Adaptive Control Of Remote Manipulator

NASA Technical Reports Server (NTRS)

Seraji, Homayoun

1989-01-01

Robotic control system causes remote manipulator to follow closely reference trajectory in Cartesian reference frame in work space, without resort to computationally intensive mathematical model of robot dynamics and without knowledge of robot and load parameters. System, derived from linear multivariable theory, uses relatively simple feedforward and feedback controllers with model-reference adaptive control.

Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work

NASA Astrophysics Data System (ADS)

Pedrammehr, Siamak; Nahavandi, Saeid; Abdi, Hamid

2018-04-01

In this research, a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work. For the first time, a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms. An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories. Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.

Investigating Preservice Mathematics Teachers' Manipulative Material Design Processes

ERIC Educational Resources Information Center

Sandir, Hakan

2016-01-01

Students use concrete manipulatives to form an imperative affiliation between conceptual and procedural knowledge (Balka, 1993). Hence, it is necessary to design specific mathematics manipulatives that focus on different mathematical concepts. Preservice teachers need to know how to make and use manipulatives that stimulate students' thinking as…

Female Preservice Teachers and Mathematics: Anxiety, Beliefs, and Stereotypes

ERIC Educational Resources Information Center

Lake, Vickie E.; Kelly, Loreen

2014-01-01

The purpose of the current study was to examine if preservice teachers' (PSTs) mathematics anxiety decreased and if their beliefs and stereotypes changed after they completed their early childhood mathematics methods course. It was hypothesized that by using and modeling concrete materials or manipulatives (Thompson, 1992; Vinson, 2001) and…

Modelling Mathematical Reasoning in Physics Education

ERIC Educational Resources Information Center

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

2012-01-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

Manipulatives and the Computer: A Powerful Partnership for Learners of All Ages.

ERIC Educational Resources Information Center

Perl, Teri

1990-01-01

Discussed is the concept of mirroring in which computer programs are used to enhance the use of mathematics manipulatives. The strengths and weaknesses of this approach are presented. The uses of the computer in modeling and as a manipulative are also described. Several software packages are suggested. (CW)

Teachers' Beliefs and Teaching Mathematics with Manipulatives

ERIC Educational Resources Information Center

Golafshani, Nahid

2013-01-01

To promote the implementation of manipulatives into mathematics instruction, this research project examined how the instructional practices of four Grade 9 applied mathematics teachers related to their beliefs about the use of manipulatives in teaching mathematics, its effects on students' learning, and enabling and disabling factors. Teacher…

Relating the Stored Magnetic Energy of a Parallel-Plate Inductor to the Work of External Forces

ERIC Educational Resources Information Center

Gauthier, N.

2007-01-01

Idealized models are often used in introductory physics courses. For one, such models involve simple mathematics, which is a definite plus since complex mathematical manipulations quickly become an obstacle rather than a tool for a beginner. Idealized models facilitate a student's understanding and grasp of a given physical phenomenon, yet they…

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.…

Teaching Mathematics to Young Children through the Use of Concrete and Virtual Manipulatives

ERIC Educational Resources Information Center

D'Angelo, Frank; Iliev, Nevin

2012-01-01

The use of manipulatives is an essential key to teaching mathematics to young children. Throughout history, different types of manipulatives have been used to aid in comprehension of mathematical concepts including quipu, abaci and pattern blocks. Today, concrete and virtual manipulatives are the tools that early childhood teachers are using in…

Revisiting Mathematics Manipulative Materials

ERIC Educational Resources Information Center

Swan, Paul; Marshall, Linda

2010-01-01

It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics…

Instructional Aids in Mathematics: Using Models as Instructional Aids

ERIC Educational Resources Information Center

Johnson, Donovan A.; And Others

1973-01-01

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

Manipulative Use and Elementary School Students' Mathematics Learning

ERIC Educational Resources Information Center

Uribe-Flórez, Lida J.; Wilkins, Jesse L. M.

2017-01-01

Using data from the Early Childhood Longitudinal Study (ECLS) 1998/1999, we examine the relationship between elementary students' (K-5) manipulative use and mathematics learning. Using a cross-sectional correlational analysis, we found no relationship between manipulative use and student mathematics "achievement". However, using a…

The Chicken or the Egg? The Direction of the Relationship Between Mathematics Anxiety and Mathematics Performance.

PubMed

Carey, Emma; Hill, Francesca; Devine, Amy; Szücs, Dénes

2015-01-01

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle.

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.

Proposal for Development of EBM-CDSS (Evidence-Based Clinical Decision Support System) to Aid Prognostication in Terminally Ill Patients

DTIC Science & Technology

2010-10-01

Mathematics , Indiana University Northwest, Gary, IN 3Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, NY 4H...however, is mathematically more parsimonious. The original DCA formulation required several mathematical manipulations making the simplicity of regret...into treatment administration examples; IH developed the mathematical formulation of the model; AV is the author of DCA; BD proposed the regret theory

Modeling, design, and control of flexible manipulator arms: Status and trends

NASA Technical Reports Server (NTRS)

Book, Wayne J.

1989-01-01

The desire for higher performance manipulators has lead to dynamic behavior in which the flexibility is an essential aspect. The mathematical representations commonly used in modeling flexible arms and arms with flexible drives are examined first. Then design considerations directly arising from the flexible nature of the arm are discussed. Finally, controls of joints for general and tip motion are discussed.

The Chicken or the Egg? The Direction of the Relationship Between Mathematics Anxiety and Mathematics Performance

PubMed Central

Carey, Emma; Hill, Francesca; Devine, Amy; Szücs, Dénes

2016-01-01

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle. PMID:26779093

On a model of the processes of maintaining a technological area by a manipulator

NASA Astrophysics Data System (ADS)

Ghukasyan, A. A.; Ordyan, A. Ya

2018-04-01

The research refers to the results of mathematical modeling of the process of maintaining a technological area which consists of unstable or fixed objects (targets) and a controlled multi-link manipulator [1–9]. It is assumed that, in the maintenance process, the dynamic characteristics and the phase vector of the manipulator state can change at certain finite times depending on the mass of the cargo or instrument [10, 11]. Some controllability problems are investigated in the case where the manipulator motion on each maintenance interval is described by linear differential equations with constant coefficients and the motions of the objects are given.

Kindergarten Children's Interactions with Touchscreen Mathematics Virtual Manipulatives: An Innovative Mixed Methods Analysis

ERIC Educational Resources Information Center

Tucker, Stephen I.; Lommatsch, Christina W.; Moyer-Packenham, Patricia S.; Anderson-Pence, Katie L.; Symanzik, Jürgen

2017-01-01

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

Virtual vs. Concrete Manipulatives in Mathematics Teacher Education: Is One Type More Effective than the Other?

ERIC Educational Resources Information Center

Hunt, Annita W.; Nipper, Kelli L.; Nash, Linda E.

2011-01-01

Are virtual manipulatives as effective as concrete (hands-on) manipulatives in building conceptual understanding of number concepts and relationships in pre-service middle grades teachers? In the past, the use of concrete manipulatives in mathematics courses for Clayton State University's pre-service middle grades teachers has been effective in…

Modal analysis and control of flexible manipulator arms. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Neto, O. M.

1974-01-01

The possibility of modeling and controlling flexible manipulator arms was examined. A modal approach was used for obtaining the mathematical model and control techniques. The arm model was represented mathematically by a state space description defined in terms of joint angles and mode amplitudes obtained from truncation on the distributed systems, and included the motion of a two link two joint arm. Three basic techniques were used for controlling the system: pole allocation with gains obtained from the rigid system with interjoint feedbacks, Simon-Mitter algorithm for pole allocation, and sensitivity analysis with respect to parameter variations. An improvement in arm bandwidth was obtained. Optimization of some geometric parameters was undertaken to maximize bandwidth for various payload sizes and programmed tasks. The controlled system is examined under constant gains and using the nonlinear model for simulations following a time varying state trajectory.

Mathematical modeling and design of a novel 2-DOF micro attraction actuator for a micro optical switch

NASA Astrophysics Data System (ADS)

Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

2004-08-01

Many studies on optical switches have been performed in an attempt to develop optical information networks to speed information technology. In reality, however, mirror manipulators cannot be applied to multiple input and output systems due to both insufficient output displacements by the mirror parts inside the manipulator, and the difficulty of designing structures and mechanisms suitable for multi-dimensional manipulation. The principal reasons for insufficient displacement are the high rigidity of the elastic parts compared to the available driving forces and the pull-in effect. Therefore, in order to develop optical switches capable of multiple input and output switching, we suggest a novel 2-DOF(degree of freedom) electrostatic microactuator. The actuator is composed of one mirror with four beams laid about it in a corkscrew pattern, with four corkscrew electrodes on the substrate below and one mirror support pyramid situated under the mirror. Using electrostatic force, one or more of the beams are attracted from their outer ends toward the substrate. The mirror is then tilted by an angle proportional to the attracted length along the beam. The inclination and direction of the mirror are determined by the combined attracted length of the four beams. In this work we derive the mathematical model for the corkscrew beam microactuator for optical switches and show that this mathematical model accurately simulates the device by comparison with finite element analysis results. We use this mathematical model for design of the microactuator. Further we show that the designed optical switch microactuator is capable of rotating the mirror from +32 to -32 degrees about two axes with a maximum operating voltage of 163 volts. Finally, stress analysis of the actuator shows that the generated stress in the structure is at most 369 MPa.

Count on It: Congruent Manipulative Displays

ERIC Educational Resources Information Center

Morin, Joe; Samelson, Vicki M.

2015-01-01

Representations that create informative visual displays are powerful tools for communicating mathematical concepts. The National Council of Teachers of Mathematics encourages the use of manipulatives (NCTM 2000). Manipulative materials are often used to present initial representations of basic numerical principles to young children, and it is…

The roles of prefrontal and posterior parietal cortex in algebra problem solving: a case of using cognitive modeling to inform neuroimaging data.

PubMed

Danker, Jared F; Anderson, John R

2007-04-15

In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments.

A Case against Computer Symbolic Manipulation in School Mathematics Today.

ERIC Educational Resources Information Center

Waits, Bert K.; Demana, Franklin

1992-01-01

Presented are two reasons discouraging computer symbol manipulation systems use in school mathematics at present: cost for computer laboratories or expensive pocket computers; and impracticality of exact solution representations. Although development with this technology in mathematics education advances, graphing calculators are recommended to…

Manipulative Apps to Support Students with Disabilities in Mathematics

ERIC Educational Resources Information Center

Bouck, Emily C.; Working, Christopher; Bone, Erin

2018-01-01

Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…

The Effect of Manipulatives on Mathematics Achievement across Different Learning Styles

ERIC Educational Resources Information Center

Kablan, Zeynel

2016-01-01

The current study investigates the influence of manipulatives used in combination with traditional approaches to mathematics education and how varying amounts of time spent on manipulative use influence student achievement across different learning styles. Three learning environments were created that incorporated varying proportions of…

An evolutionary resolution of manipulation conflict.

PubMed

González-Forero, Mauricio

2014-07-01

Individuals can manipulate the behavior of social partners. However, manipulation may conflict with the fitness interests of the manipulated individuals. Manipulated individuals can then be favored to resist manipulation, possibly reducing or eliminating the manipulated behavior in the long run. I use a mathematical model to show that conflicts where manipulation and resistance coevolve can disappear as a result of the coevolutionary process. I find that while manipulated individuals are selected to resist, they can simultaneously be favored to express the manipulated behavior at higher efficiency (i.e., providing increasing fitness effects to recipients of the manipulated behavior). Efficiency can increase to a point at which selection for resistance disappears. This process yields an efficient social behavior that is induced by social partners, and over which the inducing and induced individuals are no longer in conflict. A necessary factor is costly inefficiency. I develop the model to address the evolution of advanced eusociality via maternal manipulation (AEMM). The model predicts AEMM to be particularly likely in taxa with ancestrally imperfect resistance to maternal manipulation. Costly inefficiency occurs if the cost of delayed dispersal is larger than the benefit of exploiting the maternal patch. I discuss broader implications of the process. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.

Application of recursive Gibbs-Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko Beam Theory

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Shafei, A. M.

2013-02-01

The goal of this paper is to describe the application of Gibbs-Appell (G-A) formulation and the assumed modes method to the mathematical modeling of N-viscoelastic link manipulators. The paper's focus is on obtaining accurate and complete equations of motion which encompass the most related structural properties of lightweight elastic manipulators. In this study, two important damping mechanisms, namely, the structural viscoelasticity (Kelvin-Voigt) effect (as internal damping) and the viscous air effect (as external damping) have been considered. To include the effects of shear and rotational inertia, the assumption of Timoshenko beam (TB) theory (TBT) has been applied. Gravity, torsion, and longitudinal elongation effects have also been included in the formulations. To systematically derive the equations of motion and improve the computational efficiency, a recursive algorithm has been used in the modeling of the system. In this algorithm, all the mathematical operations are carried out by only 3×3 and 3×1 matrices. Finally, a computational simulation for a manipulator with two elastic links is performed in order to verify the proposed method.

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2016-01-01

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

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).…

Virtual Manipulatives: What They Are and How Teachers Can Use Them

ERIC Educational Resources Information Center

Bouck, Emily C.; Flanagan, Sara M.

2010-01-01

Research on the positive impact of using concrete manipulatives in mathematics for students with high-incidence disabilities is clear. Maccini and Gagnon (2000) considered manipulatives to be a best practice in terms of educating students with high-incidence disabilities in mathematics. It would follow, then, that research on virtual manipulatives…

Gender Differences in the Relationship between Taiwanese Adolescents' Mathematics Attitudes and Their Perceptions toward Virtual Manipulatives

ERIC Educational Resources Information Center

Lee, Chun-Yi; Yuan, Yuan

2010-01-01

This study explored gender differences in the relationship between young people's mathematics attitudes and their perceptions toward virtual manipulatives. Seven hundred eighty junior high school adolescents who participated in the problem-solving activity using virtual manipulatives were selected for examination. The study found the male…

The Complexity of the Affordance-Ability Relationship When Second-Grade Children Interact with Mathematics Virtual Manipulative Apps

ERIC Educational Resources Information Center

Tucker, Stephen I.; Moyer-Packenham, Patricia S.; Westenskow, Arla; Jordan, Kerry E.

2016-01-01

The purpose of this study was to explore relationships between app affordances and user abilities in second graders' interactions with mathematics virtual manipulative touchscreen tablet apps. The research questions focused on varying manifestations of affordance-ability relationships during children's interactions with mathematics virtual…

The Effectiveness of Robotics as a Manipulative in Mathematics Instruction: A Mixed Method Study

ERIC Educational Resources Information Center

Sheehy, Leonard

2017-01-01

Addition of fractions is an important foundation for students to experience success in mathematics. This mixed-methods study was conducted to measure the effectiveness of robotics as a mathematics manipulative with seventh grade students. Two groups of students were established: control and treatment. The control group received teacher-centered…

Exploitation of manipulators: 'hitch-hiking' as a parasite transmission strategy.

PubMed

Thomas; Renaud; Poulin

1998-07-01

For many parasites with complex life cycles, manipulation of host behaviour is an adaptation to increase the probability of successful transmission. Since manipulation is likely to be costly, other parasites may exploit hosts already manipulated so as to ensure their transmission without investing in manipulation. Such a cheating strategy, called 'hitch-hiking', could be adaptive in a range of situations. We first propose and discuss criteria that should be met by any parasite to be considered a hitch-hiker. Then, to understand the evolution of the hitch-hiking strategy, we use simple mathematical models to analyse the influence of several variables on the potential benefits for a nonmanipulative parasite of actively seeking a ride to the definitive host with a manipulative parasite. The models suggest that the prevalence or abundance of manipulative parasites will be a key determinant of whether hitch-hiking can be an advantageous option for other parasites. Copyright 1998 The Association for the Study of Animal Behaviour.

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Data Discretization for Novel Relationship Discovery in Information Retrieval.

ERIC Educational Resources Information Center

Benoit, G.

2002-01-01

Describes an information retrieval, visualization, and manipulation model which offers the user multiple ways to exploit the retrieval set, based on weighted query terms, via an interactive interface. Outlines the mathematical model and describes an information retrieval application built on the model to search structured and full-text files.…

Students’ Mathematical Creative Thinking through Problem Posing Learning

NASA Astrophysics Data System (ADS)

Ulfah, U.; Prabawanto, S.; Jupri, A.

2017-09-01

The research aims to investigate the differences in enhancement of students’ mathematical creative thinking ability of those who received problem posing approach assisted by manipulative media and students who received problem posing approach without manipulative media. This study was a quasi experimental research with non-equivalent control group design. Population of this research was third-grade students of a primary school in Bandung city in 2016/2017 academic year. Sample of this research was two classes as experiment class and control class. The instrument used is a test of mathematical creative thinking ability. Based on the results of the research, it is known that the enhancement of the students’ mathematical creative thinking ability of those who received problem posing approach with manipulative media aid is higher than the ability of those who received problem posing approach without manipulative media aid. Students who get learning problem posing learning accustomed in arranging mathematical sentence become matter of story so it can facilitate students to comprehend about story

A Systematic Review of the Literature on Mathematics Manipulatives to Support Students with Disabilities

ERIC Educational Resources Information Center

Bouck, Emily C.; Park, Jiyoon

2018-01-01

Manipulatives are considered a common tool for mathematics teaching and learning, for both students with and without disabilities. Yet, a systematic review of the current state of research regarding manipulatives for students with disabilities did not exist prior to this article. This manuscript presents a systematic review of the literature…

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

PubMed Central

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

2011-01-01

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

Virtual and concrete manipulatives: a comparison of approaches for solving mathematics problems for students with autism spectrum disorder.

PubMed

Bouck, Emily C; Satsangi, Rajiv; Doughty, Teresa Taber; Courtney, William T

2014-01-01

Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of concrete (physical objects that can be manipulated) and virtual (3-D objects from the Internet that can be manipulated) manipulatives to teach single- and double-digit subtraction skills. Participants in this study included three elementary-aged students (ages ranging from 6 to 10) diagnosed with ASD. Students were selected from a clinic-based setting, where all participants received medically necessary intensive services provided via one-to-one, trained therapists. Both forms of manipulatives successfully assisted students in accurately and independently solving subtraction problem. However, all three students demonstrated greater accuracy and faster independence with the virtual manipulatives as compared to the concrete manipulatives. Beyond correctly solving the subtraction problems, students were also able to generalize their learning of subtraction through concrete and virtual manipulatives to more real-world applications.

The Effects of a Grouping by Tens Manipulative on Children's Strategy Use, Base Ten Understanding and Mathematical Knowledge

ERIC Educational Resources Information Center

Pagar, Dana

2013-01-01

Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do…

Manipulators with flexible links: A simple model and experiments

NASA Technical Reports Server (NTRS)

Shimoyama, Isao; Oppenheim, Irving J.

1989-01-01

A simple dynamic model proposed for flexible links is briefly reviewed and experimental control results are presented for different flexible systems. A simple dynamic model is useful for rapid prototyping of manipulators and their control systems, for possible application to manipulator design decisions, and for real time computation as might be applied in model based or feedforward control. Such a model is proposed, with the further advantage that clear physical arguments and explanations can be associated with its simplifying features and with its resulting analytical properties. The model is mathematically equivalent to Rayleigh's method. Taking the example of planar bending, the approach originates in its choice of two amplitude variables, typically chosen as the link end rotations referenced to the chord (or the tangent) motion of the link. This particular choice is key in establishing the advantageous features of the model, and it was used to support the series of experiments reported.

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.

The Role of Affordances in Children's Learning Performance and Efficiency When Using Virtual Manipulative Mathematics Touch-Screen Apps

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Bullock, Emma K.; Shumway, Jessica F.; Tucker, Stephen I.; Watts, Christina M.; Westenskow, Arla; Anderson-Pence, Katie L.; Maahs-Fladung, Cathy; Boyer-Thurgood, Jennifer; Gulkilik, Hilal; Jordan, Kerry

2016-01-01

This paper focuses on understanding the role that affordances played in children's learning performance and efficiency during clinical interviews of their interactions with mathematics apps on touch-screen devices. One hundred children, ages 3 to 8, each used six different virtual manipulative mathematics apps during 30-40-min interviews. The…

Research on modeling and motion simulation of a spherical space robot with telescopic manipulator based on virtual prototype technology

NASA Astrophysics Data System (ADS)

Shi, Chengkun; Sun, Hanxu; Jia, Qingxuan; Zhao, Kailiang

2009-05-01

For realizing omni-directional movement and operating task of spherical space robot system, this paper describes an innovated prototype and analyzes dynamic characteristics of a spherical rolling robot with telescopic manipulator. Based on the Newton-Euler equations, the kinematics and dynamic equations of the spherical robot's motion are instructed detailedly. Then the motion simulations of the robot in different environments are developed with ADAMS. The simulation results validate the mathematics model of the system. And the dynamic model establishes theoretical basis for the latter job.

Reevaluating the two-representation model of numerical magnitude processing.

PubMed

Jiang, Ting; Zhang, Wenfeng; Wen, Wen; Zhu, Haiting; Du, Han; Zhu, Xiangru; Gao, Xuefei; Zhang, Hongchuan; Dong, Qi; Chen, Chuansheng

2016-01-01

One debate in mathematical cognition centers on the single-representation model versus the two-representation model. Using an improved number Stroop paradigm (i.e., systematically manipulating physical size distance), in the present study we tested the predictions of the two models for number magnitude processing. The results supported the single-representation model and, more importantly, explained how a design problem (failure to manipulate physical size distance) and an analytical problem (failure to consider the interaction between congruity and task-irrelevant numerical distance) might have contributed to the evidence used to support the two-representation model. This study, therefore, can help settle the debate between the single-representation and two-representation models.

Using Physical Models to Explain a Division Algorithm.

ERIC Educational Resources Information Center

Vest, Floyd

1985-01-01

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

Atmosphere behavior in gas-closed mouse-algal systems - An experimental and modelling study

NASA Technical Reports Server (NTRS)

Averner, M. M.; Moore, B., III; Bartholomew, I.; Wharton, R.

1984-01-01

A NASA-sponsored research program initiated using mathematical modelling and laboratory experimentation aimed at examining the gas-exchange characteristics of artificial animal/plant systems closed to the ambient atmosphere is studied. The development of control techniques and management strategies for maintaining the atmospheric levels of carbon dioxide and oxygen at physiological levels is considered. A mathematical model simulating the behavior of a gas-closed mouse-algal system under varying environmental conditions is described. To verify and validate the model simulations, an analytical system with which algal growth and gas exchange characteristics can be manipulated and measured is designed, fabricated, and tested. The preliminary results are presented.

Using Concrete Manipulatives in Mathematical Instruction

ERIC Educational Resources Information Center

Jones, Julie P.; Tiller, Margaret

2017-01-01

Concrete, Representational, Abstract (CRA) instruction is a process for teaching and learning mathematical concepts. Starting with manipulation of concrete materials (counters, beans, Unifix cubes), the process moves students to the representational level (tallies, dots, stamps), and peaks at the abstract level, at which numbers and symbols are…

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

PubMed

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

2008-01-01

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

Process design for microbial plastic factories: metabolic engineering of polyhydroxyalkanoates.

