known formulas in Computer Science and Bioinformatics, and they give different quantifications of how complex a sequence is. In view of how remarkably well they perform, it is very surprising that measures of sequence complexity have not even been considered as candidates to close the mentioned gap. We provide experimental evidence that the intrinsic level of combinatorial organization and information-theoretic content of subsequences within a genome are strongly correlated to the level of DNA encoded nucleosome organization discovered by Kaplan et al Our results establish an important connection between the intrinsic complexity of subsequences in a genome and the intrinsic, i.e. DNA encoded, nucleosome organization of eukaryotic genomes. It is a first step towards a mathematical characterization of this latter 'encoding'. Supplementary data are available at Bioinformatics online. futro@us.ibm.com. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Program listing for the REEDM (Rocket Exhaust Effluent Diffusion Model) computer program

NASA Technical Reports Server (NTRS)

Bjorklund, J. R.; Dumbauld, R. K.; Cheney, C. S.; Geary, H. V.

1982-01-01

The program listing for the REEDM Computer Program is provided. A mathematical description of the atmospheric dispersion models, cloud-rise models, and other formulas used in the REEDM model; vehicle and source parameters, other pertinent physical properties of the rocket exhaust cloud and meteorological layering techniques; user's instructions for the REEDM computer program; and worked example problems are contained in NASA CR-3646.

Longitudinal associations between reading and mathematics achievement.

PubMed

Grimm, Kevin J

2008-01-01

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

Placental Volumetry by 2-D Sonography with a New Mathematical Formula: Prospective Study on the Shell of a Spherical Sector Model.

PubMed

Kozinszky, Zoltan; Surányi, Andrea; Péics, Hajnalka; Molnár, András; Pál, Attila

2015-08-01

The aim of this study was to determine the utility of a new mathematical model in volumetric assessment of the placenta using 2-D ultrasound. Placental volumetry was performed in a prospective cross-sectional survey by virtual organ computer-aided analysis (VOCAL) with the help of a shell-off method in 346 uncomplicated pregnancies according to STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) guidelines. Furthermore, placental thickness, length and height were measured with the 2-D technique to estimate placental volume based on the mathematical formula for the volume of "the shell of the spherical sector." Fetal size was also assessed by 2-D sonography. The placental volumes measured by 2-D and 3-D techniques had a correlation of 0.86. In the first trimester, the correlation was 0.82, and later during pregnancy, it was 0.86. Placental volumetry using "the circle-shaped shell of the spherical sector" mathematical model with 2-D ultrasound technique may be introduced into everyday practice to screen for placental volume deviations associated with adverse pregnancy outcome. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

A Mathematical Model of the Great Solar Eclipse of 1991.

ERIC Educational Resources Information Center

Lamb, John Jr.

1991-01-01

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

Hybrid computational phantoms of the male and female newborn patient: NURBS-based whole-body models

NASA Astrophysics Data System (ADS)

Lee, Choonsik; Lodwick, Daniel; Hasenauer, Deanna; Williams, Jonathan L.; Lee, Choonik; Bolch, Wesley E.