PubMed

Aldor, Ilana S; Keasling, Jay D

2003-10-01

Implementing several metabolic engineering strategies, either individually or in combination, it is possible to construct microbial plastic factories to produce a variety of polyhydroxyalkanoate (PHA) biopolymers with desirable structures and material properties. Approaches include external substrate manipulation, inhibitor addition, recombinant gene expression, host cell genome manipulation and, most recently, protein engineering of PHA biosynthetic enzymes. In addition, mathematical models and molecular methods can be used to elucidate metabolically engineered systems and to identify targets for performance improvement.

Mathematical models of cell factories: moving towards the core of industrial biotechnology.

PubMed

Cvijovic, Marija; Bordel, Sergio; Nielsen, Jens

2011-09-01

Industrial biotechnology involves the utilization of cell factories for the production of fuels and chemicals. Traditionally, the development of highly productive microbial strains has relied on random mutagenesis and screening. The development of predictive mathematical models provides a new paradigm for the rational design of cell factories. Instead of selecting among a set of strains resulting from random mutagenesis, mathematical models allow the researchers to predict in silico the outcomes of different genetic manipulations and engineer new strains by performing gene deletions or additions leading to a higher productivity of the desired chemicals. In this review we aim to summarize the main modelling approaches of biological processes and illustrate the particular applications that they have found in the field of industrial microbiology. © 2010 The Authors. Journal compilation © 2010 Society for Applied Microbiology and Blackwell Publishing Ltd.

Concrete and App-Based Manipulatives to Support Students with Disabilities with Subtraction

ERIC Educational Resources Information Center

Bouck, Emily C.; Chamberlain, Courtney; Park, Jiyoon

2017-01-01

Manipulatives support students with and without disabilities in mathematics. However, as students age, concrete manipulatives can be limiting and potentially not age appropriate (Satsangi, 2015). An alternative is virtual manipulatives, including app-based manipulatives. This study compared the use of app-based manipulatives to concrete…

Virtual Manipulative Materials in Secondary Mathematics: A Theoretical Discussion

ERIC Educational Resources Information Center

Namukasa, Immacukate K.; Stanley, Darren; Tuchtie, Martin

2009-01-01

With the increased use of computer manipulatives in teaching there is need for theoretical discussions on the role of manipulatives. This paper reviews theoretical rationales for using manipulatives and illustrates how earlier distinctions of manipulative materials are broadened to include new forms of materials such as virtual manipulatives.…

Bringing Stories to Life: Integrating Literature and Math Manipulatives

ERIC Educational Resources Information Center

Larson, Lotta C.; Rumsey, Chepina

2018-01-01

This Teaching Tip describes the use of children's literature to help second-grade students meet Common Core State Standards for English Language Arts and for Mathematics. During a shared reading experience, students used manipulatives to represent plot and characters while demonstrating mathematical reasoning. The article offers instructional…

Derivation of three closed loop kinematic velocity models using normalized quaternion feedback for an autonomous redundant manipulator with application to inverse kinematics

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

Unseren, M.A.

1993-04-01

The report discusses the orientation tracking control problem for a kinematically redundant, autonomous manipulator moving in a three dimensional workspace. The orientation error is derived using the normalized quaternion error method of Ickes, the Luh, Walker, and Paul error method, and a method suggested here utilizing the Rodrigues parameters, all of which are expressed in terms of normalized quaternions. The analytical time derivatives of the orientation errors are determined. The latter, along with the translational velocity error, form a dosed loop kinematic velocity model of the manipulator using normalized quaternion and translational position feedback. An analysis of the singularities associatedmore » with expressing the models in a form suitable for solving the inverse kinematics problem is given. Two redundancy resolution algorithms originally developed using an open loop kinematic velocity model of the manipulator are extended to properly take into account the orientation tracking control problem. This report furnishes the necessary mathematical framework required prior to experimental implementation of the orientation tracking control schemes on the seven axis CESARm research manipulator or on the seven-axis Robotics Research K1207i dexterous manipulator, the latter of which is to be delivered to the Oak Ridge National Laboratory in 1993.« less

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

NASA Technical Reports Server (NTRS)

Zia, Omar

1989-01-01

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

Shadow-driven 4D haptic visualization.

PubMed

Zhang, Hui; Hanson, Andrew

2007-01-01

Just as we can work with two-dimensional floor plans to communicate 3D architectural design, we can exploit reduced-dimension shadows to manipulate the higher-dimensional objects generating the shadows. In particular, by taking advantage of physically reactive 3D shadow-space controllers, we can transform the task of interacting with 4D objects to a new level of physical reality. We begin with a teaching tool that uses 2D knot diagrams to manipulate the geometry of 3D mathematical knots via their projections; our unique 2D haptic interface allows the user to become familiar with sketching, editing, exploration, and manipulation of 3D knots rendered as projected imageson a 2D shadow space. By combining graphics and collision-sensing haptics, we can enhance the 2D shadow-driven editing protocol to successfully leverage 2D pen-and-paper or blackboard skills. Building on the reduced-dimension 2D editing tool for manipulating 3D shapes, we develop the natural analogy to produce a reduced-dimension 3D tool for manipulating 4D shapes. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the experience accessible to human beings. As far as we are aware, this paper reports the first interactive system with force-feedback that provides "4D haptic visualization" permitting the user to model and interact with 4D cloth-like objects.

Virtual Manipulatives in the K-12 Classroom.

ERIC Educational Resources Information Center

Moyer, Patricia S.; Bolyard, Johnna J.; Spikell, Mark A.

Innovations in technology, along with the growing prevalence of the Internet and its increasing availability in classrooms and homes throughout the world, have created a new class of manipulatives, virtual manipulatives. These "virtual manipulatives" offer a new, enhanced approach for teaching and learning mathematics using manipulatives and…

Learning Area and Perimeter with Virtual Manipulatives

ERIC Educational Resources Information Center

Bouck, Emily; Flanagan, Sara; Bouck, Mary

2015-01-01

Manipulatives are considered a best practice for educating students with disabilities, but little research exists which examines virtual manipulatives as tool for supporting students in mathematics. This project investigated the use of a virtual manipulative through the National Library of Virtual Manipulatives--polynominoes (i.e., tiles)--as a…

Not mathematics Education, not Mathematics education but Mathematics Education

ERIC Educational Resources Information Center

Galbraith, P. L.

1977-01-01

Weaknesses in the initial preparation of school mathematics teachers are proposed. Emphasis is on the underdevelopment of global understanding in lieu of the manipulation of symbols or the performing of complex algorithms. (MN)

Predictors of Achievement When Virtual Manipulatives Are Used for Mathematics Instruction

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Baker, Joseph; Westenskow, Arla; Anderson-Pence, Katie L.; Shumway, Jessica F.; Jordan, Kerry E.

2014-01-01

The purpose of this study was to determine variables that predict performance when virtual manipulatives are used for mathematics instruction. This study used a quasi-experimental design. This design was used to determine variables that predict student performance on tests of fraction knowledge for third- and fourth-grade students in two treatment…

R&D Project on Algebra Software Seen to Show Promise

ERIC Educational Resources Information Center

Trotter, Andrew

2007-01-01

Computer software that shows students visual models of mathematical concepts--and lets them manipulate those models by doing math--has a certain intuitive appeal. Now, recent research on SimCalc Mathworlds, one of the pioneering examples of such software, is providing some of the best evidence so far that the approach can lead to gains in student…

Direct adaptive control of manipulators in Cartesian space

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.

Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

PubMed Central

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

Un estudio de evaluacion educativa manipulativos en el aprendizaje de las matematicas con estudiantes hispanos adquiriendo ingles academico como segunda lengua (A Study of the Use of Manipulatives in the Assessment of Mathematics Instruction with ESL Hispanic Students).

ERIC Educational Resources Information Center

Lara-Alecio, Rafael; Parker, Richard; Aviles, Claudia; Mason, Samantha; Irby, Beverly J.

1998-01-01

As an alternative form of mathematics assessment for use with limited-English-proficient students, 14 mathematics tasks using manipulatives were administered to 45 Hispanic students in grades 1-3 and readministered 2-3 weeks later. Test reliability and validity, task difficulty, and the relationship among test subscales across grades were…

Algebraic Manipulation as Motion within a Landscape

ERIC Educational Resources Information Center

Wittmann, Michael C.; Flood, Virginia J.; Black, Katrina E.

2013-01-01

We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of…

The Case for Adopting Virtual Manipulatives in Mathematics Education for Students with Disabilities

ERIC Educational Resources Information Center

Satsangi, Rajiv; Miller, Bridget

2017-01-01

The past four decades have generated significant research toward improving the academic outcomes of students with disabilities, especially in the field of mathematics. In this effort, the role of technology in the classroom, both high- and low-tech, has garnered significant attention. For students with disabilities, the use of manipulatives is a…

The Impact of Use of Manipulatives on the Math Scores of Grade 2 Students

ERIC Educational Resources Information Center

Liggett, Robert Scott

2017-01-01

Today's society places a lot of pressure on schools, teachers, and students to improve test scores. This paper discusses the possibility of using mathematical manipulatives to improve student test scores and students' attitudes towards mathematics. Forty-three Grade 2 students with age ranges between six and eight from a rural town in Saskatchewan…

Effects of Worked Examples Using Manipulatives on Fifth Graders' Learning Performance and Attitude toward Mathematics

ERIC Educational Resources Information Center

Lee, Chun-Yi; Chen, Ming-Jang

2015-01-01

The purpose of this study was to investigate the influence of worked examples using virtual manipulatives on the learning performance and attitudes of fifth grade students toward mathematics. The results showed that: (1) the utilization of non-routine examples could promote learning performance of equivalent fractions. (2) Learning with virtual…

Comparing the Effectiveness of Virtual and Concrete Manipulatives to Teach Algebra to Secondary Students with Learning Disabilities

ERIC Educational Resources Information Center

Satsangi, Rajiv; Bouck, Emily C.; Taber-Doughty, Teresa; Bofferding, Laura; Roberts, Carly A.

2016-01-01

A sizable body of literature exists studying various technologies and pedagogical practices for teaching secondary mathematics curriculum to students with a learning disability in mathematics. However, with the growing footprint of computer-based technologies in today's classrooms, some areas of study, such as the use of virtual manipulatives,…

A Math-Box Tale

ERIC Educational Resources Information Center

Nelson, Catherine J.

2012-01-01

The author is a strong proponent of incorporating the Content and Process Standards (NCTM 2000) into the teaching of mathematics. For candidates in her methods course, she models research-based best practices anchored in the Standards. Her students use manipulatives, engage in problem-solving activities, listen to children's literature, and use…

Third-Graders Learn about Fractions Using Virtual Manipulatives: A Classroom Study

ERIC Educational Resources Information Center

Reimer, Kelly; Moyer, Patricia S.

2005-01-01

With recent advances in computer technology, it is no surprise that the manipulation of objects in mathematics classrooms now includes the manipulation of objects on the computer screen. These objects, referred to as "virtual manipulatives," are essentially replicas of physical manipulatives placed on the World Wide Web in the form of computer…

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

Unseren, M.A.

The report discusses the orientation tracking control problem for a kinematically redundant, autonomous manipulator moving in a three dimensional workspace. The orientation error is derived using the normalized quaternion error method of Ickes, the Luh, Walker, and Paul error method, and a method suggested here utilizing the Rodrigues parameters, all of which are expressed in terms of normalized quaternions. The analytical time derivatives of the orientation errors are determined. The latter, along with the translational velocity error, form a dosed loop kinematic velocity model of the manipulator using normalized quaternion and translational position feedback. An analysis of the singularities associatedmore » with expressing the models in a form suitable for solving the inverse kinematics problem is given. Two redundancy resolution algorithms originally developed using an open loop kinematic velocity model of the manipulator are extended to properly take into account the orientation tracking control problem. This report furnishes the necessary mathematical framework required prior to experimental implementation of the orientation tracking control schemes on the seven axis CESARm research manipulator or on the seven-axis Robotics Research K1207i dexterous manipulator, the latter of which is to be delivered to the Oak Ridge National Laboratory in 1993.« less

The Transition to Formal Thinking in Mathematics

ERIC Educational Resources Information Center

Tall, David

2008-01-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Correlates of Mathematics Anxiety.

ERIC Educational Resources Information Center

McCoy, Leah, P.

1992-01-01

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

Numerical image manipulation and display in solar astronomy

NASA Technical Reports Server (NTRS)

Levine, R. H.; Flagg, J. C.

1977-01-01

The paper describes the system configuration and data manipulation capabilities of a solar image display system which allows interactive analysis of visual images and on-line manipulation of digital data. Image processing features include smoothing or filtering of images stored in the display, contrast enhancement, and blinking or flickering images. A computer with a core memory of 28,672 words provides the capacity to perform complex calculations based on stored images, including computing histograms, selecting subsets of images for further analysis, combining portions of images to produce images with physical meaning, and constructing mathematical models of features in an image. Some of the processing modes are illustrated by some image sequences from solar observations.

Paper Moon: Simulating a Total Solar Eclipse

ERIC Educational Resources Information Center

Madden, Sean P.; Downing, James P.; Comstock, Jocelyne M.

2006-01-01

This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

Promoting Technology Uses in the Elementary Mathematics Classroom: Lessons in Pedagogy from Zoltan Dienes

ERIC Educational Resources Information Center

Connell, Michael; Abramovich, Sergei

2016-01-01

Today technology allows for the utilization of new classes of mathematical objects which are themselves subject to new modes of student interaction. A series of notable examples may be found in the National Library of Virtual Manipulatives. These virtual manipulatives draw much of their power from their physical embodiment in the form of hand-on…

How Concrete Is Concrete?

ERIC Educational Resources Information Center

Gravemeijer, Koeno

2011-01-01

If we want to make something concrete in mathematics education, we are inclined introduce, what we call, "manipulatives", in the form of tactile objects or visual representations. If we want to make something concrete in a everyday-life conversation, we look for an example. In the former, we try to make a concrete model of our own,…

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. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed based on several incomplete versions. The verification of the code had been conducted by comparing the results with those examples for which the exact theoretical solutions can be obtained. The theoretical background of the package and the verification examples has been reported in a technical paper submitted to the Joint Applied Mechanics & Material Conference, ASME. A brief USER'S MANUAL had been compiled, which includes three parts: (1) Input data preparation; (2) Explanation of the Subroutines; and (3) Specification of control variables. Meanwhile, a theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modeling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide an embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

How Manipulatives Affect the Mathematics Achievement of Students in Nigerian Schools

ERIC Educational Resources Information Center

Aburime, F. Ehi.

2007-01-01

Mathematics is a very important subject in Nigeria. Yet, for more than twenty years, mathematics education in Nigeria has been in a sorry state. Mathematics achievement has been very low and frustrating. So far, every effort made to save Nigerian education from the devastating effect of persistent poor mathematics achievement has failed. An…

Mathematics Anxiety and the Underprepared Student.

ERIC Educational Resources Information Center

Godbey, Cathy

This article discusses the symptoms and causes of math anxiety, and preventative measures that teachers can use to alleviate the stress some students experience in mathematics problem solving. Mathematics anxiety is defined as "feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems…

Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains.

PubMed

Fields, Chris

2013-08-01

The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.

A Single-Boundary Accumulator Model of Response Times in an Addition Verification Task

PubMed Central

Faulkenberry, Thomas J.

2017-01-01

Current theories of mathematical cognition offer competing accounts of the interplay between encoding and calculation in mental arithmetic. Additive models propose that manipulations of problem format do not interact with the cognitive processes used in calculation. Alternatively, interactive models suppose that format manipulations have a direct effect on calculation processes. In the present study, we tested these competing models by fitting participants' RT distributions in an arithmetic verification task with a single-boundary accumulator model (the shifted Wald distribution). We found that in addition to providing a more complete description of RT distributions, the accumulator model afforded a potentially more sensitive test of format effects. Specifically, we found that format affected drift rate, which implies that problem format has a direct impact on calculation processes. These data give further support for an interactive model of mental arithmetic. PMID:28769853

Do medical students with A-level mathematics have a better understanding of the principles behind evidence-based medicine?

PubMed

Ben-Shlomo, Y; Fallon, U; Sterne, J; Brookes, S

2004-12-01

With the advent of evidence-based medicine, medical students, doctors and other healthcare professionals are required to be more skilled in the interpretation and manipulation of numerical data. The authors observed that undergraduate students without A-level mathematics expressed concern as to their ability to cope with an epidemiology and biostatistics course. It was hypothesized that these anxieties reflected differences in attitudes to numerical manipulation rather than any real lack of competence. Mean exam performance scores were compared for 498 first-year medical students between 2000 and 2002 depending on whether the students did or did not have A-level mathematics. The data revealed no difference in performance. Students without mathematics A-level scored marginally worse (-1.1%, 95% CI -3.1% to 0.8%, p=0.20) but were no more likely to fail the exam (odds ratio=0.98, 95% CI 0.40 to 2.6, p=0.9). It is concluded that some students experience 'numerophobia'-- a perceived and, it is thought, disproportionate fear of numbers and simple mathematical manipulation. This may act as a psychological barrier for future evidence-based practitioners.

A Comparative Study of the Effects of Using Dynamic Geometry Software and Physical Manipulatives on the Spatial Visualisation Skills of Pre-Service Mathematics Teachers

ERIC Educational Resources Information Center

Baki, Adnan; Kosa, Temel; Guven, Bulent

2011-01-01

The study compared the effects of dynamic geometry software and physical manipulatives on the spatial visualisation skills of first-year pre-service mathematics teachers. A pre- and post-test quasi-experimental design was used. The Purdue Spatial Visualisation Test (PSVT) was used for the pre- and post-test. There were three treatment groups. The…

Enhancing prediction power of chemometric models through manipulation of the fed spectrophotometric data: A comparative study

NASA Astrophysics Data System (ADS)

Saad, Ahmed S.; Hamdy, Abdallah M.; Salama, Fathy M.; Abdelkawy, Mohamed

2016-10-01

Effect of data manipulation in preprocessing step proceeding construction of chemometric models was assessed. The same set of UV spectral data was used for construction of PLS and PCR models directly and after mathematically manipulation as per well known first and second derivatives of the absorption spectra, ratio spectra and first and second derivatives of the ratio spectra spectrophotometric methods, meanwhile the optimal working wavelength ranges were carefully selected for each model and the models were constructed. Unexpectedly, number of latent variables used for models' construction varied among the different methods. The prediction power of the different models was compared using a validation set of 8 mixtures prepared as per the multilevel multifactor design and results were statistically compared using two-way ANOVA test. Root mean squares error of prediction (RMSEP) was used for further comparison of the predictability among different constructed models. Although no significant difference was found between results obtained using Partial Least Squares (PLS) and Principal Component Regression (PCR) models, however, discrepancies among results was found to be attributed to the variation in the discrimination power of adopted spectrophotometric methods on spectral data.

CircleBoard-Pro: Concrete manipulative-based learning cycle unit for learning geometry

NASA Astrophysics Data System (ADS)

Jamhari, Wongkia, Wararat

2018-01-01

Currently, a manipulative is commonly used in mathematics education as a supported tool for teaching and learning. With engaging natural interaction of a concrete manipulative and advantages of a learning cycle approach, we proposed the concrete manipulative-based learning cycle unit to promote mathematics learning. Our main objectives are to observe possibilities on the use of a concrete manipulative in learning geometry, and to assess students' understanding of a specific topic, angle properties in a circle, of secondary level students. To meet the first objective, the concrete manipulative, called CricleBoard-Pro, was designed. CircleBoard-Pro is built for easy to writing on or deleting from, accurate angle measurement, and flexible movement. Besides, learning activities and worksheets were created for helping students to learn angle properties in a circle. Twenty eighth graders on a lower secondary school in Indonesia were voluntarily involved to learn mathematics using CircleBoard-Pro with the designed learning activities and worksheets. We informally observed students' performance by focusing on criteria of using manipulative tools in learning mathematics while the learning activities were also observed in terms of whether they work and which step of activities need to be improved. The results of this part showed that CircleBoard-Pro complied the criteria of the use of the manipulative in learning mathematics. Nevertheless, parts of learning activities and worksheets need to be improved. Based on the results of the observation, CircleBoard-Pro, learning activities, and worksheets were merged together and became the CircleBoardPro embedded on 5E (Engage - Explore - Explain - Elaborate - Evaluate) learning cycle unit. Then, students understanding were assessed to reach the second objective. Six ninth graders from an Indonesian school in Thailand were recruited to participate in this study. Conceptual tests for both pre-and post-test, and semi-structured interview were used. Students' pre-and post-test answers were analyzed not only by descriptive statistics but also in qualitatively discussion. The dialogues between the interviewer and interviewees were transcribed and analyzed to find in-depth understanding. Finally, we can conclude that the participated students had better comprehension of angle properties in a circle even they could not perform proof by themselves. For further study, we will focus on how we can help students to develop their geometric thinking.

The role of affordances in children's learning performance and efficiency when using virtual manipulative mathematics touch-screen apps

NASA Astrophysics Data System (ADS)

Moyer-Packenham, Patricia S.; Bullock, Emma K.; Shumway, Jessica F.; Tucker, Stephen I.; Watts, Christina M.; Westenskow, Arla; Anderson-Pence, Katie L.; Maahs-Fladung, Cathy; Boyer-Thurgood, Jennifer; Gulkilik, Hilal; Jordan, Kerry

2016-03-01

This paper focuses on understanding the role that affordances played in children's learning performance and efficiency during clinical interviews of their interactions with mathematics apps on touch-screen devices. One hundred children, ages 3 to 8, each used six different virtual manipulative mathematics apps during 30-40-min interviews. The study used a convergent mixed methods design, in which quantitative and qualitative data were collected concurrently to answer the research questions (Creswell and Plano Clark 2011). Videos were used to capture each child's interactions with the virtual manipulative mathematics apps, document learning performance and efficiency, and record children's interactions with the affordances within the apps. Quantitized video data answered the research question on differences in children's learning performance and efficiency between pre- and post-assessments. A Wilcoxon matched pairs signed-rank test was used to explore these data. Qualitative video data was used to identify affordance access by children when using each app, identifying 95 potential helping and hindering affordances among the 18 apps. The results showed that there were changes in children's learning performance and efficiency when children accessed a helping or a hindering affordance. Helping affordances were more likely to be accessed by children who progressed between the pre- and post-assessments, and the same affordances had helping and hindering effects for different children. These results have important implications for the design of virtual manipulative mathematics learning apps.

The microcomputer scientific software series 1: the numerical information manipulation system.

Treesearch

Harold M. Rauscher

1983-01-01

The Numerical Information Manipulation System extends the versatility provided by word processing systems for textual data manipulation to mathematical or statistical data in numeric matrix form. Numeric data, stored and processed in the matrix form, may be manipulated in a wide variety of ways. The system allows operations on single elements, entire rows, or columns...

Leveraging 35 years of Pinus taeda research in the southeastern US to constrain forest carbon cycle predictions: regional data assimilation using ecosystem experiments

Treesearch

R. Quinn Thomas; Evan B. Brooks; Annika L. Jersild; Eric J. Ward; Randolph H. Wynne; Timothy J. Albaugh; Heather Dinon-Aldridge; Harold E. Burkhart; Jean-Christophe Domec; Timothy R. Fox; Carlos A. Gonzalez-Benecke; Timothy A. Martin; Asko Noormets; David A. Sampson; Robert O. Teskey

2017-01-01

Predicting how forest carbon cycling will change in response to climate change and management depends on the collective knowledge from measurements across environmental gradients, ecosystem manipulations of global change factors, and mathematical models. Formally integrating these sources of knowledge through data assimilation, or model–data fusion, allows the use of...

Using Integer Manipulatives: Representational Determinism

ERIC Educational Resources Information Center

Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla

2016-01-01

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

An adaptive Cartesian control scheme for manipulators

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.

Third Graders' Mathematical Thinking of Place Value through the Use of Concrete and Virtual Manipulatives

ERIC Educational Resources Information Center

Burris, Justin T.

2010-01-01

As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…

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

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

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

Singularity-free dynamic equations of spacecraft-manipulator systems

NASA Astrophysics Data System (ADS)

From, Pål J.; Ytterstad Pettersen, Kristin; Gravdahl, Jan T.

2011-12-01

In this paper we derive the singularity-free dynamic equations of spacecraft-manipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange's equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spacecraft is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of free-floating and free-flying spacecraft-manipulator systems and we show how to calculate the inertia and Coriolis matrices in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. This paper represents the first detailed study of modeling of spacecraft-manipulator systems with a focus on a singularity free formulation using the proposed framework.

Undergraduate Mathematics Students' Pronumeral Misconceptions

ERIC Educational Resources Information Center

Bardini, Caroline; Vincent, Jill; Pierce, Robyn; King, Deborah

2014-01-01

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students with high tertiary entrance ranks enrolled in first semester university mathematics were found to have misconceptions relating to…

Exploring Ackermann and LQR stability control of stochastic state-space model of hexacopter equipped with robotic arm

NASA Astrophysics Data System (ADS)

Ibrahim, I. N.; Akkad, M. A. Al; Abramov, I. V.

2018-05-01

This paper discusses the control of Unmanned Aerial Vehicles (UAVs) for active interaction and manipulation of objects. The manipulator motion with an unknown payload was analysed concerning force and moment disturbances, which influence the mass distribution, and the centre of gravity (CG). Therefore, a general dynamics mathematical model of a hexacopter was formulated where a stochastic state-space model was extracted in order to build anti-disturbance controllers. Based on the compound pendulum method, the disturbances model that simulates the robotic arm with a payload was inserted into the stochastic model. This study investigates two types of controllers in order to study the stability of a hexacopter. A controller based on Ackermann’s method and the other - on the linear quadratic regulator (LQR) approach - were presented. The latter constitutes a challenge for UAV control performance especially with the presence of uncertainties and disturbances.

An Investigation of the Impact of Manipulative Type and Instructional Guidance on Preschoolers' Symbolic Development of Quantities

ERIC Educational Resources Information Center

Carbonneau, Kira J.

2013-01-01

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

Hands-On Decoding: Guidelines for Using Manipulative Letters

ERIC Educational Resources Information Center

Pullen, Paige Cullen; Lane, Holly B.

2016-01-01

Manipulative objects have long been an essential tool in the development of mathematics knowledge and skills. A growing body of evidence suggests using manipulative letters for decoding practice is an also an effective method for teaching reading, particularly in improving the phonological and decoding skills of students at risk for reading…

Promoting Mathematical Connections Using Three-Dimensional Manipulatives

ERIC Educational Resources Information Center

Safi, Farshid; Desai, Siddhi

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra.

PubMed

Fu, Zhongtao; Yang, Wenyu; Yang, Zhen

2013-08-01

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Basic Phage Mathematics.

PubMed

Abedon, Stephen T; Katsaounis, Tena I

2018-01-01

Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage-bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage-bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.

Creating Cube Nets by Using Educational Tools in Pre-School

ERIC Educational Resources Information Center

Shiakalli, Maria Angela; Zacharos, Konstantinos; Markopoulos, Christos

2015-01-01

Our research programme, a part of which is presented in this paper, looked at four year old children's ability to use manipulatives in the construction of cube models. We looked at how pre-school children managed the creation of cube nets as a mathematical problem and whether graphical representations of solutions could become a useful tool in a…

A Comparison of Pre- and Post- Levels of Mathematics Anxiety among Preservice Teacher Candidates Enrolled in a Mathematics Methods Course.

ERIC Educational Resources Information Center

Sloan, Tina Rye; Vinson, Beth; Haynes, Jonita; Gresham, Regina

This study examined the effectiveness of a methods course in the reduction of mathematics anxiety levels among three groups of preservice teachers majoring in elementary education. The sample included 61 novices enrolled in a course entitled Mathematics for the Young Child. This methods course utilized concrete manipulatives and active learning…

The Application of Contextual Approach in Learning Mathematics to Improve Students Motivation at SMPN 1 Kupang

ERIC Educational Resources Information Center

Ekowati, Ch. Krisnandari; Darwis, Muhammad; Upa, H. M. D. Pua; Tahmir, Suradi

2015-01-01

This research is an action research which aims to implement contextual teaching and learning (CTL) approach to learn mathematics, focus on the integration subjects. The approach utilizes the use of mathematics manipulative so that students can understand a mathematical concept to construct their own. The method which used in this research are…

Technology, Active Learning, and Retention in General Education Mathematics

ERIC Educational Resources Information Center

Levi, Inessa; Chahine, Iman; Garrett, Lauretta; Wang, Haifeng

2016-01-01

Difficulties in general education mathematics courses may be attributed to many factors, primarily low proficiency in symbol manipulation, a perception that mathematics is an area which eludes mastery, a lack of engagement and effective practice. Educational technology can be a powerful aid in overcoming these factors. This work describes the…

Techno-Mathematical Discourse: A Conceptual Framework for Analyzing Classroom Discussions

ERIC Educational Resources Information Center

Anderson-Pence, Katie L.

2017-01-01

Extensive research has been published on the nature of classroom mathematical discourse and on the impact of technology tools, such as virtual manipulatives (VM), on students' learning, while less research has focused on how technology tools facilitate that mathematical discourse. This paper presents an emerging construct, the Techno-Mathematical…

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review

PubMed Central

Chirikjian, G. S.

2016-01-01

Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed. PMID:27030786

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review.

PubMed

Chirikjian, G S

Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed.

Mathematical models of lignin biosynthesis

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

Faraji, Mojdeh; Fonseca, Luis; Escamilla-Trevino, Luis

Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in severalmore » reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon. Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.« less

Mathematical models of lignin biosynthesis

DOE PAGES

Faraji, Mojdeh; Fonseca, Luis; Escamilla-Trevino, Luis; ...

2018-02-09

Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in severalmore » reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon. Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.« less

Predicting reasoning from memory.

PubMed

Heit, Evan; Hayes, Brett K

2011-02-01

In an effort to assess the relations between reasoning and memory, in 8 experiments, the authors examined how well responses on an inductive reasoning task are predicted from responses on a recognition memory task for the same picture stimuli. Across several experimental manipulations, such as varying study time, presentation frequency, and the presence of stimuli from other categories, there was a high correlation between reasoning and memory responses (average r = .87), and these manipulations showed similar effects on the 2 tasks. The results point to common mechanisms underlying inductive reasoning and recognition memory abilities. A mathematical model, GEN-EX (generalization from examples), derived from exemplar models of categorization, is presented, which predicts both reasoning and memory responses from pairwise similarities among the stimuli, allowing for additional influences of subtyping and deterministic responding. (c) 2010 APA, all rights reserved.

A Comparison of Concrete and Virtual Manipulative Use in Third- and Fourth-Grade Mathematics

ERIC Educational Resources Information Center

Burns, Barbara A.; Hamm, Ellen M.

2011-01-01

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands-on) manipulatives as compared with virtual (computer-based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest-posttest design was employed with a sample of 91…

A mathematical model of nutrient influence on fungal competition.

PubMed

Jabed A Choudhury, M; M J Trevelyan, Philip; P Boswell, Graeme

2018-02-07

Fungi have a well-established role in nutrient cycling and are widely used as agents in biological control and in the remediation of polluted landscapes. Competition for resources between different fungal communities is common in these contexts and its outcome impacts on the success of such biotechnological applications. In this investigation a mathematical model is constructed to represent competition between two fungal colonies that have access to different resources. It is shown that the model equations display a multitude of travelling wave solutions and that the outcome of competition between two fungal biomasses can be controlled through the simple manipulation of the nutrient resources available to each. The model equations are also numerically integrated to illustrate the range of outcomes arising from fungal competition and these results are placed in context of established experimental observations. Copyright © 2017 Elsevier Ltd. All rights reserved.

MATHEMATICAL MANIPULATIONS OF ENANTIOMERIC DATA

EPA Science Inventory

The oral presentation describes the alternative method of peak fitting for the measurement of enantiomeric parameters such as enantiomeric ratio (ER) and enantiomer fraction (EF). The talk describes the disadvantage of using typical integrators, mathematical calculations such as...

The APU and the 1978 Mathematics Survey

ERIC Educational Resources Information Center

Bell, Alan

1977-01-01

A tentative structure for a survey concerned with assessing the whole range of outcomes of school mathematics education is outlined. The structure provides for surveying content categories, process categories, and attitudes, utilizing practical manipulative problems. (MN)

A mathematics content course and teaching efficacy beliefs of undergraduate majors in education.

PubMed

Alkhateeb, Haitham M; Abed, Adnan S

2003-10-01

This study was designed to assess the mathematics teaching efficacy beliefs of undergraduates in elementary education through a manipulative-based course in mathematics. Responses of 106 university undergraduates to the 21-item Mathematics Teaching Efficacy Beliefs administered as pre- and posttest without a control group showed a significant immediate postcourse change in their efficacy beliefs using dependent t test.

The Extensibility of an Interpreted Language Using Plugin Libraries

NASA Astrophysics Data System (ADS)

Herceg, Dorde; Radaković, Davorka

2011-09-01

Dynamic geometry software (DGS) are computer programs that allow one to create and manipulate geometrical drawings. They are mostly used in teaching and studying geometry. However, DGS can also be used to develop interactive drawings not directly related to geometry. Examples include teaching materials for numerical mathematics at secondary school and university levels, or interactive mathematical games for elementary school children. Such applications often surpass the intended purposes of the DGS and may require complicated programming on behalf of the user. In this paper we present a simple plug-in model which enables easy development and deployment of interactive GUI components for "Geometrijica", a DGS we are developing on Silverlight.

A Study Exploring Exceptional Education Pre-Service Teachers' Mathematics Anxiety

ERIC Educational Resources Information Center

Gresham, Gina

2010-01-01

Fifty-two exceptional education pre-service teachers getting a K-6 endorsement were involved in this study that investigated the changes in levels of mathematics anxiety before and after a mathematics methods course for education majors. The changes were measured with respect to the use of manipulatives and other activities to make mathematics…

Virtual and Concrete Manipulatives: A Comparison of Approaches for Solving Mathematics Problems for Students with Autism Spectrum Disorder

ERIC Educational Resources Information Center

Bouck, Emily C.; Satsangi, Rajiv; Doughty, Teresa Taber; Courtney, William T.

2014-01-01

Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of…

Effects of Manipulative Use on PK-12 Mathematics Achievement: A Meta-Analysis

ERIC Educational Resources Information Center

Holmes, Amy B.

2013-01-01

Four figures and three tables are appended.There is growing consensus among researchers, educators, and policy makers about the need for greater emphasis on ambitious student-centered mathematics instruction in light of mounting concern about student mathematics performance in the intermediate grades and beyond. To facilitate educators' adoption…

Spatial Skill Profile of Mathematics Pre-Service Teachers

NASA Astrophysics Data System (ADS)

Putri, R. O. E.

2018-01-01

This study is aimed to investigate the spatial intelligence of mathematics pre-service teachers and find the best instructional strategy that facilitates this aspect. Data were collected from 35 mathematics pre-service teachers. The Purdue Spatial Visualization Test (PSVT) was used to identify the spatial skill of mathematics pre-service teachers. Statistical analysis indicate that more than 50% of the participants possessed spatial skill in intermediate level, whereas the other were in high and low level of spatial skill. The result also shows that there is a positive correlation between spatial skill and mathematics ability, especially in geometrical problem solving. High spatial skill students tend to have better mathematical performance compare to those in two other levels. Furthermore, qualitative analysis reveals that most students have difficulty in manipulating geometrical objects mentally. This problem mostly appears in intermediate and low-level spatial skill students. The observation revealed that 3-D geometrical figures is the best method that can overcome the mentally manipulation problem and develop the spatial visualization. Computer application can also be used to improve students’ spatial skill.

Application and enhancements of MOVIE.BYU

NASA Technical Reports Server (NTRS)

Gates, R. L.; Vonofenheim, W. H.

1984-01-01

MOVIE.BYU (MOVIE.BRIGHAM YOUNG UNIVERSITY) is a system of programs for the display and manipulation of data representing mathematical, architectural, and topological models in which the geometry may be described in terms of panel (n-sided polygons) and solid elements or contour lines. The MOVIE.BYU system has been used in a series of applications of LaRC. One application has been the display, creation, and manipulation of finite element models in aeronautic/aerospace research. These models have been displayed on both vector and color raster devices, and the user has the option to modify color and shading parameters on these color raster devices. Another application involves the display of scalar functions (temperature, pressure, etc.) over the surface of a given model. This capability gives the researcher added flexibility in the analysis of the model and its accompanying data. Limited animation (frame-by-frame creation) has been another application of MOVIE.BYU in the modeling of kinematic processes in antenna structures.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

An object oriented implementation of the Yeadon human inertia model

PubMed Central

Dembia, Christopher; Moore, Jason K.; Hubbard, Mont

2015-01-01

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input. PMID:25717365

An object oriented implementation of the Yeadon human inertia model.

PubMed

Dembia, Christopher; Moore, Jason K; Hubbard, Mont

2014-01-01

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input.

The graphics calculator in mathematics education: A critical review of recent research

NASA Astrophysics Data System (ADS)

Penglase, Marina; Arnold, Stephen

1996-04-01

The graphics calculator, sometimes referred to as the "super calculator," has sparked great interest among mathematics educators. Considered by many to be a tool which has the potential to revolutionise mathematics education, a significant amount of research has been conducted into its effectiveness as a tool for instruction and learning within precalculus and calculus courses, specifically in the study of functions, graphing and modelling. Some results suggest that these devices (a) can facilitate the learning of functions and graphing concepts and the development of spatial visualisation skills; (b) promote mathematical investigation and exploration; and (c) encourage a shift in emphasis from algebraic manipulation and proof to graphical investigation and examination of the relationship between graphical, algebraic and geometric representations. Other studies, however, indicate that there is still a need for manipulative techniques in the learning of function and graphing concepts, that the use of graphics calculators may not facilitate the learning of particular precalculus topics, and that some "de-skilling" may occur, especially among males. It is the contention of this paper, however, that much of the research in this new and important field fails to provide clear guidance or even to inform debate in adequate ways regarding the role of graphics calculators in mathematics teaching and learning. By failing to distinguish the role of the tool from that of the instructional process, many studies reviewed could be more appropriately classified as "program evaluations" rather than as research on the graphics calculator per se. Further, claims regarding the effectiveness of the graphics calculator as a tool for learning frequently fail to recognise that judgments of effectiveness result directly from existing assumptions regarding both assessment practice and student "achievement."

The Impact of a Monitoring Scheme on Engagement in an Online Course

ERIC Educational Resources Information Center

Burke, Grainne; Mac an Bhaird, Ciaran; O'Shea, Ann

2012-01-01

In the National University of Ireland Maynooth, in-coming first-year mathematics students are given a diagnostic test. The purpose of this test is to measure their basic knowledge and manipulation skills in mathematics. Those who fail this test are deemed at risk of failing their mathematics modules and are enrolled in a supplementary online…

Finite Element Method-Based Kinematics and Closed-Loop Control of Soft, Continuum Manipulators.

PubMed

Bieze, Thor Morales; Largilliere, Frederick; Kruszewski, Alexandre; Zhang, Zhongkai; Merzouki, Rochdi; Duriez, Christian

2018-06-01

This article presents a modeling methodology and experimental validation for soft manipulators to obtain forward kinematic model (FKM) and inverse kinematic model (IKM) under quasi-static conditions (in the literature, these manipulators are usually classified as continuum robots. However, their main characteristic of interest in this article is that they create motion by deformation, as opposed to the classical use of articulations). It offers a way to obtain the kinematic characteristics of this type of soft robots that is suitable for offline path planning and position control. The modeling methodology presented relies on continuum mechanics, which does not provide analytic solutions in the general case. Our approach proposes a real-time numerical integration strategy based on finite element method with a numerical optimization based on Lagrange multipliers to obtain FKM and IKM. To reduce the dimension of the problem, at each step, a projection of the model to the constraint space (gathering actuators, sensors, and end-effector) is performed to obtain the smallest number possible of mathematical equations to be solved. This methodology is applied to obtain the kinematics of two different manipulators with complex structural geometry. An experimental comparison is also performed in one of the robots, between two other geometric approaches and the approach that is showcased in this article. A closed-loop controller based on a state estimator is proposed. The controller is experimentally validated and its robustness is evaluated using Lypunov stability method.

Task- and age-dependent effects of visual stimulus properties on children's explicit numerosity judgments.

PubMed

Defever, Emmy; Reynvoet, Bert; Gebuis, Titia

2013-10-01

Researchers investigating numerosity processing manipulate the visual stimulus properties (e.g., surface). This is done to control for the confound between numerosity and its visual properties and should allow the examination of pure number processes. Nevertheless, several studies have shown that, despite different visual controls, visual cues remained to exert their influence on numerosity judgments. This study, therefore, investigated whether the impact of the visual stimulus manipulations on numerosity judgments is dependent on the task at hand (comparison task vs. same-different task) and whether this impact changes throughout development. In addition, we examined whether the influence of visual stimulus manipulations on numerosity judgments plays a role in the relation between performance on numerosity tasks and mathematics achievement. Our findings confirmed that the visual stimulus manipulations affect numerosity judgments; more important, we found that these influences changed with increasing age and differed between the comparison and the same-different tasks. Consequently, direct comparisons between numerosity studies using different tasks and age groups are difficult. No meaningful relationship between the performance on the comparison and same-different tasks and mathematics achievement was found in typically developing children, nor did we find consistent differences between children with and without mathematical learning disability (MLD). Copyright © 2013 Elsevier Inc. All rights reserved.

Use of symbolic computation in robotics education

NASA Technical Reports Server (NTRS)

Vira, Naren; Tunstel, Edward

1992-01-01

An application of symbolic computation in robotics education is described. A software package is presented which combines generality, user interaction, and user-friendliness with the systematic usage of symbolic computation and artificial intelligence techniques. The software utilizes MACSYMA, a LISP-based symbolic algebra language, to automatically generate closed-form expressions representing forward and inverse kinematics solutions, the Jacobian transformation matrices, robot pose error-compensation models equations, and Lagrange dynamics formulation for N degree-of-freedom, open chain robotic manipulators. The goal of such a package is to aid faculty and students in the robotics course by removing burdensome tasks of mathematical manipulations. The software package has been successfully tested for its accuracy using commercially available robots.

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1975-01-01

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Mathematical model of temephos resistance in Aedes aegypti mosquito population

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

So, Here's the Story

ERIC Educational Resources Information Center

Columba, Lynn

2013-01-01

Mathematics is about reasoning, patterns, and making sense of things. Children's literature provides a powerful opportunity to foster unique experiences in mathematics learning. Storybooks, thinking strategies, and manipulatives offer a winning combination for mastering multiplication facts based on conceptual ideas and relationships. The most…

Chalk It up to Experience: Using Chalkboard Paint to Create Mathematical Manipulatives

ERIC Educational Resources Information Center

Young, Andrea; Bruhns, Kathryn

2016-01-01

In this article, we give two examples of creating portable chalkboards using chalkboard paint for students to use during cooperative learning. This provides a creative method for professors to facilitate active learning in the undergraduate mathematics classroom.

Chalk it up to experience: using chalkboard paint to create mathematical manipulatives

NASA Astrophysics Data System (ADS)

Young, Andrea; Bruhns, Kathryn

2016-08-01

In this article, we give two examples of creating portable chalkboards using chalkboard paint for students to use during cooperative learning. This provides a creative method for professors to facilitate active learning in the undergraduate mathematics classroom.

Moving beyond Type I and Type II neuron types.

PubMed

Skinner, Frances K

2013-01-01

In 1948, Hodgkin delineated different classes of axonal firing.  This has been mathematically translated allowing insight and understanding to emerge.  As such, the terminology of 'Type I' and 'Type II' neurons is commonplace in the Neuroscience literature today.  Theoretical insights have helped us realize that, for example, network synchronization depends on whether neurons are Type I or Type II.  Mathematical models are precise with analyses (considering Type I/II aspects), but experimentally, the distinction can be less clear.  On the other hand, experiments are becoming more sophisticated in terms of distinguishing and manipulating particular cell types but are limited in terms of being able to consider network aspects simultaneously.   Although there is much work going on mathematically and experimentally, in my opinion it is becoming common that models are either superficially linked with experiment or not described in enough detail to appreciate the biological context.  Overall, we all suffer in terms of impeding our understanding of brain networks and applying our understanding to neurological disease.  I suggest that more modelers become familiar with experimental details and that more experimentalists appreciate modeling assumptions. In other words, we need to move beyond our comfort zones.

The transition to formal thinking in mathematics

NASA Astrophysics Data System (ADS)

Tall, David

2008-09-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of `three worlds of mathematics'- the `conceptual-embodied' world based on perception, action and thought experiment, the `proceptual-symbolic' world of calculation and algebraic manipulation compressing processes such as counting into concepts such as number, and the `axiomatic-formal' world of set-theoretic concept definitions and mathematical proof. Each `world' has its own sequence of development and its own forms of proof that may be blended together to give a rich variety of ways of thinking mathematically. This reveals mathematical thinking as a blend of differing knowledge structures; for instance, the real numbers blend together the embodied number line, symbolic decimal arithmetic and the formal theory of a complete ordered field. Theoretical constructs are introduced to describe how genetic structures set before birth enable the development of mathematical thinking, and how experiences that the individual has met before affect their personal growth. These constructs are used to consider how students negotiate the transition from school to university mathematics as embodiment and symbolism are blended with formalism. At a higher level, structure theorems proved in axiomatic theories link back to more sophisticated forms of embodiment and symbolism, revealing the intimate relationship between the three worlds.

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.

Affordance Access Matters: Preschool Children's Learning Progressions While Interacting with Touch-Screen Mathematics Apps

ERIC Educational Resources Information Center

Bullock, Emma P.; Shumway, Jessica F.; Watts, Christina M.; Moyer-Packenham, Patricia S.

2017-01-01

The purpose of this study was to contribute to the research on mathematics app use by very young children, and specifically mathematics apps for touch-screen mobile devices that contain virtual manipulatives. The study used a convergent parallel mixed methods design, in which quantitative and qualitative data were collected in parallel, analyzed…

Using Virtual Manipulative Instruction to Teach the Concepts of Area and Perimeter to Secondary Students with Learning Disabilities

ERIC Educational Resources Information Center

Satsangi, Rajiv; Bouck, Emily C.