2007-07-01

Anthropomorphic computational phantoms are computer models of the human body for use in the evaluation of dose distributions resulting from either internal or external radiation sources. Currently, two classes of computational phantoms have been developed and widely utilized for organ dose assessment: (1) stylized phantoms and (2) voxel phantoms which describe the human anatomy via mathematical surface equations or 3D voxel matrices, respectively. Although stylized phantoms based on mathematical equations can be very flexible in regard to making changes in organ position and geometrical shape, they are limited in their ability to fully capture the anatomic complexities of human internal anatomy. In turn, voxel phantoms have been developed through image-based segmentation and correspondingly provide much better anatomical realism in comparison to simpler stylized phantoms. However, they themselves are limited in defining organs presented in low contrast within either magnetic resonance or computed tomography images—the two major sources in voxel phantom construction. By definition, voxel phantoms are typically constructed via segmentation of transaxial images, and thus while fine anatomic features are seen in this viewing plane, slice-to-slice discontinuities become apparent in viewing the anatomy of voxel phantoms in the sagittal or coronal planes. This study introduces the concept of a hybrid computational newborn phantom that takes full advantage of the best features of both its stylized and voxel counterparts: flexibility in phantom alterations and anatomic realism. Non-uniform rational B-spline (NURBS) surfaces, a mathematical modeling tool traditionally applied to graphical animation studies, was adopted to replace the limited mathematical surface equations of stylized phantoms. A previously developed whole-body voxel phantom of the newborn female was utilized as a realistic anatomical framework for hybrid phantom construction. The construction of a hybrid phantom is performed in three steps: polygonization of the voxel phantom, organ modeling via NURBS surfaces and phantom voxelization. Two 3D graphic tools, 3D-DOCTOR™ and Rhinoceros™, were utilized to polygonize the newborn voxel phantom and generate NURBS surfaces, while an in-house MATLAB™ code was used to voxelize the resulting NURBS model into a final computational phantom ready for use in Monte Carlo radiation transport calculations. A total of 126 anatomical organ and tissue models, including 38 skeletal sites and 31 cartilage sites, were described within the hybrid phantom using either NURBS or polygon surfaces. A male hybrid newborn phantom was constructed following the development of the female phantom through the replacement of female-specific organs with male-specific organs. The outer body contour and internal anatomy of the NURBS-based phantoms were adjusted to match anthropometric and reference newborn data reported by the International Commission on Radiological Protection in their Publication 89. The voxelization process was designed to accurately convert NURBS models to a voxel phantom with minimum volumetric change. A sensitivity study was additionally performed to better understand how the meshing tolerance and voxel resolution would affect volumetric changes between the hybrid-NURBS and hybrid-voxel phantoms. The male and female hybrid-NURBS phantoms were constructed in a manner so that all internal organs approached their ICRP reference masses to within 1%, with the exception of the skin (-6.5% relative error) and brain (-15.4% relative error). Both hybrid-voxel phantoms were constructed with an isotropic voxel resolution of 0.663 mm—equivalent to the ICRP 89 reference thickness of the newborn skin (dermis and epidermis). Hybrid-NURBS phantoms used to create their voxel counterpart retain the non-uniform scalability of stylized phantoms, while maintaining the anatomic realism of segmented voxel phantoms with respect to organ shape, depth and inter-organ positioning. This work was supported by the National Cancer Institute.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Multiscale Mathematical Modeling in Dental Tissue Engineering: Toward Computer-Aided Design of a Regenerative System Based on Hydroxyapatite Granules, Focussing on Early and Mid-Term Stiffness Recovery

PubMed Central

Scheiner, Stefan; Komlev, Vladimir S.; Gurin, Alexey N.; Hellmich, Christian

2016-01-01

We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall conglomerate-type scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions. In this context, the question arises how the compound stiffness is driven by the key design parameters of the tissue engineering system: macroporosity, crack density, as well as scaffold resorption/bone formation rates. We here tackle this question by combining the latest state-of-the-art mathematical modeling techniques in the field of multiscale micromechanics, into an unprecedented suite of highly efficient, semi-analytically defined computation steps resolving several levels of hierarchical organization, from the millimeter- down to the nanometer-scale. This includes several types of homogenization schemes, namely such for porous polycrystals with elongated solid elements, for cracked matrix-inclusion composites, as well as for assemblies of coated spherical compounds. Together with the experimentally known stiffnesses of hydroxyapatite crystals and mandibular bone tissue, the new mathematical model suggests that early stiffness recovery (i.e., within several weeks) requires total avoidance of microcracks in the hydroxyapatite scaffolds, while mid-term stiffness recovery (i.e., within several months) is additionally promoted by provision of small granule sizes, in combination with high bone formation and low scaffold resorption rates. PMID:27708584