2015-01-01

Secondary students with a learning disability in mathematics often struggle with the academic demands presented in advanced mathematics courses, such as algebra and geometry. With greater emphasis placed on problem solving and higher level thinking skills in these subject areas, students with a learning disability in mathematics often fail to keep…

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

ERIC Educational Resources Information Center

Donabella, Mark A.; Rule, Audrey C.

2008-01-01

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

Behavioural manipulation of insect hosts by Baculoviridae as a process of niche construction.

PubMed

Hamblin, Steven; Tanaka, Mark M

2013-08-16

Niche construction has received increasing attention in recent years as a vital force in evolution and examples of niche construction have been identified in a wide variety of taxa, but viruses are conspicuously absent. In this study we explore how niche construction can lead to viruses engineering their hosts (including behavioural manipulation) with feedback on selective pressures for viral transmission and virulence. To illustrate this concept we focus on Baculoviridae, a family of invertebrate viruses that have evolved to modify the feeding behaviour of their lepidopteran hosts and liquefy their cadavers as part of the course of infection. We present a mathematical model showing how niche construction leads to feedback from the behavioural manipulation to the liquefaction of the host, linking the evolution of both of these traits, and show how this association arises from the action of niche construction. Model results show that niche construction is plausible in this system and delineates the conditions under which niche construction will occur. Niche construction in this system is also shown to be sensitive to parameter values that reflect ecological forces. Our model demonstrates that niche construction can be a potent force in viral evolution and can lead to the acquisition and maintenance of the behavioural manipulation and liquefaction traits in Baculoviridae via the niche constructing effects on the host. These results show the potential for niche construction theory to provide new insights into viral evolution.

[Comparative analysis of the efficacy of a playful-narrative program to teach mathematics at pre-school level].

PubMed

Gil Llario, M D; Vicent Catalá, Consuelo

2009-02-01

Comparative analysis of the efficacy of a playful-narrative program to teach mathematics at pre-school level. In this paper, the effectiveness of a programme comprising several components that are meant to consolidate mathematical concepts and abilities at the pre-school level is analyzed. The instructional methodology of this programme is compared to other methodologies. One-hundred 5-6 year-old children made up the sample that was distributed in the following conditions: (1) traditional methodology; (2) methodology with perceptual and manipulative components, and (3) methodology with language and playful components. Mathematical competence was assessed with the Mathematical Criterial Pre-school Test and the subtest of quantitative-numeric concepts of BADyG. Participants were evaluated before and after the academic course during which they followed one of these methodologies. The results show that the programme with language and playful components is more effective than the traditional methodology (p<.000) and also more effective than the perceptual and manipulative methodology (p<.000). Implications of the results for instructional practices are analyzed.

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

Tapping into Trapezoid

ERIC Educational Resources Information Center

Wanko, Jeffrey J.

2005-01-01

Trapezoids help in understanding the role of definition in mathematics in investigating other mathematical ideas and in understanding the examples of symbolic manipulation and multiple representations. Trapezoids offers additional exposure to a polygon that gets little attention in the school curriculum yet provides for a number of rich…

Quantitative model validation of manipulative robot systems

NASA Astrophysics Data System (ADS)

Kartowisastro, Iman Herwidiana

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

Multi-scale modelling of rubber-like materials and soft tissues: an appraisal

PubMed Central

Puglisi, G.

2016-01-01

We survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro- and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties. PMID:27118927

39 CFR 3050.1 - Definitions applicable to this part.

Code of Federal Regulations, 2010 CFR

2010-07-01

..., mathematical, or statistical theory, precept, or assumption applied by the Postal Service in producing a... manipulation technique whose validity does not require the acceptance of a particular economic, mathematical, or statistical theory, precept, or assumption. A change in quantification technique should not change...

Multiplayer Activities That Develop Mathematical Coordination.

ERIC Educational Resources Information Center

Bricker, Lauren J.; Tanimoto, Steven L.; Rothenberg, Alex I.; Hutama, Danny C.; Wong, Tina H.

Four computer applications are presented that encourage students to develop "mathematical coordination"--the ability to manipulate numerical variables in cooperation with other students so as to achieve a definite goal. The programs enable a form of computer-supported cooperative learning (CSCL). This paper describes the rationale and…

Technology to Develop Algebraic Reasoning

ERIC Educational Resources Information Center

Polly, Drew

2011-01-01

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

Technology's Impact on Fraction Learning: An Experimental Comparison of Virtual and Physical Manipulatives

ERIC Educational Resources Information Center

Mendiburo, Maria; Hasselbring, Ted

2011-01-01

Fractions are among the most difficult mathematical concepts for elementary school students to master (Behr, Harel, Post, & Lesh, 1992; Bezuk & Cramer, 1989; Moss & Case, 1999). Research indicates that manipulatives (e.g. fractions circles, fractions strips) positively impact students' conceptual and procedural understanding of…

Manipulative and Numerical Spreadsheet Templates for the Study of Discrete Structures.

ERIC Educational Resources Information Center

Abramovich, Sergei

1998-01-01

Argues that basic components of discrete mathematics can be introduced to students through gradual elaboration of experiences with iconic spreadsheet-based simulations of concrete materials. Suggests that the study of homogeneous and heterogeneous patterns of manipulative spreadsheet templates allows for appreciation of the development of…

Scratch Your Brain Where It Itches: Math Games, Tricks and Quick Activities, Book C-1.

ERIC Educational Resources Information Center

Brumbaugh, Doug

This resource book contains mathematical games, tricks, and quick activities for the classroom. Categories of activities include computation, manipulative challenges, puzzlers, picky puzzlers, patterns, measurement, money, and riddles. The computation section contains 13 classroom games and activities along with 4 manipulative challenges.…

Creating Tesselations with Pavement Chalk: Implementing Best Practices in Mathematics

ERIC Educational Resources Information Center

Furner, Joseph M.; Goodman, Barbara; Meeks, Shirley

2004-01-01

Implementing best practices like cooperative learning, using concrete manipulatives, problem solving, technology, active learning, multi-age grouping, and team teaching have shown benefits for students when learning mathematics concepts within the curriculum (Zemelman, Daniels & Hyde, 1998; NCTM, 2000). What started as a professional development…

The reasonable effectiveness of mathematics in the natural sciences

NASA Astrophysics Data System (ADS)

Harvey, Alex

2011-12-01

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.

Concurrent processing simulation of the space station

NASA Technical Reports Server (NTRS)

Gluck, R.; Hale, A. L.; Sunkel, John W.

1989-01-01

The development of a new capability for the time-domain simulation of multibody dynamic systems and its application to the study of a large angle rotational maneuvers of the Space Station is described. The effort was divided into three sequential tasks, which required significant advancements of the state-of-the art to accomplish. These were: (1) the development of an explicit mathematical model via symbol manipulation of a flexible, multibody dynamic system; (2) the development of a methodology for balancing the computational load of an explicit mathematical model for concurrent processing; and (3) the implementation and successful simulation of the above on a prototype Custom Architectured Parallel Processing System (CAPPS) containing eight processors. The throughput rate achieved by the CAPPS operating at only 70 percent efficiency, was 3.9 times greater than that obtained sequentially by the IBM 3090 supercomputer simulating the same problem. More significantly, analysis of the results leads to the conclusion that the relative cost effectiveness of concurrent vs. sequential digital computation will grow substantially as the computational load is increased. This is a welcomed development in an era when very complex and cumbersome mathematical models of large space vehicles must be used as substitutes for full scale testing which has become impractical.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed

Morgan, Paul L; Farkas, George; Maczuga, Steve

2015-06-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1 st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement-three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1 st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ES s = .05-.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ES s = .03-.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

PubMed

Luong, Tuan Anh; Cho, Kyeong Ho; Song, Min Geun; Koo, Ja Choon; Choi, Hyouk Ryeol; Moon, Hyungpil

2018-04-01

Artificial muscle actuators made from commercial nylon fishing lines have been recently introduced and shown as a new type of actuator with high performance. However, the actuators also exhibit significant nonlinearities, which make them difficult to control, especially in precise trajectory-tracking applications. In this article, we present a nonlinear mathematical model of a conductive supercoiled polymer (SCP) actuator driven by Joule heating for model-based feedback controls. Our efforts include modeling of the hysteresis behavior of the actuator. Based on nonlinear modeling, we design a sliding mode controller for SCP actuator-driven manipulators. The system with proposed control law is proven to be asymptotically stable using the Lyapunov theory. The control performance of the proposed method is evaluated experimentally and compared with that of a proportional-integral-derivative (PID) controller through one-degree-of-freedom SCP actuator-driven manipulators. Experimental results show that the proposed controller's performance is superior to that of a PID controller, such as the tracking errors are nearly 10 times smaller compared with those of a PID controller, and it is more robust to external disturbances such as sensor noise and actuator modeling error.

Cactus: Writing an Article

ERIC Educational Resources Information Center

Hyde, Hartley; Spencer, Toby

2010-01-01

Some people became mathematics or science teachers by default. There was once such a limited range of subjects that students who could not write essays did mathematics and science. Computers changed that. Word processor software helped some people overcome huge spelling and grammar hurdles and made it easy to edit and manipulate text. Would-be…

A Design To Improve Children's Competencies in Solving Mathematical Word Problems.

ERIC Educational Resources Information Center

Zimmerman, Helene

A discrepancy exists between children's ability to compute and their ability to solve mathematical word problems. The literature suggests a variety of methods that have been attempted to improve this skill with varying success. The utilization of manipulatives, visualization, illustration, and emphasis on improving listening skills all were…

Upper-Division Student Difficulties with the Dirac Delta Function

ERIC Educational Resources Information Center

Wilcox, Bethany R.; Pollock, Steven J.

2015-01-01

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…

Mathematics Education and Manipulatives: Which, When, How?

ERIC Educational Resources Information Center

Larkin, Kevin

2016-01-01

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

From Sailing Ships to Subtraction Symbols: Multiple Representations to Support Abstraction

ERIC Educational Resources Information Center

Jao, Limin

2013-01-01

Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…

A Graphical Approach to Teaching Amplifier Design at the Undergraduate Level

ERIC Educational Resources Information Center

Assaad, R. S.; Silva-Martinez, J.

2009-01-01

Current methods of teaching basic amplifier design at the undergraduate level need further development to match today's technological advances. The general class approach to amplifier design is analytical and heavily based on mathematical manipulations. However, the students mathematical abilities are generally modest, creating a void in which…

Robot Manipulations: A Synergy of Visualization, Computation and Action for Spatial Instruction

ERIC Educational Resources Information Center

Verner, Igor M.

2004-01-01

This article considers the use of a learning environment, RoboCell, where manipulations of objects are performed by robot operations specified through the learner's application of mathematical and spatial reasoning. A curriculum is proposed relating to robot kinematics and point-to-point motion, rotation of objects, and robotic assembly of spatial…

The Use of Manipulatives in Mathematics Education

ERIC Educational Resources Information Center

Larbi, Ernest; Mavis, Okyere

2016-01-01

The study was designed to investigate the efficacy of using algebra tile manipulatives in junior high school students' performance. The study sample comprised 56 students from two schools purposely selected from two towns within the Komenda Edina Eguafo Abirem municipality. The students were made up of two groups; the experimental and the control…

Visualizing Three-Dimensional Calculus Concepts: The Study of a Manipulative's Effectiveness

ERIC Educational Resources Information Center

McGee, Daniel, Jr.; Moore-Russo, Deborah; Ebersole, Dennis; Lomen, David O.; Quintero, Maider Marin

2012-01-01

With the help of the National Science Foundation, the Department of Mathematics at the University of Puerto Rico in Mayaguez has developed a set of manipulatives to help students of science and engineering visualize concepts relating to points, surfaces, curves, contours, and vectors in three dimensions. This article will present the manipulatives…

Supporting Teachers' Technological Pedagogical Content Knowledge of Fractions through Co-Designing a Virtual Manipulative

ERIC Educational Resources Information Center

Hansen, Alice; Mavrikis, Manolis; Geraniou, Eirini

2016-01-01

This study explores the impact that co-designing a virtual manipulative, Fractions Lab, had on teachers' professional development. Tapping into an existing community of practice of mathematics specialist teachers, the study identifies how a cooperative enquiry approach utilising workshops and school-based visits challenged 23 competent primary…

Learning Mathematics with Technology: The Influence of Virtual Manipulatives on Different Achievement Groups

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia; Suh, Jennifer

2012-01-01

This study examined the influence of virtual manipulatives on different achievement groups during a teaching experiment in four fifth-grade classrooms. During a two-week unit focusing on two rational number concepts (fraction equivalence and fraction addition with unlike denominators) one low achieving, two average achieving, and one high…

Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

ERIC Educational Resources Information Center

Ozgun-Koca, S. Ash

2010-01-01

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

Behavioural manipulation of insect hosts by Baculoviridae as a process of niche construction

PubMed Central

2013-01-01

Background Niche construction has received increasing attention in recent years as a vital force in evolution and examples of niche construction have been identified in a wide variety of taxa, but viruses are conspicuously absent. In this study we explore how niche construction can lead to viruses engineering their hosts (including behavioural manipulation) with feedback on selective pressures for viral transmission and virulence. To illustrate this concept we focus on Baculoviridae, a family of invertebrate viruses that have evolved to modify the feeding behaviour of their lepidopteran hosts and liquefy their cadavers as part of the course of infection. Results We present a mathematical model showing how niche construction leads to feedback from the behavioural manipulation to the liquefaction of the host, linking the evolution of both of these traits, and show how this association arises from the action of niche construction. Model results show that niche construction is plausible in this system and delineates the conditions under which niche construction will occur. Niche construction in this system is also shown to be sensitive to parameter values that reflect ecological forces. Conclusions Our model demonstrates that niche construction can be a potent force in viral evolution and can lead to the acquisition and maintenance of the behavioural manipulation and liquefaction traits in Baculoviridae via the niche constructing effects on the host. These results show the potential for niche construction theory to provide new insights into viral evolution. PMID:23953199

Robot Control Based On Spatial-Operator Algebra

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo; Kreutz, Kenneth K.; Jain, Abhinandan

1992-01-01

Method for mathematical modeling and control of robotic manipulators based on spatial-operator algebra providing concise representation and simple, high-level theoretical frame-work for solution of kinematical and dynamical problems involving complicated temporal and spatial relationships. Recursive algorithms derived immediately from abstract spatial-operator expressions by inspection. Transition from abstract formulation through abstract solution to detailed implementation of specific algorithms to compute solution greatly simplified. Complicated dynamical problems like two cooperating robot arms solved more easily.

The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-06-01

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming.

PubMed

Ashkenazi, Sarit

2018-02-05

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.

Construction of a model demonstrating neural pathways and reflex arcs.

PubMed

Chan, V; Pisegna, J M; Rosian, R L; DiCarlo, S E

1996-12-01

Employment opportunities in the future will require higher skills and an understanding of mathematics and science. As a result of the growing number of careers that require solid science and mathematics training, the methods of science education are undergoing major reform. To adequately equip students for technologically advanced positions, new teaching methods must be developed that prepare tomorrow's workforce for the challenges of the 21st century. One such method is the use of models. By actively building and manipulating concrete models that represent scientific concepts, students are involved in the most basic level of Piaget's learning scheme: the sensorimotor stage. Models are useful in reaching all students at the foundational levels of learning, and further learning experiences are rapidly moved through higher learning levels. This success ensures greater comprehension and understanding compared with the traditional methods of rote memorization. We developed an exercise for the construction of an inexpensive, easy-to-build model demonstrating neural pathways and reflex arcs. Our exercise also includes many supplemental teaching tools. The exercise is designed to fulfill the need of sound physiological teaching materials for high school students.

Manipulatives and Problem Situations as Escalators for Students' Geometric Understanding: A Semiotic Analysis

ERIC Educational Resources Information Center

Daher, Wajeeh M.

2014-01-01

Mathematical learning and teaching are increasingly seen as a multimodal experience involved in cultural and social semiotic registers and means, and as such social-cultural semiotic analysis is expected to shed light on learning and teaching processes occurring in the mathematics classroom. In this research, three social-cultural semiotic…

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…

Students' Attention When Using Touchscreens and Pen Tablets in a Mathematics Classroom

ERIC Educational Resources Information Center

Chen, Cheng-Huan; Chiu, Chiung-Hui; Lin, Chia-Ping; Chou, Ying-Chun

2017-01-01

Aim/Purpose: The present study investigated and compared students' attention in terms of time-on-task and number of distractors between using a touchscreen and a pen tablet in mathematical problem solving activities with virtual manipulatives. Background: Although there is an increasing use of these input devices in educational practice, little…

Fostering Mathematical Understanding through Physical and Virtual Manipulatives

ERIC Educational Resources Information Center

Loong, Esther Yook Kin

2014-01-01

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

The Relationship between the Use of Virtual Manipulatives and Mathematics Performance among Fifth Grade Students

ERIC Educational Resources Information Center

Bryan, Rosemarie

2014-01-01

Students in U.S. public schools have consistently recorded substandard scores on measures of school performance in mathematics. This substandard performance could adversely affect the nation's future economic competitiveness, growth, and welfare. Educational and political leaders have sought school reforms that will result in U.S. students scoring…

Mathematics Hiding in the Nets for a Cube

ERIC Educational Resources Information Center

Jeon, Kyungsoon

2009-01-01

Whether they are third graders or teacher candidates, students can learn about perimeter and area while having fun manipulating two-dimensional figures into three-dimensional objects. In this article, the author describes a common mathematical activity for geometry students by creating nets for a cube. By making connections between nets in two…

Cards in the Classroom: Mathematics and Methods.

ERIC Educational Resources Information Center

Baker, Robert N.

This report researches the use of a standard deck of playing cards in entry-level college mathematics classrooms. The study looks at published research on the use of cards, and reviews pedagogic concerns directly related to the implementation of playing cards in the classroom--including the appropriateness of manipulatives, the link to cooperative…

Focus in High School Mathematics: Reasoning and Sense Making in Algebra

ERIC Educational Resources Information Center

Graham, Karen; Cuoco, Albert; Zimmermann, Gwendolyn

2010-01-01

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

A randomized trial testing the efficacy of modifications to the nutrition facts table on comprehension and use of nutrition information by adolescents and young adults in Canada.

PubMed

Hobin, E; Sacco, J; Vanderlee, L; White, C M; Zuo, F; Sheeshka, J; McVey, G; Fodor O'Brien, M; Hammond, D

2015-12-01

Given the proposed changes to nutrition labelling in Canada and the dearth of research examining comprehension and use of nutrition facts tables (NFts) by adolescents and young adults, our objective was to experimentally test the efficacy of modifications to NFts on young Canadians' ability to interpret, compare and mathematically manipulate nutrition information in NFts on prepackaged food. An online survey was conducted among 2010 Canadians aged 16 to 24 years drawn from a consumer sample. Participants were randomized to view two NFts according to one of six experimental conditions, using a between-groups 2 x 3 factorial design: serving size (current NFt vs. standardized serving-sizes across similar products) x percent daily value (% DV) (current NFt vs. "low/med/high" descriptors vs. colour coding). The survey included seven performance tasks requiring participants to interpret, compare and mathematically manipulate nutrition information on NFts. Separate modified Poisson regression models were conducted for each of the three outcomes. The ability to compare two similar products was significantly enhanced in NFt conditions that included standardized serving-sizes (p ≤ .001 for all). Adding descriptors or colour coding of % DV next to calories and nutrients on NFts significantly improved participants' ability to correctly interpret % DV information (p ≤ .001 for all). Providing both standardized serving-sizes and descriptors of % DV had a modest effect on participants' ability to mathematically manipulate nutrition information to calculate the nutrient content of multiple servings of a product (relative ratio = 1.19; 95% confidence limit: 1.04-1.37). Standardizing serving-sizes and adding interpretive % DV information on NFts improved young Canadians' comprehension and use of nutrition information. Some caution should be exercised in generalizing these findings to all Canadian youth due to the sampling issues associated with the study population. Further research is needed to replicate this study in a more heterogeneous sample in Canada and across a range of food products and categories.

Dialogue-Based Activities and Manipulatives to Engage Liberal Arts Majors in Mathematics

ERIC Educational Resources Information Center

Price, James C.

2015-01-01

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature.

PubMed

Caviola, Sara; Carey, Emma; Mammarella, Irene C; Szucs, Denes

2017-01-01

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth "strategy selection") in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

Ultrasonic Apparatus and Method to Assess Compartment Syndrome

NASA Technical Reports Server (NTRS)

Yost, William T. (Inventor); Ueno, Toshiaki (Inventor); Hargens, Alan R. (Inventor)

2009-01-01

A process and apparatus for measuring pressure buildup in a body compartment that encases muscular tissue. The method includes assessing the body compartment configuration and identifying the effect of pulsatible components on compartment dimensions and muscle tissue characteristics. This process is used in preventing tissue necrosis, and in decisions of whether to perform surgery on the body compartment for prevention of Compartment Syndrome. An apparatus is used for measuring pressure build-up in the body compartment having components for imparting ultrasonic waves such as a transducer, placing the transducer to impart the ultrasonic waves, capturing the imparted ultrasonic waves, mathematically manipulating the captured ultrasonic waves and categorizing pressure build-up in the body compartment from the mathematical manipulations.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed Central

Morgan, Paul L.; Farkas, George; Maczuga, Steve

2015-01-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement—three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ESs = .05–.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ESs = .03–.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD. PMID:26180268

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

NASA Astrophysics Data System (ADS)

Klewicki, J. C.; Chini, G. P.; Gibson, J. F.

2017-03-01

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.

The role of the real-time simulation facility, SIMFAC, in the design, development and performance verification of the Shuttle Remote Manipulator System (SRMS) with man-in-the-loop

NASA Technical Reports Server (NTRS)

Mccllough, J. R.; Sharpe, A.; Doetsch, K. H.

1980-01-01

The SIMFAC has played a vital role in the design, development, and performance verification of the shuttle remote manipulator system (SRMS) to be installed in the space shuttle orbiter. The facility provides for realistic man-in-the-loop operation of the SRMS by an operator in the operator complex, a flightlike crew station patterned after the orbiter aft flight deck with all necessary man machine interface elements, including SRMS displays and controls and simulated out-of-the-window and CCTV scenes. The characteristics of the manipulator system, including arm and joint servo dynamics and control algorithms, are simulated by a comprehensive mathematical model within the simulation subsystem of the facility. Major studies carried out using SIMFAC include: SRMS parameter sensitivity evaluations; the development, evaluation, and verification of operating procedures; and malfunction simulation and analysis of malfunction performance. Among the most important and comprehensive man-in-the-loop simulations carried out to date on SIMFAC are those which support SRMS performance verification and certification when the SRMS is part of the integrated orbiter-manipulator system.

Biological Aging - Criteria for Modeling and a New Mechanistic Model

NASA Astrophysics Data System (ADS)

Pletcher, Scott D.; Neuhauser, Claudia

To stimulate interaction and collaboration across scientific fields, we introduce a minimum set of biological criteria that theoretical models of aging should satisfy. We review results of several recent experiments that examined changes in age-specific mortality rates caused by genetic and environmental manipulation. The empirical data from these experiments is then used to test mathematical models of aging from several different disciplines, including molecular biology, reliability theory, physics, and evolutionary biology/population genetics. We find that none of the current models are consistent with all of the published experimental findings. To provide an example of how our criteria might be applied in practice, we develop a new conceptual model of aging that is consistent with our observations.

Research Reporting Sections, Annual Meeting of the National Council of Teachers of Mathematics (57th, Boston, Massachusetts, April 18-21, 1979).

ERIC Educational Resources Information Center

Higgins, Jon L., Ed.

This document provides abstracts of 20 research reports. Topics covered include: children's comprehension of simple story problems; field independence and group instruction; problem-solving competence and memory; spatial visualization and the use of manipulative materials; effects of games on mathematical skills; problem-solving ability and right…

Elementary School Teachers' Perceptions toward ICT: The Case of Using Magic Board for Teaching Mathematics

ERIC Educational Resources Information Center

Yuan, Yuan; Lee, Chun-Yi

2012-01-01

This study aims at investigating elementary school teachers' perceptions toward to the use of ICT. Magic Board, an interactive web-based environment which provides a set of virtual manipulatives for elementary mathematics, is used as the case of ICT. After participating in Magic Board workshops, 250 elementary school teachers in Taiwan responded…

3D Designing for Mathematical Learning

ERIC Educational Resources Information Center

Greenstein, Steven; Leszczynski, Eliza; Fernández, Eileen

2017-01-01

Inspired by the promise of new 3D technologies and the proposition that new tools make innovation possible, this article provides a case study of how a tool called Thirty6 was designed and used in classrooms by mathematics teachers in their own varied and invented ways. Unlike established manipulatives that are designed to support the learning of…

Less Is More--Mathematical Manipulatives in Early Childhood Education

ERIC Educational Resources Information Center

Björklund, Camilla

2014-01-01

This article is a discussion drawing on a learning study with a teacher working with one- and two-year-olds. The focal interest is a scrutiny of the use of manipulative objects, emanating from observations of a teacher's and children's use of, and responses to the use of, different objects. The concept of size and the notions "large" and…

An Analytical Framework for Categorizing the Use of CAS Symbolic Manipulation in Textbooks

ERIC Educational Resources Information Center

Davis, Jon D.; Fonger, Nicole L.

2015-01-01

The symbolic manipulation capabilities of computer algebra systems, which we refer to as CAS-S, are now becoming instantiated within secondary mathematics textbooks in the United States for the first time. While a number of research studies have examined how teachers use this technology in their classrooms, one of the most important factors in how…

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes.

PubMed

Handy, Gregory; Taheri, Marsa; White, John A; Borisyuk, Alla

2017-06-01

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

Kinematic Determination of an Unmodeled Serial Manipulator by Means of an IMU

NASA Astrophysics Data System (ADS)

Ciarleglio, Constance A.

Kinematic determination for an unmodeled manipulator is usually done through a-priori knowledge of the manipulator physical characteristics or external sensor information. The mathematics of the kinematic estimation, often based on Denavit- Hartenberg convention, are complex and have high computation requirements, in addition to being unique to the manipulator for which the method is developed. Analytical methods that can compute kinematics on-the fly have the potential to be highly beneficial in dynamic environments where different configurations and variable manipulator types are often required. This thesis derives a new screw theory based method of kinematic determination, using a single inertial measurement unit (IMU), for use with any serial, revolute manipulator. The method allows the expansion of reconfigurable manipulator design and simplifies the kinematic process for existing manipulators. A simulation is presented where the theory of the method is verified and characterized with error. The method is then implemented on an existing manipulator as a verification of functionality.

Contrasting response to nutrient manipulation in Arctic mesocosms are reproduced by a minimum microbial food web model.

PubMed

Larsen, Aud; Egge, Jorun K; Nejstgaard, Jens C; Di Capua, Iole; Thyrhaug, Runar; Bratbak, Gunnar; Thingstad, T Frede

2015-03-01

A minimum mathematical model of the marine pelagic microbial food web has previously shown to be able to reproduce central aspects of observed system response to different bottom-up manipulations in a mesocosm experiment Microbial Ecosystem Dynamics (MEDEA) in Danish waters. In this study, we apply this model to two mesocosm experiments (Polar Aquatic Microbial Ecology (PAME)-I and PAME-II) conducted at the Arctic location Kongsfjorden, Svalbard. The different responses of the microbial community to similar nutrient manipulation in the three mesocosm experiments may be described as diatom-dominated (MEDEA), bacteria-dominated (PAME-I), and flagellated-dominated (PAME-II). When allowing ciliates to be able to feed on small diatoms, the model describing the diatom-dominated MEDEA experiment give a bacteria-dominated response as observed in PAME I in which the diatom community comprised almost exclusively small-sized cells. Introducing a high initial mesozooplankton stock as observed in PAME-II, the model gives a flagellate-dominated response in accordance with the observed response also of this experiment. The ability of the model originally developed for temperate waters to reproduce population dynamics in a 10°C colder Arctic fjord, does not support the existence of important shifts in population balances over this temperature range. Rather, it suggests a quite resilient microbial food web when adapted to in situ temperature. The sensitivity of the model response to its mesozooplankton component suggests, however, that the seasonal vertical migration of Arctic copepods may be a strong forcing factor on Arctic microbial food webs.

Contrasting response to nutrient manipulation in Arctic mesocosms are reproduced by a minimum microbial food web model

PubMed Central

Larsen, Aud; Egge, Jorun K; Nejstgaard, Jens C; Di Capua, Iole; Thyrhaug, Runar; Bratbak, Gunnar; Thingstad, T Frede

2015-01-01

A minimum mathematical model of the marine pelagic microbial food web has previously shown to be able to reproduce central aspects of observed system response to different bottom-up manipulations in a mesocosm experiment Microbial Ecosystem Dynamics (MEDEA) in Danish waters. In this study, we apply this model to two mesocosm experiments (Polar Aquatic Microbial Ecology (PAME)-I and PAME-II) conducted at the Arctic location Kongsfjorden, Svalbard. The different responses of the microbial community to similar nutrient manipulation in the three mesocosm experiments may be described as diatom-dominated (MEDEA), bacteria-dominated (PAME-I), and flagellated-dominated (PAME-II). When allowing ciliates to be able to feed on small diatoms, the model describing the diatom-dominated MEDEA experiment give a bacteria-dominated response as observed in PAME I in which the diatom community comprised almost exclusively small-sized cells. Introducing a high initial mesozooplankton stock as observed in PAME-II, the model gives a flagellate-dominated response in accordance with the observed response also of this experiment. The ability of the model originally developed for temperate waters to reproduce population dynamics in a 10°C colder Arctic fjord, does not support the existence of important shifts in population balances over this temperature range. Rather, it suggests a quite resilient microbial food web when adapted to in situ temperature. The sensitivity of the model response to its mesozooplankton component suggests, however, that the seasonal vertical migration of Arctic copepods may be a strong forcing factor on Arctic microbial food webs. PMID:26074626

Engineering bacteria to solve the Burnt Pancake Problem

PubMed Central

Haynes, Karmella A; Broderick, Marian L; Brown, Adam D; Butner, Trevor L; Dickson, James O; Harden, W Lance; Heard, Lane H; Jessen, Eric L; Malloy, Kelly J; Ogden, Brad J; Rosemond, Sabriya; Simpson, Samantha; Zwack, Erin; Campbell, A Malcolm; Eckdahl, Todd T; Heyer, Laurie J; Poet, Jeffrey L

2008-01-01

Background We investigated the possibility of executing DNA-based computation in living cells by engineering Escherichia coli to address a classic mathematical puzzle called the Burnt Pancake Problem (BPP). The BPP is solved by sorting a stack of distinct objects (pancakes) into proper order and orientation using the minimum number of manipulations. Each manipulation reverses the order and orientation of one or more adjacent objects in the stack. We have designed a system that uses site-specific DNA recombination to mediate inversions of genetic elements that represent pancakes within plasmid DNA. Results Inversions (or "flips") of the DNA fragment pancakes are driven by the Salmonella typhimurium Hin/hix DNA recombinase system that we reconstituted as a collection of modular genetic elements for use in E. coli. Our system sorts DNA segments by inversions to produce different permutations of a promoter and a tetracycline resistance coding region; E. coli cells become antibiotic resistant when the segments are properly sorted. Hin recombinase can mediate all possible inversion operations on adjacent flippable DNA fragments. Mathematical modeling predicts that the system reaches equilibrium after very few flips, where equal numbers of permutations are randomly sorted and unsorted. Semiquantitative PCR analysis of in vivo flipping suggests that inversion products accumulate on a time scale of hours or days rather than minutes. Conclusion The Hin/hix system is a proof-of-concept demonstration of in vivo computation with the potential to be scaled up to accommodate larger and more challenging problems. Hin/hix may provide a flexible new tool for manipulating transgenic DNA in vivo. PMID:18492232

The use of physical and virtual manipulatives in an undergraduate mechanical engineering (Dynamics) course

NASA Astrophysics Data System (ADS)

Pan, Edward A.

Science, technology, engineering, and mathematics (STEM) education is a national focus. Engineering education, as part of STEM education, needs to adapt to meet the needs of the nation in a rapidly changing world. Using computer-based visualization tools and corresponding 3D printed physical objects may help nontraditional students succeed in engineering classes. This dissertation investigated how adding physical or virtual learning objects (called manipulatives) to courses that require mental visualization of mechanical systems can aid student performance. Dynamics is one such course, and tends to be taught using lecture and textbooks with static diagrams of moving systems. Students often fail to solve the problems correctly and an inability to mentally visualize the system can contribute to student difficulties. This study found no differences between treatment groups on quantitative measures of spatial ability and conceptual knowledge. There were differences between treatments on measures of mechanical reasoning ability, in favor of the use of physical and virtual manipulatives over static diagrams alone. There were no major differences in student performance between the use of physical and virtual manipulatives. Students used the physical and virtual manipulatives to test their theories about how the machines worked, however their actual time handling the manipulatives was extremely limited relative to the amount of time they spent working on the problems. Students used the physical and virtual manipulatives as visual aids when communicating about the problem with their partners, and this behavior was also seen with Traditional group students who had to use the static diagrams and gesture instead. The explanations students gave for how the machines worked provided evidence of mental simulation; however, their causal chain analyses were often flawed, probably due to attempts to decrease cognitive load. Student opinions about the static diagrams and dynamic models varied by type of model (static, physical, virtual), but were generally favorable. The Traditional group students, however, indicated that the lack of adequate representation of motion in the static diagrams was a problem, and wished they had access to the physical and virtual models.

Analysing the lack of Demand Organisation

NASA Astrophysics Data System (ADS)

Boxer, Philip; Cohen, Bernard

1998-07-01

We seek to develop means of intervention in Enterprises that will enable them to react in an effective, sustainable and timely fashion to changes in the ways that markets and demand are organized; that is, to act strategically. We take an enterprise to be some entity that seeks to provide its clients with services that they value while maintaining its ability to do so in the face of changes in the demands of its clients and in the resources at its disposal. The services that clients value form around what the organization of their demands lack. The concept of strategy therefore rests on critically evaluating the ontology and semantics of the Enterprise in relation to these holes in demand organization. We access ontology and semantics by constructing and manipulating hypothetical, first-order, mathematical models of the Enterprise's services and of its value-adding processes. Because an enterprise is an anticipatory system, its semantic domain must include representations of the enterprise's model of itself and of the market and demand organizations within which it competes. First-order (set) theory provides adequate expressive power here, but alternative, higher order, mathematical frameworks, such as Dubois' hyperincursion, provide inadequate power, particularly in relation to the analysis of the properties of emergence. Knowing exactly why and where this mathematical lack manifests in the analysis process enables effective collaboration between systems analysts and psychoanalysts, and suggest directions for mathematical research.

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature

PubMed Central

Caviola, Sara; Carey, Emma; Mammarella, Irene C.; Szucs, Denes

2017-01-01

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth “strategy selection”) in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research. PMID:28919870

Memory and cognitive control circuits in mathematical cognition and learning.

PubMed

Menon, V

2016-01-01

Numerical cognition relies on interactions within and between multiple functional brain systems, including those subserving quantity processing, working memory, declarative memory, and cognitive control. This chapter describes recent advances in our understanding of memory and control circuits in mathematical cognition and learning. The working memory system involves multiple parietal-frontal circuits which create short-term representations that allow manipulation of discrete quantities over several seconds. In contrast, hippocampal-frontal circuits underlying the declarative memory system play an important role in formation of associative memories and binding of new and old information, leading to the formation of long-term memories that allow generalization beyond individual problem attributes. The flow of information across these systems is regulated by flexible cognitive control systems which facilitate the integration and manipulation of quantity and mnemonic information. The implications of recent research for formulating a more comprehensive systems neuroscience view of the neural basis of mathematical learning and knowledge acquisition in both children and adults are discussed. © 2016 Elsevier B.V. All rights reserved.

Memory and cognitive control circuits in mathematical cognition and learning

PubMed Central

Menon, V.

2018-01-01

Numerical cognition relies on interactions within and between multiple functional brain systems, including those subserving quantity processing, working memory, declarative memory, and cognitive control. This chapter describes recent advances in our understanding of memory and control circuits in mathematical cognition and learning. The working memory system involves multiple parietal–frontal circuits which create short-term representations that allow manipulation of discrete quantities over several seconds. In contrast, hippocampal–frontal circuits underlying the declarative memory system play an important role in formation of associative memories and binding of new and old information, leading to the formation of long-term memories that allow generalization beyond individual problem attributes. The flow of information across these systems is regulated by flexible cognitive control systems which facilitate the integration and manipulation of quantity and mnemonic information. The implications of recent research for formulating a more comprehensive systems neuroscience view of the neural basis of mathematical learning and knowledge acquisition in both children and adults are discussed. PMID:27339012

The Influence of Gender, School Location and Socio-Economic Status on Students' Academic Achievement in Mathematics

ERIC Educational Resources Information Center

Alordiah, Caroline Ochuko; Akpadaka, Grace; Oviogbodu, Christy Oritseweyimi

2015-01-01

The study investigated the influence of gender, school location, and socio-economic status (SES) on students' academic achievement in mathematics. The study was an ex-post factor design in which the variables were not manipulated nor controlled. Four research questions and three hypotheses were formulated to guide the study. The stratified random…

Building a Concrete Foundation: A Mixed-Method Study of Teaching Styles and the Use of Concrete, Representational, and Abstract Mathematics Instruction

ERIC Educational Resources Information Center

Thigpen, L. Christine

2012-01-01

The purpose of this study was to explore teaching styles and how frequently teachers with a variety of teaching styles incorporate multiple representations, such as manipulatives, drawings, counters, etc., in the middle school mathematics classroom. Through this explanatory mixed methods study it was possible to collect the quantitative data in…

Formal logic rewrite system bachelor in teaching mathematical informatics

NASA Astrophysics Data System (ADS)

Habiballa, Hashim; Jendryscik, Radek

2017-07-01

The article presents capabilities of the formal rewrite logic system - Bachelor - for teaching theoretical computer science (mathematical informatics). The system Bachelor enables constructivist approach to teaching and therefore it may enhance the learning process in hard informatics essential disciplines. It brings not only detailed description of formal rewrite process but also it can demonstrate algorithmical principles for logic formulae manipulations.

Acoustic radiation force of a Bessel beam on a porous sphere.

PubMed

Azarpeyvand, Mahdi

2012-06-01

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-05-01

This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

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

PubMed

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

2016-09-01

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

Animal models for studying transport across the blood-brain barrier.

PubMed

Bonate, P L

1995-01-01

There are many reasons for wishing to determine the rate of uptake of a drug from blood into brain parenchyma. However, when faced with doing so for the first time, choosing a method can be a formidable task. There are at least 7 methods from which to choose: indicator dilution, brain uptake index, microdialysis, external registration, PET scanning, in situ perfusion, and compartmental modeling. Each method has advantages and disadvantages. Some methods require very little equipment while others require equipment that can cost millions of dollars. Some methods require very little technical experience whereas others require complex surgical manipulation. The mathematics alone for the various methods range from simple algebra to complex integral calculus and differential equations. Like most things in science, as the complexity of the technique increases, so does the quantity of information it provides. This review is meant to serve as a starting point for the researcher who wishes to study transport and uptake across the blood-brain barrier in animal models. An overview of the mathematical theory, as well as an introduction to the techniques, is presented.

Students' conceptual performance on synthesis physics problems with varying mathematical complexity

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-06-01

A body of research on physics problem solving has focused on single-concept problems. In this study we use "synthesis problems" that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students' conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students (N =179 ) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students' conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students' conceptual performance. This difference may be explained by the students' familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

Blood flow analysis with considering nanofluid effects in vertical channel

NASA Astrophysics Data System (ADS)

Noreen, S.; Rashidi, M. M.; Qasim, M.

2017-06-01

Manipulation of heat convection of copper particles in blood has been considered peristaltically. Two-phase flow model is used in a channel with insulating walls. Flow analysis has been approved by assuming small Reynold number and infinite length of wave. Coupled equations are solved. Numerical solution are computed for the pressure gradient, axial velocity function and temperature. Influence of attention-grabbing parameters on flow entities has been analyzed. This study can be considered as mathematical representation to the vibrance of physiological systems/tissues/organs provided with medicine.

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.

A Study of Students' Achievement in Algebra: Considering the Effect of Gender and Types of Schools

ERIC Educational Resources Information Center

Saleh, Salmiza; Rahman, Muhamad Asyrah Abdul

2016-01-01

Algebra is a branch of mathematics that deals with symbols and also the rules for manipulating those symbols, which are used to represent numbers and quantities in mathematical formulae and equations. It is needed and used in our everyday lives. The purpose of this study was to examine students' performance in algebra related to gender and types…

Parallelism in Manipulator Dynamics. Revision.

DTIC Science & Technology

1983-12-01

computing the motor torques required to drive a lower-pair kinematic chain (e.g., a typical manipulator arm in free motion, or a mechanical leg in the... computations , and presents two "mathematically exact" formulationsespecially suited to high-speed, highly parallel implementa- tions using special-purpose...YNAMICS by I(IIAR) IIAROLI) LATIROP .4ISTRACT This paper addresses the problem of efficiently computing the motor torques required to drive a lower-pair

Computational techniques to enable visualizing shapes of objects of extra spatial dimensions

NASA Astrophysics Data System (ADS)

Black, Don Vaughn, II

Envisioning extra dimensions beyond the three of common experience is a daunting challenge for three dimensional observers. Intuition relies on experience gained in a three dimensional environment. Gaining experience with virtual four dimensional objects and virtual three manifolds in four-space on a personal computer may provide the basis for an intuitive grasp of four dimensions. In order to enable such a capability for ourselves, it is first necessary to devise and implement a computationally tractable method to visualize, explore, and manipulate objects of dimension beyond three on the personal computer. A technology is described in this dissertation to convert a representation of higher dimensional models into a format that may be displayed in realtime on graphics cards available on many off-the-shelf personal computers. As a result, an opportunity has been created to experience the shape of four dimensional objects on the desktop computer. The ultimate goal has been to provide the user a tangible and memorable experience with mathematical models of four dimensional objects such that the user can see the model from any user selected vantage point. By use of a 4D GUI, an arbitrary convex hull or 3D silhouette of the 4D model can be rotated, panned, scrolled, and zoomed until a suitable dimensionally reduced view or Aspect is obtained. The 4D GUI then allows the user to manipulate a 3-flat hyperplane cutting tool to slice the model at an arbitrary orientation and position to extract or "pluck" an embedded 3D slice or "aspect" from the embedding four-space. This plucked 3D aspect can be viewed from all angles via a conventional 3D viewer using three multiple POV viewports, and optionally exported to a third party CAD viewer for further manipulation. Plucking and Manipulating the Aspect provides a tangible experience for the end-user in the same manner as any 3D Computer Aided Design viewing and manipulation tool does for the engineer or a 3D video game provides for the nascent student.

The Origin of Mathematics and Number Sense in the Cerebellum: with Implications for Finger Counting and Dyscalculia.

PubMed

Vandervert, Larry

2017-01-01

Mathematicians and scientists have struggled to adequately describe the ultimate foundations of mathematics. Nobel laureates Albert Einstein and Eugene Wigner were perplexed by this issue, with Wigner concluding that the workability of mathematics in the real world is a mystery we cannot explain. In response to this classic enigma, the major purpose of this article is to provide a theoretical model of the ultimate origin of mathematics and "number sense" (as defined by S. Dehaene) that is proposed to involve the learning of inverse dynamics models through the collaboration of the cerebellum and the cerebral cortex (but prominently cerebellum-driven). This model is based upon (1) the modern definition of mathematics as the "science of patterns," (2) cerebellar sequence (pattern) detection, and (3) findings that the manipulation of numbers is automated in the cerebellum. This cerebro-cerebellar approach does not necessarily conflict with mathematics or number sense models that focus on brain functions associated with especially the intraparietal sulcus region of the cerebral cortex. A direct corollary purpose of this article is to offer a cerebellar inner speech explanation for difficulty in developing "number sense" in developmental dyscalculia. It is argued that during infancy the cerebellum learns (1) a first tier of internal models for a primitive physics that constitutes the foundations of visual-spatial working memory, and (2) a second (and more abstract) tier of internal models based on (1) that learns "number" and relationships among dimensions across the primitive physics of the first tier. Within this context it is further argued that difficulty in the early development of the second tier of abstraction (and "number sense") is based on the more demanding attentional requirements imposed on cerebellar inner speech executive control during the learning of cerebellar inverse dynamics models. Finally, it is argued that finger counting improves (does not originate) "number sense" by extending focus of attention in executive control of silent cerebellar inner speech. It is suggested that (1) the origin of mathematics has historically been an enigma only because it is learned below the level of conscious awareness in cerebellar internal models, (2) understandings of the development of "number sense" and developmental dyscalculia can be advanced by first understanding the ultimate foundations of number and mathematics do not simply originate in the cerebral cortex, but rather in cerebro-cerebellar collaboration (predominately driven by the cerebellum). It is concluded that difficulty with "number sense" results from the extended demands on executive control in learning inverse dynamics models associated with cerebellar inner speech related to the second tier of abstraction (numbers) of the infant's primitive physics.

Modelling the core magnetic field of the earth

NASA Technical Reports Server (NTRS)

Harrison, C. G. A.; Carle, H. M.

1982-01-01

It is suggested that radial off-center dipoles located within the core of the earth be used instead of spherical harmonics of the magnetic potential in modeling the core magnetic field. The off-center dipoles, in addition to more realistically modeling the physical current systems within the core, are if located deep within the core more effective at removing long wavelength signals of either potential or field. Their disadvantage is that their positions and strengths are more difficult to compute, and such effects as upward and downward continuation are more difficult to manipulate. It is nevertheless agreed with Cox (1975) and Alldredge and Hurwitz (1964) that physical realism in models is more important than mathematical convenience. A radial dipole model is presented which agrees with observations of secular variation and excursions.

The speed-accuracy tradeoff: history, physiology, methodology, and behavior

PubMed Central

Heitz, Richard P.