Condor-COPASI: high-throughput computing for biochemical networks

PubMed Central

2012-01-01

Background Mathematical modelling has become a standard technique to improve our understanding of complex biological systems. As models become larger and more complex, simulations and analyses require increasing amounts of computational power. Clusters of computers in a high-throughput computing environment can help to provide the resources required for computationally expensive model analysis. However, exploiting such a system can be difficult for users without the necessary expertise. Results We present Condor-COPASI, a server-based software tool that integrates COPASI, a biological pathway simulation tool, with Condor, a high-throughput computing environment. Condor-COPASI provides a web-based interface, which makes it extremely easy for a user to run a number of model simulation and analysis tasks in parallel. Tasks are transparently split into smaller parts, and submitted for execution on a Condor pool. Result output is presented to the user in a number of formats, including tables and interactive graphical displays. Conclusions Condor-COPASI can effectively use a Condor high-throughput computing environment to provide significant gains in performance for a number of model simulation and analysis tasks. Condor-COPASI is free, open source software, released under the Artistic License 2.0, and is suitable for use by any institution with access to a Condor pool. Source code is freely available for download at http://code.google.com/p/condor-copasi/, along with full instructions on deployment and usage. PMID:22834945

Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future

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

Brown, D L; Bell, J; Estep, D

2008-02-15

Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as themore » high-performance computers on which these codes run. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception. Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those that involve the energy, environmental and national security needs of the country. As the capability of high-performance computers continues to increase, the types of questions that can be answered by applying this huge computational power become more varied and more complex. It will be essential that we find new ways to develop and apply the mathematics necessary to enable the new scientific and engineering discoveries that are needed. In August 2007, a panel of experts in applied, computational and statistical mathematics met for a day and a half in Berkeley, California to understand the mathematical developments required to meet the future science and engineering needs of the DOE. It is important to emphasize that the panelists were not asked to speculate only on advances that might be made in their own research specialties. Instead, the guidance this panel was given was to consider the broad science and engineering challenges that the DOE faces and identify the corresponding advances that must occur across the field of mathematics for these challenges to be successfully addressed. As preparation for the meeting, each panelist was asked to review strategic planning and other informational documents available for one or more of the DOE Program Offices, including the Offices of Science, Nuclear Energy, Fossil Energy, Environmental Management, Legacy Management, Energy Efficiency & Renewable Energy, Electricity Delivery & Energy Reliability and Civilian Radioactive Waste Management as well as the National Nuclear Security Administration. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: (1) Can we predict the operating characteristics of a clean coal power plant? (2) How stable is the plasma containment in a tokamak? (3) How quickly is climate change occurring and what are the uncertainties in the predicted time scales? (4) How quickly can an introduced bio-weapon contaminate the agricultural environment in the US? (5) How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types? (6) How quickly can the United States recover if part of the power grid became inoperable? (7) What are optimal locations and communication protocols for sensing devices in a remote-sensing network? (8) How can new materials be designed with a specified desirable set of properties? In comparing and contrasting these and other questions of importance to DOE, the panel found that while the scientific breadth of the requirements is enormous, a central theme emerges: Scientists are being asked to identify or provide technology, or to give expert analysis to inform policy-makers that requires the scientific understanding of increasingly complex physical and engineered systems. In addition, as the complexity of the systems of interest increases, neither experimental observation nor mathematical and computational modeling alone can access all components of the system over the entire range of scales or conditions needed to provide the required scientific understanding.« less

A combinatorial model of malware diffusion via bluetooth connections.

PubMed

Merler, Stefano; Jurman, Giuseppe

2013-01-01

We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression.

A systemic approach for modeling biological evolution using Parallel DEVS.

PubMed

Heredia, Daniel; Sanz, Victorino; Urquia, Alfonso; Sandín, Máximo

2015-08-01

A new model for studying the evolution of living organisms is proposed in this manuscript. The proposed model is based on a non-neodarwinian systemic approach. The model is focused on considering several controversies and open discussions about modern evolutionary biology. Additionally, a simplification of the proposed model, named EvoDEVS, has been mathematically described using the Parallel DEVS formalism and implemented as a computer program using the DEVSLib Modelica library. EvoDEVS serves as an experimental platform to study different conditions and scenarios by means of computer simulations. Two preliminary case studies are presented to illustrate the behavior of the model and validate its results. EvoDEVS is freely available at http://www.euclides.dia.uned.es. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Oliveira, Nuno M.C.