2014-01-01

There are few behavioral effects as ubiquitous as the speed-accuracy tradeoff (SAT). From insects to rodents to primates, the tendency for decision speed to covary with decision accuracy seems an inescapable property of choice behavior. Recently, the SAT has received renewed interest, as neuroscience approaches begin to uncover its neural underpinnings and computational models are compelled to incorporate it as a necessary benchmark. The present work provides a comprehensive overview of SAT. First, I trace its history as a tractable behavioral phenomenon and the role it has played in shaping mathematical descriptions of the decision process. Second, I present a “users guide” of SAT methodology, including a critical review of common experimental manipulations and analysis techniques and a treatment of the typical behavioral patterns that emerge when SAT is manipulated directly. Finally, I review applications of this methodology in several domains. PMID:24966810

Influence of proportional number relationships on item accessibility and students' strategies

NASA Astrophysics Data System (ADS)

Carney, Michele B.; Smith, Everett; Hughes, Gwyneth R.; Brendefur, Jonathan L.; Crawford, Angela

2016-12-01

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically manipulating the location of an integer multiplier—to press the scalar or functional relationship—on item difficulty and student solution strategies. We administered short-answer assessment forms to 473 students in grades 6-8 (approximate ages 11-14) and analyzed the data quantitatively with the Rasch model to examine item accessibility and qualitatively to examine student solution strategies. We found that manipulating the location of the integer multiplier encouraged students to make use of different aspects of proportional relationships without decreasing item accessibility. Implications for proportional reasoning curricular materials, instruction, and assessment are addressed.

Causality

NASA Astrophysics Data System (ADS)

Pearl, Judea

2000-03-01

Written by one of the pre-eminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artifical intelligence, business, epidemiology, social science and economics. Students in these areas will find natural models, simple identification procedures, and precise mathematical definitions of causal concepts that traditional texts have tended to evade or make unduly complicated. This book will be of interest to professionals and students in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.

An Investigation of Mental Coding Mechanisms and Heuristics Used in Electronics Troubleshooting.

DTIC Science & Technology

1980-04-01

that is, the particular program to be used for the decision making or problem solving exercise at hand. The relationships between LTM, the processor...stimulus input according to previously learned classifications. Norman continued by writing that the encoded information is the material which is stored...the manipulation of algebraic or other mathematical symbols according to the rules embodied in mathematical logic. Once these essentially content free

Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

NASA Astrophysics Data System (ADS)

Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew

2013-06-01

Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.

Differentiating the persistency and permanency of some two stages DNA splicing language via Yusof-Goode (Y-G) approach

NASA Astrophysics Data System (ADS)

Mudaber, M. H.; Yusof, Y.; Mohamad, M. S.

2017-09-01

Predicting the existence of restriction enzymes sequences on the recombinant DNA fragments, after accomplishing the manipulating reaction, via mathematical approach is considered as a convenient way in terms of DNA recombination. In terms of mathematics, for this characteristic of the recombinant DNA strands, which involve the recognition sites of restriction enzymes, is called persistent and permanent. Normally differentiating the persistency and permanency of two stages recombinant DNA strands using wet-lab experiment is expensive and time-consuming due to running the experiment at two stages as well as adding more restriction enzymes on the reaction. Therefore, in this research, by using Yusof-Goode (Y-G) model the difference between persistent and permanent splicing language of some two stages is investigated. Two theorems were provided, which show the persistency and non-permanency of two stages DNA splicing language.

Generic Equations for Constructing Smooth Paths Along Circles and Tangent Lines With Application to Airport Ground Paths

NASA Technical Reports Server (NTRS)

Barker, L. Keith

1998-01-01

The primary purpose of this publication is to develop a mathematical model to describe smooth paths along any combination of circles and tangent lines. Two consecutive circles in a path are either tangent (externally or internally) or they appear on the same (lateral) or opposite (transverse) sides of a connecting tangent line. A path may start or end on either a segment or circle. The approach is to use mathematics common to robotics to design the path as a multilink manipulator. This approach allows a hierarchical view of the problem and keeps the notation manageable. A user simply specifies a few parameters to configure a path. Necessary and sufficient conditions automatically ensure the consistency of the inputs for a smooth path. Two example runway exit paths are given, and an angle to go assists in knowing when to switch from one path element to the next.

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

Digit replacement: A generic map for nonlinear dynamical systems.

PubMed

García-Morales, Vladimir

2016-09-01

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

Method and apparatus to assess compartment syndrome

NASA Technical Reports Server (NTRS)

Hargens, Alan R. (Inventor); Yost, William T. (Inventor); Ueno, Toshiaki (Inventor)

2008-01-01

A method and apparatus for measuring pressure buildup in a body compartment that encases muscular tissue. The method includes assessing the body compartment configuration and identifying the effect of pulsatile components on at least one compartment dimension. This process is used in preventing tissue necrosis, and in decisions of whether to perform surgery on the body compartment for prevention of Compartment Syndrome. An apparatus is used for measuring excess pressure in the body compartment having components for imparting ultrasonic waves such as a transducer, placing the transducer to impart the ultrasonic waves, capturing the reflected imparted ultrasonic waves, and converting them to electrical signals, a pulsed phase-locked loop device for assessing a body compartment configuration and producing an output signal, and means for mathematically manipulating the output signal to thereby categorize pressure build-up in the body compartment from the mathematical manipulations.

A perceptual account of symbolic reasoning

PubMed Central

Landy, David; Allen, Colin; Zednik, Carlos

2014-01-01

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures. PMID:24795662

Orexinergic Neurotransmission in Temperature Responses to Methamphetamine and Stress: Mathematical Modeling as a Data Assimilation Approach

PubMed Central

Behrouzvaziri, Abolhassan; Fu, Daniel; Tan, Patrick; Yoo, Yeonjoo; Zaretskaia, Maria V.; Rusyniak, Daniel E.; Molkov, Yaroslav I.; Zaretsky, Dmitry V.

2015-01-01

Experimental Data Orexinergic neurotransmission is involved in mediating temperature responses to methamphetamine (Meth). In experiments in rats, SB-334867 (SB), an antagonist of orexin receptors (OX1R), at a dose of 10 mg/kg decreases late temperature responses (t>60 min) to an intermediate dose of Meth (5 mg/kg). A higher dose of SB (30 mg/kg) attenuates temperature responses to low dose (1 mg/kg) of Meth and to stress. In contrast, it significantly exaggerates early responses (t<60 min) to intermediate and high doses (5 and 10 mg/kg) of Meth. As pretreatment with SB also inhibits temperature response to the stress of injection, traditional statistical analysis of temperature responses is difficult. Mathematical Modeling We have developed a mathematical model that explains the complexity of temperature responses to Meth as the interplay between excitatory and inhibitory nodes. We have extended the developed model to include the stress of manipulations and the effects of SB. Stress is synergistic with Meth on the action on excitatory node. Orexin receptors mediate an activation of on both excitatory and inhibitory nodes by low doses of Meth, but not on the node activated by high doses (HD). Exaggeration of early responses to high doses of Meth involves disinhibition: low dose of SB decreases tonic inhibition of HD and lowers the activation threshold, while the higher dose suppresses the inhibitory component. Using a modeling approach to data assimilation appears efficient in separating individual components of complex response with statistical analysis unachievable by traditional data processing methods. PMID:25993564

Mathematical Modeling of Cellular Cross-Talk Between Endothelial and Tumor Cells Highlights Counterintuitive Effects of VEGF-Targeted Therapies.

PubMed

Jain, Harsh; Jackson, Trachette

2018-05-01

Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the expression of pro-angiogenic growth factors, including members of the vascular endothelial growth factor (VEGF) family of ligands. VEGF ligands are overexpressed in a wide variety of solid tumors and therefore have inspired optimism that inhibition of the different axes of the VEGF pathway-alone or in combination-would represent powerful anti-angiogenic therapies for most cancer types. When considering treatments that target VEGF and its receptors, it is difficult to tease out the differential anti-angiogenic and anti-tumor effects of all combinations experimentally because tumor cells and vascular endothelial cells are engaged in a dynamic cross-talk that impacts key aspects of tumorigenesis, independent of angiogenesis. Here we develop a mathematical model that connects intracellular signaling responsible for both endothelial and tumor cell proliferation and death to population-level cancer growth and angiogenesis. We use this model to investigate the effect of bidirectional communication between endothelial cells and tumor cells on treatments targeting VEGF and its receptors both in vitro and in vivo. Our results underscore the fact that in vitro therapeutic outcomes do not always translate to the in vivo situation. For example, our model predicts that certain therapeutic combinations result in antagonism in vivo that is not observed in vitro. Mathematical modeling in this direction can shed light on the mechanisms behind experimental observations that manipulating VEGF and its receptors is successful in some cases but disappointing in others.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

PubMed Central

Klewicki, J. C.; Chini, G. P.; Gibson, J. F.

2017-01-01

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167585

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number.

PubMed

Klewicki, J C; Chini, G P; Gibson, J F

2017-03-13

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Past and future perspectives on mathematical models of tick-borne pathogens.

PubMed

Norman, R A; Worton, A J; Gilbert, L

2016-06-01

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

Individual Differences in Inhibitory Control, Not Non-Verbal Number Acuity, Correlate with Mathematics Achievement

PubMed Central

Gilmore, Camilla; Attridge, Nina; Clayton, Sarah; Cragg, Lucy; Johnson, Samantha; Marlow, Neil; Simms, Victoria; Inglis, Matthew

2013-01-01

Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate. PMID:23785521

Robust acoustic wave manipulation of bubbly liquids

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

Gumerov, N. A., E-mail: gumerov@umiacs.umd.edu; Center for Micro- and Nanoscale Dynamics of Dispersed Systems, Bashkir State University, Ufa 450076; Akhatov, I. S.

Experiments with water–air bubbly liquids when exposed to acoustic fields of frequency ∼100 kHz and intensity below the cavitation threshold demonstrate that bubbles ∼30 μm in diameter can be “pushed” away from acoustic sources by acoustic radiation independently from the direction of gravity. This manifests formation and propagation of acoustically induced transparency waves (waves of the bubble volume fraction). In fact, this is a collective effect of bubbles, which can be described by a mathematical model of bubble self-organization in acoustic fields that matches well with our experiments.

An intermediate-level course on Biological Physics

NASA Astrophysics Data System (ADS)

Nelson, Phil

2004-03-01

I describe both undergraduate and graduate 1-semester courses designed to give a survey of Biological Physics. The courses cover classical as well as recent topics. The undergraduate version requires calculus-based first-year physics as its prerequisite. With this level of assumed background, we can arrive at topics such as molecular motors, manipulation of single molecules, and the propagation of nerve impulses. Students majoring in physics, chemistry, biochemistry, and every engineering major (as well as a few in biology), end up taking this course. The graduate course covers the same material but includes exercises with symbolic mathematics packages and data modeling.

Proceedings of the 1977 MACSYMA users' conference (NASA)

NASA Technical Reports Server (NTRS)

1977-01-01

The MACSYMA program for symbolic and algebraic manipulation enables exact, symbolic mathematical computations to be performed on a computer. This program is rather large, and various approaches to the hardware and software problems are examined.

Mathematics and morphogenesis of cities: A geometrical approach

NASA Astrophysics Data System (ADS)

Courtat, Thomas; Gloaguen, Catherine; Douady, Stephane

2011-03-01

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city’s current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of the traditional models, from random graphs, complex networks theory, or stochastic geometry, takes into account the geometrical, functional, and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating, and explaining cities’ overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division or extension of space. We propose a dynamical model that mimics this logic and that, from simple general rules and a few parameters, succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.

Atmosphere behavior in gas-closed mouse-algal systems: An experimental and modelling study

NASA Astrophysics Data System (ADS)

Averner, Maurice M.; Moore, Berrien; Bartholomew, Irene; Wharton, Robert

Concepts of biologically-based regenerative life support systems anticipate the use of photosynthetic organisms for air revitalization. However, mismatches in the rates of production and uptake of oxygen or carbon dioxide between the crew and the plants will lead to an accumulation or depletion of these gases beyond tolerable limits. One method for correcting these atmospheric changes is to use physicochemical devices. This would conflict with the constraint of minimal size and weight imposed upon the successful development of a competitive bioregenerative system. An alternate control strategy is based upon reducing the gas exchange mismatch by manipulation of those environmental parameters known to affect plant or algae gas exchange ratios. We have initiated a research program using a dual approach of mathematical modelling and laboratory experimentation aimed at examining the gas exchange characteristics of artificial animal/plant systems closed to the ambient atmosphere. Our goal is to develop control techniques and management strategies for maintaining the atmospheric levels of carbon dioxide and oxygen at physiological levels. A mathematical model simulating the atmospheric behavior in these systems has been developed and an experimental gas-closed system has been constructed. These will be described and preliminary results will be presented.

Hard and Soft Constraints in Reliability-Based Design Optimization

NASA Technical Reports Server (NTRS)

Crespo, L.uis G.; Giesy, Daniel P.; Kenny, Sean P.

2006-01-01

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

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

PubMed

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

2015-06-09

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

Mathematical Basis of Knowledge Discovery and Autonomous Intelligent Architectures - Technology for the Creation of Virtual objects in the Real World

DTIC Science & Technology

2005-12-14

control of position/orientation of mobile TV cameras. 9 Unit 9 Force interaction system Unit 6 Helmet mounted displays robot like device drive...joints of the master arm (see Unit 1) which joint coordinates are tracked by the virtual manipulator. Unit 6 . Two displays built in the helmet...special device for simulating the tactile- kinaesthetic effect of immersion. When virtual body is a manipulator it comprises: − master arm with 6

Computer algebra and operators

NASA Technical Reports Server (NTRS)

Fateman, Richard; Grossman, Robert

1989-01-01

The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

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

PubMed

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

2018-01-01

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

A new criterion for acquisition of nicotine self-administration in rats.

PubMed

Peartree, Natalie A; Sanabria, Federico; Thiel, Kenneth J; Weber, Suzanne M; Cheung, Timothy H C; Neisewander, Janet L

2012-07-01

Acquisition of nicotine self-administration in rodents is relatively difficult to establish and measures of acquisition rate are sometimes confounded by manipulations used to facilitate the process. This study examined acquisition of nicotine self-administration without such manipulations and used mathematical modeling to define the criterion for acquisition. Rats were given 20 daily 2-h sessions occurring 6 days/week in chambers equipped with active and inactive levers. Each active lever press resulted in nicotine reinforcement (0-0.06 mg/kg, IV) and retraction of both levers for a 20-s time out, whereas inactive lever presses had no consequences. Acquisition was defined for individual rats by the higher likelihood of reinforcers obtained across sessions fitting a logistic over a constant function according to the corrected Akaike Information Criterion (AICc). For rats that acquired self-administration, an AICc-based multi-model comparison demonstrated that the asymptote (highest number of reinforcers/session) and mid-point of the acquisition curve (h; the number of sessions necessary to reach half the asymptote) varied by nicotine dose, with both exhibiting a negative relationship (the higher the dose, the lower number of reinforcers and the lower h). The modeling approach used in this study provides a way of defining acquisition of nicotine self-administration that takes advantage of all data from individual subjects and the procedure used is sensitive to dose differences in the absence of manipulations that influence acquisition (e.g., food restriction, prior food reinforcement, conditioned reinforcers). Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Enhanced dopamine release by dopamine transport inhibitors described by a restricted diffusion model and fast scan cyclic voltammetry

PubMed Central

Hoffman, Alexander F.; Spivak, Charles E.; Lupica, Carl R.

2016-01-01

Fast-scan cyclic voltammetry (FSCV) using carbon fiber electrodes is widely used to rapidly monitor changes in dopamine (DA) levels in vitro and in vivo. Current analytical approaches utilize parameters such as peak oxidation current amplitude and decay times to estimate release and uptake processes, respectively. However, peak amplitude changes are often observed with uptake inhibitors, thereby confounding the interpretation of these parameters. To overcome this limitation, we demonstrate that a simple, 5 parameter, two compartment model mathematically describes DA signals as a balance of release (r/ke) and uptake (ku), summed with adsorption (kads and kdes) of DA to the carbon electrode surface. Using non-linear regression, we demonstrate that our model precisely describes measured DA signals obtained in brain slice recordings. The parameters extracted from these curves were then validated using pharmacological manipulations that selectively alter vesicular release or DA transporter (DAT)-mediated uptake. Manipulation of DA release through altered Ca2+/Mg2+ ratio or tetrodotoxin (TTX), reduced the release parameter with no effect on the uptake parameter. The DAT inhibitors methylenedioxypyrovalerone (MDPV), cocaine, and nomifensine significantly reduced uptake and increased vesicular DA release. In contrast, a low concentration of amphetamine reduced uptake but had no effect on DA release. Finally, the kappa-opioid receptor (KOR) agonist U50,488 significantly reduced vesicular DA release but had no effect on uptake. Together, these data demonstrate a novel analytical approach to distinguish the effects of manipulations on DA release or uptake that can be used to interpret FSCV data. PMID:27018734

Enhanced Dopamine Release by Dopamine Transport Inhibitors Described by a Restricted Diffusion Model and Fast-Scan Cyclic Voltammetry.

PubMed

Hoffman, Alexander F; Spivak, Charles E; Lupica, Carl R

2016-06-15

Fast-scan cyclic voltammetry (FSCV) using carbon fiber electrodes is widely used to rapidly monitor changes in dopamine (DA) levels in vitro and in vivo. Current analytical approaches utilize parameters such as peak oxidation current amplitude and decay times to estimate release and uptake processes, respectively. However, peak amplitude changes are often observed with uptake inhibitors, thereby confounding the interpretation of these parameters. To overcome this limitation, we demonstrate that a simple five-parameter, two-compartment model mathematically describes DA signals as a balance of release (r/ke) and uptake (ku), summed with adsorption (kads and kdes) of DA to the carbon electrode surface. Using nonlinear regression, we demonstrate that our model precisely describes measured DA signals obtained in brain slice recordings. The parameters extracted from these curves were then validated using pharmacological manipulations that selectively alter vesicular release or DA transporter (DAT)-mediated uptake. Manipulation of DA release through altering the Ca(2+)/Mg(2+) ratio or adding tetrodotoxin reduced the release parameter with no effect on the uptake parameter. DAT inhibitors methylenedioxypyrovalerone, cocaine, and nomifensine significantly reduced uptake and increased vesicular DA release. In contrast, a low concentration of amphetamine reduced uptake but had no effect on DA release. Finally, the kappa opioid receptor agonist U50,488 significantly reduced vesicular DA release but had no effect on uptake. Together, these data demonstrate a novel analytical approach to distinguish the effects of manipulations on DA release or uptake that can be used to interpret FSCV data.

Improved Collision-Detection Method for Robotic Manipulator

NASA Technical Reports Server (NTRS)

Leger, Chris

2003-01-01

An improved method has been devised for the computational prediction of a collision between (1) a robotic manipulator and (2) another part of the robot or an external object in the vicinity of the robot. The method is intended to be used to test commanded manipulator trajectories in advance so that execution of the commands can be stopped before damage is done. The method involves utilization of both (1) mathematical models of the robot and its environment constructed manually prior to operation and (2) similar models constructed automatically from sensory data acquired during operation. The representation of objects in this method is simpler and more efficient (with respect to both computation time and computer memory), relative to the representations used in most prior methods. The present method was developed especially for use on a robotic land vehicle (rover) equipped with a manipulator arm and a vision system that includes stereoscopic electronic cameras. In this method, objects are represented and collisions detected by use of a previously developed technique known in the art as the method of oriented bounding boxes (OBBs). As the name of this technique indicates, an object is represented approximately, for computational purposes, by a box that encloses its outer boundary. Because many parts of a robotic manipulator are cylindrical, the OBB method has been extended in this method to enable the approximate representation of cylindrical parts by use of octagonal or other multiple-OBB assemblies denoted oriented bounding prisms (OBPs), as in the example of Figure 1. Unlike prior methods, the OBB/OBP method does not require any divisions or transcendental functions; this feature leads to greater robustness and numerical accuracy. The OBB/OBP method was selected for incorporation into the present method because it offers the best compromise between accuracy on the one hand and computational efficiency (and thus computational speed) on the other hand.

Mr.CAS-A minimalistic (pure) Ruby CAS for fast prototyping and code generation

NASA Astrophysics Data System (ADS)

Ragni, Matteo

There are Computer Algebra System (CAS) systems on the market with complete solutions for manipulation of analytical models. But exporting a model that implements specific algorithms on specific platforms, for target languages or for particular numerical library, is often a rigid procedure that requires manual post-processing. This work presents a Ruby library that exposes core CAS capabilities, i.e. simplification, substitution, evaluation, etc. The library aims at programmers that need to rapidly prototype and generate numerical code for different target languages, while keeping separated mathematical expression from the code generation rules, where best practices for numerical conditioning are implemented. The library is written in pure Ruby language and is compatible with most Ruby interpreters.

Mathematics Around the World.

ERIC Educational Resources Information Center

Smyth, Mitzi

1983-01-01

The author comments on varying factors she noted as she observed 125 primary schools in 32 countries. Of particular interest to her were approaches in Australia and New Zealand using manipulative materials. Several conclusions pertinent to U.S. schools are drawn. (MNS)

Shock and Vibration Control of a Golf-Swing Robot at Impacting the Ball

NASA Astrophysics Data System (ADS)

Hoshino, Yohei; Kobayashi, Yukinori

A golf swing robot is a kind of fast motion manipulator with a flexible link. A robot manipulator is greatly affected by Corioli's and centrifugal forces during fast motion. Nonlinearity due to these forces can have an adverse effect on the performance of feedback control. In the same way, ordinary state observers of a linear system cannot accurately estimate the states of nonlinear systems. This paper uses a state observer that considers disturbances to improve the performance of state estimation and feedback control. A mathematical model of the golf robot is derived by Hamilton's principle. A linear quadratic regulator (LQR) that considers the vibration of the club shaft is used to stop the robot during the follow-through action. The state observer that considers disturbances estimates accurate state variables when the disturbances due to Corioli's and centrifugal forces, and impact forces work on the robot. As a result, the performance of the state feedback control is improved. The study compares the results of the numerical simulations with experimental results.

Adaptive Strategies for Controls of Flexible Arms. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yuan, Bau-San

1989-01-01

An adaptive controller for a modern manipulator has been designed based on asymptotical stability via the Lyapunov criterion with the output error between the system and a reference model used as the actuating control signal. Computer simulations were carried out to test the design. The combination of the adaptive controller and a system vibration and mode shape estimator show that the flexible arm should move along a pre-defined trajectory with high-speed motion and fast vibration setting time. An existing computer-controlled prototype two link manipulator, RALF (Robotic Arm, Large Flexible), with a parallel mechanism driven by hydraulic actuators was used to verify the mathematical analysis. The experimental results illustrate that assumed modes found from finite element techniques can be used to derive the equations of motion with acceptable accuracy. The robust adaptive (modal) control is implemented to compensate for unmodelled modes and nonlinearities and is compared with the joint feedback control in additional experiments. Preliminary results show promise for the experimental control algorithm.

Computer program for diagnostic X-ray exposure conversion.

PubMed

Lewis, S

1984-01-01

Presented is a computer program designed to convert any given set of exposure factors sequentially into another, yielding either an equivalent photographic density or one increased or decreased by a specifiable proportion. In addition to containing the wherewithal with which to manipulate a set of exposure factors, the facility to print hard (paper) copy is included enabling the results to be pasted into a notebook and used at any time. This program was originally written as an investigative exercise into examining the potential use of computers for practical radiographic purposes as conventionally encountered. At the same time, its possible use as an educational tool was borne in mind. To these ends, the current version of this program may be used as a means whereby exposure factors used in a diagnostic department may be altered to suit a particular requirement or may be used in the school as a mathematical model to describe the behaviour of exposure factors under manipulation without patient exposure.

Geodynamics for Everyone: Robust Finite-Difference Heat Transfer Models using MS Excel 2007 Spreadsheets

NASA Astrophysics Data System (ADS)

Grose, C. J.

2008-05-01

Numerical geodynamics models of heat transfer are typically thought of as specialized topics of research requiring knowledge of specialized modelling software, linux platforms, and state-of-the-art finite-element codes. I have implemented analytical and numerical finite-difference techniques with Microsoft Excel 2007 spreadsheets to solve for complex solid-earth heat transfer problems for use by students, teachers, and practicing scientists without specialty in geodynamics modelling techniques and applications. While implementation of equations for use in Excel spreadsheets is occasionally cumbersome, once case boundary structure and node equations are developed, spreadsheet manipulation becomes routine. Model experimentation by modifying parameter values, geometry, and grid resolution makes Excel a useful tool whether in the classroom at the undergraduate or graduate level or for more engaging student projects. Furthermore, the ability to incorporate complex geometries and heat-transfer characteristics makes it ideal for first and occasionally higher order geodynamics simulations to better understand and constrain the results of professional field research in a setting that does not require the constraints of state-of-the-art modelling codes. The straightforward expression and manipulation of model equations in excel can also serve as a medium to better understand the confusing notations of advanced mathematical problems. To illustrate the power and robustness of computation and visualization in spreadsheet models I focus primarily on one-dimensional analytical and two-dimensional numerical solutions to two case problems: (i) the cooling of oceanic lithosphere and (ii) temperatures within subducting slabs. Excel source documents will be made available.

Random medium model for cusping of plane waves.

PubMed

Li, Jia; Korotkova, Olga

2017-09-01

We introduce a model for a three-dimensional (3D) Schell-type stationary medium whose degree of potential's correlation satisfies the Fractional Multi-Gaussian (FMG) function. Compared with the scattered profile produced by the Gaussian Schell-model (GSM) medium, the Fractional Multi-Gaussian Schell-model (FMGSM) medium gives rise to a sharp concave intensity apex in the scattered field. This implies that the FMGSM medium also accounts for a larger than Gaussian's power in the bucket (PIB) in the forward scattering direction, hence being a better candidate than the GSM medium for generating highly-focused (cusp-like) scattered profiles in the far zone. Compared to other mathematical models for the medium's correlation function which can produce similar cusped scattered profiles the FMG function offers unprecedented tractability being the weighted superposition of Gaussian functions. Our results provide useful applications to energy counter problems and particle manipulation by weakly scattered fields.

Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators.

PubMed

Yang, Chifu; Zhao, Jinsong; Li, Liyi; Agrawal, Sunil K

2018-01-01

Robotic spine brace based on parallel-actuated robotic system is a new device for treatment and sensing of scoliosis, however, the strong dynamic coupling and anisotropy problem of parallel manipulators result in accuracy loss of rehabilitation force control, including big error in direction and value of force. A novel active force control strategy named modal space force control is proposed to solve these problems. Considering the electrical driven system and contact environment, the mathematical model of spatial parallel manipulator is built. The strong dynamic coupling problem in force field is described via experiments as well as the anisotropy problem of work space of parallel manipulators. The effects of dynamic coupling on control design and performances are discussed, and the influences of anisotropy on accuracy are also addressed. With mass/inertia matrix and stiffness matrix of parallel manipulators, a modal matrix can be calculated by using eigenvalue decomposition. Making use of the orthogonality of modal matrix with mass matrix of parallel manipulators, the strong coupled dynamic equations expressed in work space or joint space of parallel manipulator may be transformed into decoupled equations formulated in modal space. According to this property, each force control channel is independent of others in the modal space, thus we proposed modal space force control concept which means the force controller is designed in modal space. A modal space active force control is designed and implemented with only a simple PID controller employed as exampled control method to show the differences, uniqueness, and benefits of modal space force control. Simulation and experimental results show that the proposed modal space force control concept can effectively overcome the effects of the strong dynamic coupling and anisotropy problem in the physical space, and modal space force control is thus a very useful control framework, which is better than the current joint space control and work space control. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Designer: A Knowledge-Based Graphic Design Assistant.

DTIC Science & Technology

1986-07-01

pro- pulsion. The system consists of a color graphics interface to a mathematical simulation. One can view and manipulate this simulation at a number of...valve vaive graph 50- mufi -plot graph 100 4 0 80 6.. 30 60 4 20 .... 40 2 10 V 20 0 2 4 6 8 10 0 20 40 60 80 100 FIGURE 4. Icon Sampler. This view...in Computing Systems. New York: ACM, 1983. 8306. Paul Smolensky. Harmony Theory: A Mathematical Framework for Stochastic Parallel Pro- cessing

Support of mathematical thinking through embodied cognition: Nondigital and digital approaches.

PubMed

Tran, Cathy; Smith, Brandon; Buschkuehl, Martin

2017-01-01

Research on mathematics education has shown that learners' actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical thinking. This is especially crucial given the increasing accessibility of technology-such as digital touch devices, 3D printers, and location sensors-for constructing embodied experiences. Providing guidance for incorporating those tools, we focus on the role that embodied cognition can play in communicating mathematical concepts as well as in allowing learners to experiment and evolve their ideas. To inspire future integration of theory in the development of technologically enhanced embodied mathematics experiences, we provide examples of how this can be done. Finally, we outline future directions in the areas of design, implementation, and assessment of embodied learning of mathematics.

Local position control: A new concept for control of manipulators

NASA Technical Reports Server (NTRS)

Kelly, Frederick A.

1988-01-01

Resolved motion rate control is currently one of the most frequently used methods of manipulator control. It is currently used in the Space Shuttle remote manipulator system (RMS) and in prosthetic devices. Position control is predominately used in locating the end-effector of an industrial manipulator along a path with prescribed timing. In industrial applications, resolved motion rate control is inappropriate since position error accumulates. This is due to velocity being the control variable. In some applications this property is an advantage rather than a disadvantage. It may be more important for motion to end as soon as the input command is removed rather than reduce the position error to zero. Local position control is a new concept for manipulator control which retains the important properties of resolved motion rate control, but reduces the drift. Local position control can be considered to be a generalization of resolved position and resolved rate control. It places both control schemes on a common mathematical basis.

Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks.

PubMed

Amalric, Marie; Dehaene, Stanislas

2017-02-19

Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

A systems theoretic approach to analysis and control of mammalian circadian dynamics

PubMed Central

Abel, John H.; Doyle, Francis J.

2016-01-01

The mammalian circadian clock is a complex multi-scale, multivariable biological control system. In the past two decades, methods from systems engineering have led to numerous insights into the architecture and functionality of this system. In this review, we examine the mammalian circadian system through a process systems lens. We present a mathematical framework for examining the cellular circadian oscillator, and show recent extensions for understanding population-scale dynamics. We provide an overview of the routes by which the circadian system can be systemically manipulated, and present in silico proof of concept results for phase resetting of the clock via model predictive control. PMID:28496287

Dynamic control of photosynthetic photon flux for lettuce production in CELSS

NASA Technical Reports Server (NTRS)

Chun, C.; Mitchell, C. A.

1996-01-01

A new dynamic control of photosynthetic photon flux (PPF) was tested using lettuce canopies growing in the Minitron II plant-growth/canopy gas-exchange system. Canopy photosynthetic rates (Pn) were measured in real time and fedback for further environment control. Pn can be manipulated by changing PPF, which is a good environmental parameter for dynamic control of crop production in a Controlled Ecological Life-Support Systems CELSS. Decision making that combines empirical mathematical models with rule sets developed from recent experimental data was tested. With comparable yield indices and potential for energy savings, dynamic control strategies will contribute greatly to the sustainability of space-deployed CELSS.

An Interpreted Language and System for the Visualization of Unstructured Meshes

NASA Technical Reports Server (NTRS)

Moran, Patrick J.; Gerald-Yamasaki, Michael (Technical Monitor)

1998-01-01

We present an interpreted language and system supporting the visualization of unstructured meshes and the manipulation of shapes defined in terms of mesh subsets. The language features primitives inspired by geometric modeling, mathematical morphology and algebraic topology. The adaptation of the topology ideas to an interpreted environment, along with support for programming constructs such, as user function definition, provide a flexible system for analyzing a mesh and for calculating with shapes defined in terms of the mesh. We present results demonstrating some of the capabilities of the language, based on an implementation called the Shape Calculator, for tetrahedral meshes in R^3.

Infiltration of MHD liquid into a deformable porous material

NASA Astrophysics Data System (ADS)

Naseem, Anum; Mahmood, Asif; Siddique, J. I.; Zhao, Lifeng

2018-03-01

We analyze the capillary rise dynamics for magnetohydrodynamics (MHD) fluid flow through deformable porous material in the presence of gravity effects. The modeling is performed using mixture theory approach and mathematical manipulation yields a nonlinear free boundary problem. Due to the capillary rise action, the pressure gradient in the liquid generates a stress gradient that results in the deformation of porous substrate. The capillary rise process for MHD fluid slows down as compared to Newtonian fluid case. Numerical solutions are obtained using a method of lines approach. The graphical results are presented for important physical parameters, and comparison is presented with Newtonian fluid case.

Transport phenomena governing nicotine emissions from electronic cigarettes: model formulation and experimental investigation

PubMed Central

Talih, Soha; Balhas, Zainab; Salman, Rola; El-Hage, Rachel; Karaoghlanian, Nareg; El-Hellani, Ahmad; Baassiri, Mohamad; Jaroudi, Ezzat; Eissenberg, Thomas; Saliba, Najat; Shihadeh, Alan

2017-01-01

Electronic cigarettes (ECIGs) electrically heat and aerosolize a liquid containing propylene glycol (PG), vegetable glycerin (VG), flavorants, water, and nicotine. ECIG effects and proposed methods to regulate them are controversial. One regulatory focal point involves nicotine emissions. We describe a mathematical model that predicts ECIG nicotine emissions. The model computes the vaporization rate of individual species by numerically solving the unsteady species and energy conservation equations. To validate model predictions, yields of nicotine, total particulate matter, PG, and VG were measured while manipulating puff topography, electrical power, and liquid composition across 100 conditions. Nicotine flux, the rate at which nicotine is emitted per unit time, was the primary outcome. Across conditions, the measured and computed nicotine flux were highly correlated (r = 0.85, p<.0001). As predicted, device power, nicotine concentration, PG/VG ratio, and puff duration influenced nicotine flux (p<.05), while water content and puff velocity did not. Additional empirical investigation revealed that PG/VG liquids act as ideal solutions, that liquid vaporization accounts for more than 95% of ECIG aerosol mass emissions, and that as device power increases the aerosol composition shifts towards the less volatile components of the parent liquid. To the extent that ECIG regulations focus on nicotine emissions, mathematical models like this one can be used to predict ECIG nicotine emissions and to test the effects of proposed regulation of factors that influence nicotine flux. PMID:28706340

A Five-Dimensional Mathematical Model for Regional and Global Changes in Cardiac Uptake and Motion

NASA Astrophysics Data System (ADS)

Pretorius, P. H.; King, M. A.; Gifford, H. C.

2004-10-01

The objective of this work was to simultaneously introduce known regional changes in contraction pattern and perfusion to the existing gated Mathematical Cardiac Torso (MCAT) phantom heart model. We derived a simple integral to calculate the fraction of the ellipsoidal volume that makes up the left ventricle (LV), taking into account the stationary apex and the moving base. After calculating the LV myocardium volume of the existing beating heart model, we employed the property of conservation of mass to manipulate the LV ejection fraction to values ranging between 13.5% and 68.9%. Multiple dynamic heart models that differ in degree of LV wall thickening, base-to-apex motion, and ejection fraction, are thus available for use with the existing MCAT methodology. To introduce more complex regional LV contraction and perfusion patterns, we used composites of dynamic heart models to create a central region with little or no motion or perfusion, surrounded by a region in which the motion and perfusion gradually reverts to normal. To illustrate this methodology, the following gated cardiac acquisitions for different clinical situations were simulated analytically: 1) reduced regional motion and perfusion; 2) same perfusion as in (1) without motion intervention; and 3) washout from the normal and diseased myocardial regions. Both motion and perfusion can change dynamically during a single rotation or multiple rotations of a simulated single-photon emission computed tomography acquisition system.

State-transition diagrams for biologists.

PubMed

Bersini, Hugues; Klatzmann, David; Six, Adrien; Thomas-Vaslin, Véronique

2012-01-01

It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of state-transitions of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model. First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute with no need to plunge into the Java or Fortran lines.

State-Transition Diagrams for Biologists

PubMed Central

Bersini, Hugues; Klatzmann, David; Six, Adrien; Thomas-Vaslin, Véronique

2012-01-01

It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of state-transitions of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model. First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute with no need to plunge into the Java or Fortran lines. PMID:22844438

An electrophysiological investigation of non-symbolic magnitude processing: numerical distance effects in children with and without mathematical learning disabilities.

PubMed

Heine, Angela; Wissmann, Jacqueline; Tamm, Sascha; De Smedt, Bert; Schneider, Michael; Stern, Elsbeth; Verschaffel, Lieven; Jacobs, Arthur M

2013-09-01

The aim of the present study was to probe electrophysiological effects of non-symbolic numerical processing in 20 children with mathematical learning disabilities (mean age = 99.2 months) compared to a group of 20 typically developing matched controls (mean age = 98.4 months). EEG data were obtained while children were tested with a standard non-symbolic numerical comparison paradigm that allowed us to investigate the effects of numerical distance manipulations for different set sizes, i.e., the classical subitizing, counting and estimation ranges. Effects of numerical distance manipulations on event-related potential (ERP) amplitudes as well as activation patterns of underlying current sources were analyzed. In typically developing children, the amplitudes of a late parietal positive-going ERP component showed systematic numerical distance effects that did not depend on set size. For the group of children with mathematical learning disabilities, ERP distance effects were found only for stimuli within the subitizing range. Current source density analysis of distance-related group effects suggested that areas in right inferior parietal regions are involved in the generation of the parietal ERP amplitude differences. Our results suggest that right inferior parietal regions are recruited differentially by controls compared to children with mathematical learning disabilities in response to non-symbolic numerical magnitude processing tasks, but only for stimuli with set sizes that exceed the subitizing range. Copyright © 2012 Elsevier Ltd. All rights reserved.

Dynamic modeling and hierarchical compound control of a novel 2-DOF flexible parallel manipulator with multiple actuation modes

NASA Astrophysics Data System (ADS)

Liang, Dong; Song, Yimin; Sun, Tao; Jin, Xueying

2018-03-01

This paper addresses the problem of rigid-flexible coupling dynamic modeling and active control of a novel flexible parallel manipulator (PM) with multiple actuation modes. Firstly, based on the flexible multi-body dynamics theory, the rigid-flexible coupling dynamic model (RFDM) of system is developed by virtue of the augmented Lagrangian multipliers approach. For completeness, the mathematical models of permanent magnet synchronous motor (PMSM) and piezoelectric transducer (PZT) are further established and integrated with the RFDM of mechanical system to formulate the electromechanical coupling dynamic model (ECDM). To achieve the trajectory tracking and vibration suppression, a hierarchical compound control strategy is presented. Within this control strategy, the proportional-differential (PD) feedback controller is employed to realize the trajectory tracking of end-effector, while the strain and strain rate feedback (SSRF) controller is developed to restrain the vibration of the flexible links using PZT. Furthermore, the stability of the control algorithm is demonstrated based on the Lyapunov stability theory. Finally, two simulation case studies are performed to illustrate the effectiveness of the proposed approach. The results indicate that, under the redundant actuation mode, the hierarchical compound control strategy can guarantee the flexible PM achieves singularity-free motion and vibration attenuation within task workspace simultaneously. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and efficient controller design of other flexible PMs, especially the emerging ones with multiple actuation modes.

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.

Formation and maintenance of tubular membrane projections: experiments and numerical calculations.

PubMed

Umeda, Tamiki; Inaba, Takehiko; Ishijima, Akihiko; Takiguchi, Kingo; Hotani, Hirokazu

2008-01-01

To study the mechanical properties of lipid membranes, we manipulated liposomes by using a system comprising polystyrene beads and laser tweezers, and measured the force required to transform their shapes. When two beads pushed the membrane from inside, spherical liposomes transformed into a lemon-shape. Then a discontinuous shape transformation occurred to form a membrane tube from either end of the liposomes, and the force dropped drastically. We analyzed these processes using a mathematical model based on the bending elasticity of the membranes. Numerical calculations showed that when the bead size was taken into account, the model reproduced both the liposomal shape transformation and the force-extension relation. This result suggests that the size of the beads is responsible for the existence of a force barrier for the tube formation.

Supporting Teachers' Use of Virtual Manipulatives

ERIC Educational Resources Information Center

Reiten, Lindsay

2017-01-01

Technology integration is a critical and longstanding issue in mathematics education. As access to various technology resources increases, so too has the expectation for teachers to use technology to enhance student engagement and understanding. Despite the potential benefits to integrating technology into teachers' instructional practices,…

Free Software and Multivariable Calculus

ERIC Educational Resources Information Center

Nord, Gail M.

2011-01-01

Calculators and computers make new modes of instruction possible; yet, at the same time they pose hardships for school districts and mathematics educators trying to incorporate technology with limited monetary resources. In the "Standards," a recommended classroom is one in which calculators, computers, courseware, and manipulative materials are…

Modeling and control for micro and nano manipulation

NASA Astrophysics Data System (ADS)

Wejinya, Uchechukwu C.

Manipulation of micro and nano entities implies the movement of micro and nano entities from an initial position (location) to the desire position (location). This operation is not only necessary, but a required task with great precision. The tools needed for the manipulation needs to be chosen properly because the capabilities of the human hand are very restricted. Smart micro and nano manipulation are becoming of great interest in many applications including medicine and industry. In industry, high precision manipulation systems are especially needed for mass production of both micro and nano systems which consist of different component in respective scales. The transition from assembling and manipulating micro and nano entities manually to mass products with high quality is only attainable by automated assembly and manipulation systems. An example is the testing of integrated circuits which can be carried out by exchanging the manipulation tool by an electric probe. Furthermore, in medical research it is customary to pick up a single cell (human, plant, or animal), and carry it to another device which is used to further analyze the cell. Consequently, the cell of interest has to be separated from the other cells and picked up using the appropriate micro/nano tool. Hence it becomes absolutely necessary that the appropriate tool be used for specific micro or nano entity manipulation and assembly. In this research, we focus on developing micro tool for manipulating micro and nano entities in liquid environment using a micro fluidic end effector system with in-situ Polyvinylidene Fluoride (PVDF) sensing. The microfluidic end effector system consists of a DC micro-diaphragm pump and compressor, one region of flexible latex tube, a Polyvinylidene Fluoride (PVDF) sensor for in-situ measurement of micro drag force, and a micro pipette. The micro pipette of the novel microfluidic end effector system has an internal diameter (ID) smaller than 20mum used for microfluidic handling and deposition of micro and nano entities such as carbon nanotubes (CNT), DNA, and for droplet control. The novel microfluidic end effector system with force sensing can significantly improve the success rate for handling/depositing micro/nano entities in the case of carbon nanotubes between micro electrodes. The design, calibration, and experimental implementation of the novel microfluidic end effector is carried out in this research. The experimental results show the success rate for carbon nanotube(s) deposition between micro electrodes can reach close to 80%. Furthermore, carbon nanotubes are of particular interest because they are good candidates for many electronics and sensing applications. The interests in using carbon nanotubes to manufacture electronics and sensors have increased in recent years because of the increase need for making electronics smaller, and their excellent electrical and mechanical properties. These potentials can be achieved if CNTs with semiconducting and metallic band structure can be successfully deposited and separated. The use of dielectrophoresis (DEP) has been established as a course towards the efficient deposition and separation of metallic carbon nanotubes from semiconducting carbon nanotubes. For this reason, this research presents a new mathematical model for dielectrophoresis and electrorotation of carbon nanotubes. Simulation results are presented in this research to validate the developed model. The combination of both the micro robotic manipulation system and the atomic force microscopy (AFM) based nano-robotic system will provide a powerful tool for micro and nano manipulation. Additional applications of this research are endless considering the rapid development of micro and nano technologies.

Mathematical modelling of the antibiotic-induced morphological transition of Pseudomonas aeruginosa

PubMed Central

Keen, Emma; Smith, David J.

2018-01-01

Here we formulate a mechanistic mathematical model to describe the growth dynamics of P. aeruginosa in the presence of the β-lactam antibiotic meropenem. The model is mechanistic in the sense that carrying capacity is taken into account through the dynamics of nutrient availability rather than via logistic growth. In accordance with our experimental results we incorporate a sub-population of cells, differing in morphology from the normal bacillary shape of P. aeruginosa bacteria, which we assume have immunity from direct antibiotic action. By fitting this model to experimental data we obtain parameter values that give insight into the growth of a bacterial population that includes different cell morphologies. The analysis of two parameters sets, that produce different long term behaviour, allows us to manipulate the system theoretically in order to explore the advantages of a shape transition that may potentially be a mechanism that allows P. aeruginosa to withstand antibiotic effects. Our results suggest that inhibition of this shape transition may be detrimental to bacterial growth and thus suggest that the transition may be a defensive mechanism implemented by bacterial machinery. In addition to this we provide strong theoretical evidence for the potential therapeutic strategy of using antimicrobial peptides (AMPs) in combination with meropenem. This proposed combination therapy exploits the shape transition as AMPs induce cell lysis by forming pores in the cytoplasmic membrane, which becomes exposed in the spherical cells. PMID:29481562

A mathematical model of a shallow and eutrophic lake (the Keszthely Basin, Lake Balaton) and simulation of restorative manipulations.

PubMed

Sagehashi, M; Sakoda, A; Suzuki, M

2001-05-01

Concern about the overall management of lakes has been growing, and a lake ecological model provides the guidelines necessary for such management. In this study, an ecological model describing the ecosystem of the Keszthely Basin, Lake Balaton, Hungary, one of the typical shallow and eutrophic lakes, was proposed. This model includes three types of zooplankton and two types of fish as well as two types of algae and nutrients. Parameters concerning the algae and fish were estimated based on observations in the basin between 1991 and 1995. The other parameters and the structure of the model were determined by our previous study. The parameters of the model were calibrated with the Monte Carlo technique, and its predictability was confirmed. The effects on the basin's ecosystem of three restorative manipulations, namely a biomanipulation, reduction of loading phosphorus, and dredging the sediment, were assessed by simulation studies using the proposed model. The simulation results indicated that a biomanipulation that removed 90% of the bream should suppress the growth of algae temporarily through bottom-up regulation; however, this effect seemed to not be perpetuated in this basin. The reduction of loading phosphorus seemed to be the most effective means to suppress algal growth, while dredging of sediment seemed to be the most desirable restoration method from the standpoint of the overall management of the lake, because it was expected to accelerate the growth of fish population as well as to suppress algal growth. Furthermore, the algal growth suppression mechanism of the dredging was discussed on the basis of the model calculations.