2015-01-01

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D–, A– and E–optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D–optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice. PMID:26949279

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C

2016-02-15

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D -, A - and E -optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D -optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

Computer-aided light sheet flow visualization using photogrammetry

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1994-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and a visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) results, was chosen to interactively display the reconstructed light sheet images with the numerical surface geometry for the model or aircraft under study. The photogrammetric reconstruction technique and the image processing and computer graphics techniques and equipment are described. Results of the computer-aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images with CFD solutions in the same graphics environment is also demonstrated.

Computer-Aided Light Sheet Flow Visualization

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1993-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Computer-aided light sheet flow visualization

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1993-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

An investigation of constraint-based component-modeling for knowledge representation in computer-aided conceptual design

NASA Technical Reports Server (NTRS)

Kolb, Mark A.

1990-01-01

Originally, computer programs for engineering design focused on detailed geometric design. Later, computer programs for algorithmically performing the preliminary design of specific well-defined classes of objects became commonplace. However, due to the need for extreme flexibility, it appears unlikely that conventional programming techniques will prove fruitful in developing computer aids for engineering conceptual design. The use of symbolic processing techniques, such as object-oriented programming and constraint propagation, facilitate such flexibility. Object-oriented programming allows programs to be organized around the objects and behavior to be simulated, rather than around fixed sequences of function- and subroutine-calls. Constraint propagation allows declarative statements to be understood as designating multi-directional mathematical relationships among all the variables of an equation, rather than as unidirectional assignments to the variable on the left-hand side of the equation, as in conventional computer programs. The research has concentrated on applying these two techniques to the development of a general-purpose computer aid for engineering conceptual design. Object-oriented programming techniques are utilized to implement a user-extensible database of design components. The mathematical relationships which model both geometry and physics of these components are managed via constraint propagation. In addition, to this component-based hierarchy, special-purpose data structures are provided for describing component interactions and supporting state-dependent parameters. In order to investigate the utility of this approach, a number of sample design problems from the field of aerospace engineering were implemented using the prototype design tool, Rubber Airplane. The additional level of organizational structure obtained by representing design knowledge in terms of components is observed to provide greater convenience to the program user, and to result in a database of engineering information which is easier both to maintain and to extend.

Automatic Reconstruction of Spacecraft 3D Shape from Imagery

NASA Astrophysics Data System (ADS)

Poelman, C.; Radtke, R.; Voorhees, H.

We describe a system that computes the three-dimensional (3D) shape of a spacecraft from a sequence of uncalibrated, two-dimensional images. While the mathematics of multi-view geometry is well understood, building a system that accurately recovers 3D shape from real imagery remains an art. A novel aspect of our approach is the combination of algorithms from computer vision, photogrammetry, and computer graphics. We demonstrate our system by computing spacecraft models from imagery taken by the Air Force Research Laboratory's XSS-10 satellite and DARPA's Orbital Express satellite. Using feature tie points (each identified in two or more images), we compute the relative motion of each frame and the 3D location of each feature using iterative linear factorization followed by non-linear bundle adjustment. The "point cloud" that results from this traditional shape-from-motion approach is typically too sparse to generate a detailed 3D model. Therefore, we use the computed motion solution as input to a volumetric silhouette-carving algorithm, which constructs a solid 3D model based on viewpoint consistency with the image frames. The resulting voxel model is then converted to a facet-based surface representation and is texture-mapped, yielding realistic images from arbitrary viewpoints. We also illustrate other applications of the algorithm, including 3D mensuration and stereoscopic 3D movie generation.

Computer simulation of the activity of the elderly person living independently in a Health Smart Home.

PubMed

Noury, N; Hadidi, T

2012-12-01

We propose a simulator of human activities collected with presence sensors in our experimental Health Smart Home "Habitat Intelligent pour la Sante (HIS)". We recorded 1492 days of data on several experimental HIS during the French national project "AILISA". On these real data, we built a mathematical model of the behavior of the data series, based on "Hidden Markov Models" (HMM). The model is then played on a computer to produce simulated data series with added flexibility to adjust the parameters in various scenarios. We also tested several methods to measure the similarity between our real and simulated data. Our simulator can produce large data base which can be further used to evaluate the algorithms to raise an alarm in case of loss in autonomy. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Integration of a CAS/DGS as a CAD System in the Mathematics Curriculum for Architecture Students

ERIC Educational Resources Information Center

Falcon, R. M.

2011-01-01

Students of Architecture and Building Engineering Degrees work with Computer Aided Design systems daily in order to design and model architectonic constructions. Since this kind of software is based on the creation and transformation of geometrical objects, it seems to be a useful tool in Maths classes in order to capture the attention of the…

SDI Software Technology Program Plan Version 1.5

DTIC Science & Technology

1987-06-01

computer generation of auditory communication of meaningful speech. Most speech synthesizers are based on mathematical models of the human vocal tract, but...oral/ auditory and multimodal communications. Although such state-of-the-art interaction technology has not fully matured, user experience has...superior I pattern matching capabilities and the subliminal intuitive deduction capability. The error performance of humans can be helped by careful

Laboratories for Teaching of Mathematical Subjects

ERIC Educational Resources Information Center

Berežný, Štefan

2017-01-01

We have adapted our two laboratories at our department based on our research results, which were presented at the conference CADGME 2014 in Halle and published in the journal. In this article we describe the hardware and software structure of the Laboratory 1: LabIT4KT-1: Laboratory of Computer Modelling and the Laboratory 2: LabIT4KT-2:…

Proposed standards for peer-reviewed publication of computer code

USDA-ARS?s Scientific Manuscript database

Computer simulation models are mathematical abstractions of physical systems. In the area of natural resources and agriculture, these physical systems encompass selected interacting processes in plants, soils, animals, or watersheds. These models are scientific products and have become important i...

CFD Analysis of the SBXC Glider Airframe

DTIC Science & Technology

2016-06-01

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

Computational Toxicology at the US EPA

EPA Science Inventory

Computational toxicology is the application of mathematical and computer models to help assess chemical hazards and risks to human health and the environment. Supported by advances in informatics, high-throughput screening (HTS) technologies, and systems biology, EPA is developin...

Facilitating mathematics learning for students with upper extremity disabilities using touch-input system.

PubMed

Choi, Kup-Sze; Chan, Tak-Yin

2015-03-01

To investigate the feasibility of using tablet device as user interface for students with upper extremity disabilities to input mathematics efficiently into computer. A touch-input system using tablet device as user interface was proposed to assist these students to write mathematics. User-switchable and context-specific keyboard layouts were designed to streamline the input process. The system could be integrated with conventional computer systems only with minor software setup. A two-week pre-post test study involving five participants was conducted to evaluate the performance of the system and collect user feedback. The mathematics input efficiency of the participants was found to improve during the experiment sessions. In particular, their performance in entering trigonometric expressions by using the touch-input system was significantly better than that by using conventional mathematics editing software with keyboard and mouse. The participants rated the touch-input system positively and were confident that they could operate at ease with more practice. The proposed touch-input system provides a convenient way for the students with hand impairment to write mathematics and has the potential to facilitate their mathematics learning. Implications for Rehabilitation Students with upper extremity disabilities often face barriers to learning mathematics which is largely based on handwriting. Conventional computer user interfaces are inefficient for them to input mathematics into computer. A touch-input system with context-specific and user-switchable keyboard layouts was designed to improve the efficiency of mathematics input. Experimental results and user feedback suggested that the system has the potential to facilitate mathematics learning for the students.

Students, Computers and Mathematics the Golden Trilogy in the Teaching-Learning Process

ERIC Educational Resources Information Center

García-Santillán, Arturo; Escalera-Chávez, Milka Elena; López-Morales, José Satsumi; Córdova Rangel, Arturo

2014-01-01

In this paper we examine the relationships between students' attitudes towards mathematics and technology, therefore, we take a Galbraith and Hines' scale (1998, 2000) about mathematics confidence, computer confidence, computer and mathematics interaction, mathematics motivation, computer motivation, and mathematics engagement. 164 questionnaires…

Effects of Virtual Manipulatives with Different Approaches on Students' Knowledge of Slope

ERIC Educational Resources Information Center

Demir, Mustafa

2018-01-01

Virtual Manipulatives (VMs) are computer-based, dynamic, and visual representations of mathematical concepts, provide interactive learning environments to advance mathematics instruction (Moyer et al., 2002). Despite their broad use, few research explored the integration of VMs into mathematics instruction (Moyer-Packenham & Westenskow, 2013).…

Using E-Exercise Bases in Mathematics: Case Studies at University

ERIC Educational Resources Information Center

Cazes, Claire; Gueudet, Ghislaine; Hersant, Magali; Vandebrouck, Fabrice

2006-01-01

E-Exercise Bases (EEB) are now used in the teaching of mathematics, especially at university. We discuss here the consequences of their use on the students' activity during computer lab sessions. Results stem from observations of several teaching designs organised in different French universities with three e-exercise bases. The analysis focuses…

The art of fault-tolerant system reliability modeling

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Johnson, Sally C.

1990-01-01

A step-by-step tutorial of the methods and tools used for the reliability analysis of fault-tolerant systems is presented. Emphasis is on the representation of architectural features in mathematical models. Details of the mathematical solution of complex reliability models are not presented. Instead the use of several recently developed computer programs--SURE, ASSIST, STEM, PAWS--which automate the generation and solution of these models is described.

PREDICTING ATTENUATION OF VIRUSES DURING PERCOLATION IN SOILS: 2. USER'S GUIDE TO THE VIRULO 1.0 COMPUTER MODEL

EPA Science Inventory

In the EPA document Predicting Attenuation of Viruses During Percolation in Soils 1. Probabilistic Model the conceptual, theoretical, and mathematical foundations for a predictive screening model were presented. In this current volume we present a User's Guide for the computer mo...

A Combinatorial Model of Malware Diffusion via Bluetooth Connections

PubMed Central

Merler, Stefano; Jurman, Giuseppe

2013-01-01

We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression. PMID:23555677

Building polyhedra by self-assembly: theory and experiment.

PubMed

Kaplan, Ryan; Klobušický, Joseph; Pandey, Shivendra; Gracias, David H; Menon, Govind

2014-01-01

We investigate the utility of a mathematical framework based on discrete geometry to model biological and synthetic self-assembly. Our primary biological example is the self-assembly of icosahedral viruses; our synthetic example is surface-tension-driven self-folding polyhedra. In both instances, the process of self-assembly is modeled by decomposing the polyhedron into a set of partially formed intermediate states. The set of all intermediates is called the configuration space, pathways of assembly are modeled as paths in the configuration space, and the kinetics and yield of assembly are modeled by rate equations, Markov chains, or cost functions on the configuration space. We review an interesting interplay between biological function and mathematical structure in viruses in light of this framework. We discuss in particular: (i) tiling theory as a coarse-grained description of all-atom models; (ii) the building game-a growth model for the formation of polyhedra; and (iii) the application of these models to the self-assembly of the bacteriophage MS2. We then use a similar framework to model self-folding polyhedra. We use a discrete folding algorithm to compute a configuration space that idealizes surface-tension-driven self-folding and analyze pathways of assembly and dominant intermediates. These computations are then compared with experimental observations of a self-folding dodecahedron with side 300 μm. In both models, despite a combinatorial explosion in the size of the configuration space, a few pathways and intermediates dominate self-assembly. For self-folding polyhedra, the dominant intermediates have fewer degrees of freedom than comparable intermediates, and are thus more rigid. The concentration of assembly pathways on a few intermediates with distinguished geometric properties is biologically and physically important, and suggests deeper mathematical structure.

An efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors

NASA Technical Reports Server (NTRS)

Rahmat-Samii, Y.

1983-01-01

Based on the works of Ruze (1966) and Vu (1969), a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors. In this model, both nonuniform root mean square (rms) surface errors and nonuniform illumination functions are employed. In addition, the model incorporates the dependence on F/D in the construction of the solution. The mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna, the geometrical rms surface value is known. It is shown that closed-form expressions can then be derived, which result in a very efficient computational method for the average power pattern. Detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels. The results clearly demonstrate that as sidelobe levels decrease, their dependence on the surface rms/wavelength becomes much stronger and, for a specified tolerance level, a considerably smaller rms/wavelength is required to maintain the low sidelobes within the required bounds.