Manipulatives and problem situations as escalators for students' geometric understanding: a semiotic analysis

NASA Astrophysics Data System (ADS)

Daher, Wajeeh M.

2014-04-01

Mathematical learning and teaching are increasingly seen as a multimodal experience involved in cultural and social semiotic registers and means, and as such social-cultural semiotic analysis is expected to shed light on learning and teaching processes occurring in the mathematics classroom. In this research, three social-cultural semiotic frameworks were utilised to analyse elementary school students' learning of a geometric relation: the semiotic bundle, the space of action, production and communication and the theoretical framework of attention, awareness and objectification. Educational mathematical situations are described, in addition to semiotic sets, registers and means emerging in the different mathematical situations and that are relevant to the three social-cultural semiotic frameworks which the current research utilizes. Further, the students, as a consequence of (1) their multimodal experience, (2) their connecting between the different mathematical situations and semiotic registers, and (3) the teacher's questions and tasks, could objectify the geometric relation between the lengths of the triangle's edges.

Mathematical formula recognition using graph grammar

NASA Astrophysics Data System (ADS)

Lavirotte, Stephane; Pottier, Loic

1998-04-01

This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.

Analytical derivation: An epistemic game for solving mathematically based physics problems

NASA Astrophysics Data System (ADS)

Bajracharya, Rabindra R.; Thompson, John R.

2016-06-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Brain-Building Math Games.

ERIC Educational Resources Information Center

Jung, Loretta Welk

1983-01-01

Index cards, masking tape, pizza shells, golf tees, and empty soda bottles can be used to make manipulative objects to be used in children's mathematics games. Twenty-two games that provide practice in number drills and problem solving are described, along with instructions for making objects needed for the games. (PP)

Demographic Computer Library.

ERIC Educational Resources Information Center

Shaw, David C.; Johnson, Dorothy M.

The complete comprehension of this paper requires a firm grasp of both mathematical demography and FORTRAN programming. The paper aims at the establishment of a language with which complex demographic manipulations can be briefly expressed in a form intelligible both to demographic analysts and to computers. The Demographic Computer Library (DCL)…

Large sex difference in adolescents on a timed line judgment task: attentional contributors and task relationship to mathematics.

PubMed

Collaer, Marcia L; Hill, Erica M

2006-01-01

Visuospatial performance, assessed with the new, group-administered Judgment of Line Angle and Position test (JLAP-13), varied with sex and mathematical competence in a group of adolescents. The JLAP-13, a low-level perceptual task, was modeled after a neuropsychological task dependent upon functioning of the posterior region of the right hemisphere [Benton et al, 1994 Contributions to Neuropsychological Assessment: A Clinical Manual (New York: Oxford University Press)]. High-school boys (N = 52) performed better than girls (N = 62), with a large effect for sex (d = 1.11). Performance increased with mathematical competence, but the sex difference did not vary significantly across different levels of mathematics coursework. On the basis of earlier work, it was predicted that male, but not female, performance in line judgment would decline with disruptions to task geometry (page frame), and that the sex difference would disappear with disruptions to geometry. These predictions were supported by a number of univariate and sex-specific analyses, although an omnibus repeated-measures analysis did not detect the predicted interaction, most likely owing to limitations in power. Thus, there is partial support for the notion that attentional predispositions or strategies may contribute to visuospatial sex differences, with males more likely than females to attend to, and rely upon, internal or external representations of task geometry. Additional support for this hypothesis may require development of new measures or experimental manipulations with more powerful geometrical disruptions.

Morphological optimization for access to dual oxidants in biofilms

PubMed Central

Kempes, Christopher P.; Okegbe, Chinweike; Mears-Clarke, Zwoisaint; Follows, Michael J.; Dietrich, Lars E. P.

2014-01-01

A major theme driving research in biology is the relationship between form and function. In particular, a longstanding goal has been to understand how the evolution of multicellularity conferred fitness advantages. Here we show that biofilms of the bacterium Pseudomonas aeruginosa produce structures that maximize cellular reproduction. Specifically, we develop a mathematical model of resource availability and metabolic response within colony features. This analysis accurately predicts the measured distribution of two types of electron acceptors: oxygen, which is available from the atmosphere, and phenazines, redox-active antibiotics produced by the bacterium. Using this model, we demonstrate that the geometry of colony structures is optimal with respect to growth efficiency. Because our model is based on resource dynamics, we also can anticipate shifts in feature geometry based on changes to the availability of electron acceptors, including variations in the external availability of oxygen and genetic manipulation that renders the cells incapable of phenazine production. PMID:24335705

Computational neural learning formalisms for manipulator inverse kinematics

NASA Technical Reports Server (NTRS)

Gulati, Sandeep; Barhen, Jacob; Iyengar, S. Sitharama

1989-01-01

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints.

Ultrasound acoustic energy for microbubble manipulation

NASA Astrophysics Data System (ADS)

Bakhtiari-Nejad, Marjan; Elnahhas, Ahmed; Jung, Sunghwan; Shahab, Shima

2017-04-01

Many bio-medical applications entail the problems of spatially manipulating of bubbles by means of acoustic radiation. The examples are ultrasonic noninvasive-targeted drug delivery and therapeutic applications. This paper investigates the nonlinear coupling between radial pulsations, axisymmetric modes of shape oscillations and translational motion of a single spherical gas bubble in a host liquid, when it is subjected to an acoustic pressure wave field. A mathematical model is developed to account for both small and large amplitudes of bubble oscillations. The coupled system dynamics under various conditions is studied. Specifically, oscillating behaviors of a bubble (e.g. the amplitudes and instability of oscillations) undergoing resonance and off-resonance excitation in low- and high- intensity acoustic fields are studied. Instability of the shape modes of a bubble, which is contributing to form the translational instability, known as dancing motion, is analyzed. Dynamic responses of the bubble exposed to low- and high-intensity acoustic excitation are compared in terms of translational motion and surface shape of the bubble. Acoustic streaming effects caused by radial pulsations of the bubble in the surrounding liquid domain are also reported.

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

NASA Technical Reports Server (NTRS)

Li, Feiyue; Bainum, Peter M.; Xu, Jianke

1991-01-01

The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e., centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulations is initiated. Two numerical examples show that the response of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Mathematical anxiety is linked to reduced cognitive reflection: a potential road from discomfort in the mathematics classroom to susceptibility to biases.

PubMed

Morsanyi, Kinga; Busdraghi, Chiara; Primi, Caterina

2014-09-01

When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181-185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25-42, 2005). The CRT is a measure of a person's ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking. In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs. Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1-3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection. Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals' ability to make advantageous choices and good decisions.

Teaching Polygons

ERIC Educational Resources Information Center

Scahill, Jillian

2006-01-01

Teachers assume that by the end of primary school, students should know the essentials regarding shape. For example, the NSW Mathematics K-6 syllabus states by year six students should be able manipulate, classify and draw two-dimensional shapes and describe side and angle properties. The reality is, that due to the pressure for students to…

Using Scratch: An Integrated Problem-Solving Approach to Mathematical Thinking

ERIC Educational Resources Information Center

Calder, Nigel

2010-01-01

"Scratch" is a media-rich digital environment that utilises a building block command structure to manipulate graphic, audio, and video aspects. It incorporates elements of Logo including "tinkerability" in the programming process. In "Scratch" students use geometric and measurement concepts such as coordinates, angle, and length measurements. It…

Sawtooth Functions. Classroom Notes

ERIC Educational Resources Information Center

Hirst, Keith

2004-01-01

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

Visual Servoing via Navigation Functions

DTIC Science & Technology

2002-02-06

kernel was adequate). The PC is equipped with a Data Translations12 DT3155 frame grabber connected to a standard 30Hz NTSC video camera. Using MATLAB’s C...Richard M. Murray, Zexiang Li, and S. Shankar Sastry. A Mathematical Introduction to Robotic Manipulation. CRC Press, Reading, Mass., 1994. [26] Dan Pedoe

Effects of Perceptually Rich Manipulatives on Preschoolers' Counting Performance: Established Knowledge Counts

ERIC Educational Resources Information Center

Petersen, Lori A.; McNeil, Nicole M.

2013-01-01

Educators often use concrete objects to help children understand mathematics concepts. However, findings on the effectiveness of concrete objects are mixed. The present study examined how two factors--perceptual richness and established knowledge of the objects--combine to influence children's counting performance. In two experiments, preschoolers…

A Historical Perspective on Teaching and Learning Calculus

ERIC Educational Resources Information Center

Doorman, Michiel; van Maanen, Jan

2008-01-01

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

Teaching with New Technology: Four "Early Majority" Teachers

ERIC Educational Resources Information Center

Pierce, Robyn; Stacey, Kaye

2013-01-01

This paper explores how four good teachers, who do not have a special interest in technology, meet the challenge of introducing the rapidly developing mathematics analysis software (e.g. spreadsheets, function graphers, symbolic algebra manipulation and dynamic geometry) into their classrooms. These teachers' practice is viewed through the…

Zooming in on Children's Thinking

ERIC Educational Resources Information Center

Tucker, Steven; Shumway, Jessica F.; Moyer-Packenham, Patricia S.; Jordan, Kerry E.

2016-01-01

Teachers increasingly use virtual manipulatives and other apps on touch-screen devices (e.g., "iPads") in an effort to help students understand mathematics concepts. However, students experience these apps and their affordances in different ways. The purpose of this article is to inform teachers' decisions about app implementation in the…

Teaching Multistep Equations with Virtual Manipulatives to Secondary Students with Learning Disabilities

ERIC Educational Resources Information Center

Satsangi, Rajiv; Hammer, Rachel; Evmenova, Anya S.

2018-01-01

Students with learning disabilities often struggle with the academic demands presented in secondary mathematics curricula. To combat these students' struggles, researchers have studied various pedagogical practices and classroom technologies for teaching standards covered in subjects such as algebra and geometry. However, as the role of computer-…

Fractions in Origami Pinwheels

ERIC Educational Resources Information Center

Russell, R. Alan

2017-01-01

Paper folding is an easy and inexpensive way to engage students artistically, culturally, and mathematically. The pinwheel base is the source for many origami playthings, from a pinwheel to a boat to a butterfly. This article explores a fourth grade activity that repurposes the pinwheel base into a rich and inexpensive manipulative for the review…

Easy Absolute Values? Absolutely

ERIC Educational Resources Information Center

Taylor, Sharon E.; Mittag, Kathleen Cage

2015-01-01

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

Measuring the Effectiveness of Educational Technology: What Are We Attempting to Measure?

ERIC Educational Resources Information Center

Jenkinson, Jodie

2009-01-01

In many academic areas, students' success depends upon their ability to envision and manipulate complex multidimensional information spaces. Fields in which students struggle with mastering these types of representations include (but are by no means limited to) mathematics, science, medicine, and engineering. There has been some educational…

Robust algebraic image enhancement for intelligent control systems

NASA Technical Reports Server (NTRS)

Lerner, Bao-Ting; Morrelli, Michael

1993-01-01

Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

A biokinetic model to describe consequences of inhibition/stimulation in DNA-proofreading and repair-1. Development of the model.

PubMed

Haschke, H

2001-10-21

A biokinetic model is described which deals with the mathematical consequences of the inhibition or stimulation of DNA proofreading. It demonstrates the development of the number of DNA mismatch-dependent cells (e.g. cells with a malignant phenotype), where such mismatches arise by the in situ interaction of various substances with nucleotides of the DNA. The model can test for consequences by a logic gating on an "if-then" type of analysis in relation to the separate and consecutive processes of proofreading and repair. In particular, the consequences are considered in cases where either (i) the efficacy of proofreading and repair are reduced/prevented (inhibited) or (ii) are increased by some form of stimulation. On the chosen kinetic parameters, the model is accessible to manipulation as new data arising from further investigations become available and are introduced. The model is based on recently published data which show that an increased "mutant fraction" (see note on terms) arises in DNA replication when intracellular nucleotide pools show "asymmetries" (see note on terms). Extraordinarily high mutant fractions can be predicted/have been recorded in the presence of proofreading inhibitors. The model expresses data in mathematical terms of the competition between the development of mismatch-dependent cells and those with authentic genetic information. (Feedback and metastasis-effects and those of wild-type replicates are included.) A computerized (numerical) integration of the corresponding set of differential equations is offered. (A diskette with the program CANCER.xls is available upon request.) Copyright 2001 Academic Press

Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

NASA Astrophysics Data System (ADS)

Ali, Maselan; Sufahani, Suliadi; Ahmad, Wan N. A. W.; Ghazali Kamardan, M.; Saifullah Rusiman, Mohd; Che-Him, Norziha

2018-04-01

Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students’ symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piaget’s ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students’ reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

When is working memory important for arithmetic? The impact of strategy and age.

PubMed

Cragg, Lucy; Richardson, Sophie; Hubber, Paula J; Keeble, Sarah; Gilmore, Camilla

2017-01-01

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition.

Software for Training in Pre-College Mathematics

NASA Technical Reports Server (NTRS)

Shelton, Robert O.; Moebes, Travis A.; VanAlstine, Scot

2003-01-01

The Intelligent Math Tutor (IMT) is a computer program for training students in pre-college and college-level mathematics courses, including fundamentals, intermediate algebra, college algebra, and trigonometry. The IMT can be executed on a server computer for access by students via the Internet; alternatively, it can be executed on students computers equipped with compact- disk/read-only-memory (CD-ROM) drives. The IMT provides interactive exercises, assessment, tracking, and an on-line graphing calculator with algebraic-manipulation capabilities. The IMT provides an innovative combination of content, delivery mechanism, and artificial intelligence. Careful organization and presentation of the content make it possible to provide intelligent feedback to the student based on performance on exercises and tests. The tracking and feedback mechanisms are implemented within the capabilities of a commercial off-the-shelf development software tool and are written in the Unified Modeling Language to maximize reuse and minimize development cost. The graphical calculator is a standard feature of most college and pre-college algebra and trigonometry courses. Placing this functionality in a Java applet decreases the cost, provides greater capabilities, and provides an opportunity to integrate the calculator with the lessons.

Effective Student Learning of Fractions with an Interactive Simulation

ERIC Educational Resources Information Center

Hensberry, Karina K. R.; Moore, Emily B.; Perkins, Katherine K.

2015-01-01

Computer technology, when coupled with reform-based teaching practices, has been shown to be an effective way to support student learning of mathematics. The quality of the technology itself, as well as how it is used, impacts how much students learn. Interactive simulations are dynamic virtual environments similar to virtual manipulatives that…

Truth, Damn Truth, and Statistics

ERIC Educational Resources Information Center

Velleman, Paul F.

2008-01-01

Statisticians and Statistics teachers often have to push back against the popular impression that Statistics teaches how to lie with data. Those who believe incorrectly that Statistics is solely a branch of Mathematics (and thus algorithmic), often see the use of judgment in Statistics as evidence that we do indeed manipulate our results. In the…

Discrete and Continuous Reasoning about Change in Primary School Classrooms

ERIC Educational Resources Information Center

de Beer, Huub; Gravemeijer, Koeno; van Eijck, Michiel

2015-01-01

To prepare students for participation in our society, where interpreting, representing, and manipulating of dynamic phenomena are becoming key activities, we believe that one should start developing a mathematical understanding of change at an early age. We therefore started a design research project to teach the concept of instantaneous speed in…

GUIDE FOR COURSE OF STUDY FOR COOK (HOTEL AND RESTAURANT) (ENTRY).

ERIC Educational Resources Information Center

GUNN, VIRLAH

DESIGNED FOR TEACHER USE, THIS GUIDE FOR TRAINING COOKS IN HOTEL AND RESTAURANT OCCUPATIONS AIMS--(1) TO DEVELOP MANIPULATIVE SKILLS, (2) TO DEVELOP UNDERSTANDING OF THE BASIC PRINCIPLES OF SCIENCE, MATHEMATICS, AND RELATED KNOWLEDGE THAT CONDITION THESE SKILLS, (3) TO UNDERSTAND THE ADVANTAGES OF STEADY EMPLOYMENT, (4) TO DEVELOP HIGH STANDARDS…

Scribble Scrabble: Ready-in-a-Minute Math Games.

ERIC Educational Resources Information Center

Sharp, Richard M.; And Others

Mathematics research has discovered two elements that are consistently linked to student achievement: parental involvement and manipulative materials. This book offers a rich assortment of spinner, matrix, and card learning games which can be used in the classroom or at home. The concepts and skills range from whole number operations to geometry.…

Exploring the Solar System? Let the Math Teachers Help!

ERIC Educational Resources Information Center

Charles, Karen; Canales, J. D.; Smith, Angela; Zimmerman, Natalie

2012-01-01

Scale measurement and ratio and proportion are topics that fall clearly in the middle-grades mathematics curriculum in Texas. So does the solar system. In their experience, the authors have found that students have trouble manipulating, much less comprehending, very large numbers and very small numbers. These concepts can be brought into students'…

A Paradigmatic Example of an Artificially Intelligent Instructional System.

ERIC Educational Resources Information Center

Brown, John Seely; Burton, Richard R.

This paper describes the philosophy of intelligent instructional systems and presents an example of one such system in the domain of manipulative mathematics--BLOCKS. The notion of BLOCKS as a paradigmatic system is explicated from both the system development and educational viewpoints. From a developmental point of view, the modular design of…

Enhancing Eighth Grade Student Presentations of Scientific Research with Technology.

ERIC Educational Resources Information Center

Shreiner, Berdella H.

This practicum was designed to improve the research and communication skills of eighth-grade students with the integration of technology, mathematics, and science when doing real-experience problem solving. Four units were developed that related the use of technology to skills that are also used in gathering, organizing, and manipulating research…

L’eggo My Ego: Reducing the Gender Gap in Math by Unlinking the Self from Performance

PubMed Central

Zhang, Shen; Schmader, Toni; Hall, William M.

2012-01-01

Stereotype threat can vary in source, with targets being threatened at the individual and/or group level. This study examines specifically the role of self-reputational threat in women’s underperformance in mathematics. A pilot study shows that women report concerns about experiencing self-reputational threat that are distinct from group threat in the domain of mathematics. In the main study, we manipulated whether performance was linked to the self by asking both men and women to complete a math test using either their real name or a fictitious name. Women who used a fictitious name, and thus had their self unlinked from the math test, showed significantly higher math performance and reported less self-threat and distraction, relative to those who used their real names. Men were unaffected by the manipulation. These findings suggest that women’s impaired math performance is often due to the threat of confirming a negative stereotype as being true of the self. The implications for understanding the different types of threats faced by stereotyped groups, particularly among women in math settings, are discussed. PMID:24223027

Mathematical anxiety is linked to reduced cognitive reflection: a potential road from discomfort in the mathematics classroom to susceptibility to biases

PubMed Central

2014-01-01

Background When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking. Methods In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs. Results Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection. Conclusions Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions. PMID:25179230

Approximate numerical abilities and mathematics: Insight from correlational and experimental training studies.

PubMed

Hyde, D C; Berteletti, I; Mou, Y

2016-01-01

Humans have the ability to nonverbally represent the approximate numerosity of sets of objects. The cognitive system that supports this ability, often referred to as the approximate number system (ANS), is present in early infancy and continues to develop in precision over the life span. It has been proposed that the ANS forms a foundation for uniquely human symbolic number and mathematics learning. Recent work has brought two types of evidence to bear on the relationship between the ANS and human mathematics: correlational studies showing individual differences in approximate numerical abilities correlate with individual differences in mathematics achievement and experimental studies showing enhancing effects of nonsymbolic approximate numerical training on exact, symbolic mathematical abilities. From this work, at least two accounts can be derived from these empirical data. It may be the case that the ANS and mathematics are related because the cognitive and brain processes responsible for representing numerical quantity in each format overlap, the Representational Overlap Hypothesis, or because of commonalities in the cognitive operations involved in mentally manipulating the representations of each format, the Operational Overlap hypothesis. The two hypotheses make distinct predictions for future work to test. © 2016 Elsevier B.V. All rights reserved.

Experimental modeling of the effect of hurricane wind forces on driving behavior and vehicle performance.

PubMed

Rodriguez, Jose M; Codjoe, Julius; Osman, Osama; Ishak, Sherif; Wolshon, Brian

2015-01-01

While traffic planning is important for developing a hurricane evacuation plan, vehicle performance on the roads during extreme weather conditions is critical to the success of the planning process. This novel study investigates the effect of gusty hurricane wind forces on the driving behavior and vehicle performance. The study explores how the parameters of a driving simulator could be modified to reproduce wind loadings experienced by three vehicle types (passenger car, ambulance, and bus) during gusty hurricane winds, through manipulation of appropriate software. Thirty participants were then tested on the modified driving simulator under five wind conditions (ranging from normal to hurricane category 4). The driving performance measures used were heading error and lateral displacement. The results showed that higher wind forces resulted in more varied and greater heading error and lateral displacement. The ambulance had the greatest heading errors and lateral displacements, which were attributed to its large lateral surface area and light weight. Two mathematical models were developed to estimate the heading error and lateral displacements for each of the vehicle types for a given change in lateral wind force. Through a questionnaire, participants felt the different characteristics while driving each vehicle type. The findings of this study demonstrate the valuable use of a driving simulator to model the behavior of different vehicle types and to develop mathematical models to estimate and quantify driving behavior and vehicle performance under hurricane wind conditions.

Effectiveness of working memory training among children with dyscalculia: evidence for transfer effects on mathematical achievement-a pilot study.

PubMed

Layes, Smail; Lalonde, Robert; Bouakkaz, Yamina; Rebai, Mohamed

2017-12-22

We examined whether the working memory (WM) capacity of developmentally dyscalculic children can be improved by a WM training program and whether outcomes relate to mathematical performance. The experimental design comprised two groups with developmental dyslexia with grade 4 schooling: an experimental group (n = 14; mean age = 129.74 months) and a control group (n = 14; mean age = 126.9 months). All participants were assessed on measures of WM, mathematic attainment, and nonverbal mental ability (Raven test) before and after training. The WM training program focused on manipulating and maintaining arithmetic information. The results show that both WM and mathematical performances improved significantly after intervention, indicating a strong relationship between these two constructs. The control group improved slightly in Raven's progressive matrices and a reading number task. These findings are discussed in terms of near and far transfer toward trained and untrained skills and stress the positive impact of WM training on learning mathematics in children with dyscalculia.

Experimental test of contemporary mathematical models of visual letter recognition.

PubMed

Townsend, J T; Ashby, F G

1982-12-01

A letter confusion experiment that used brief durations manipulated payoffs across the four stimulus letters, which were composed of line segments equal in length. The observers were required to report the features they perceived as well as to give a letter response. The early feature-sampling process is separated from the later letter-decision process in the substantive feature models, and predictions are thus obtained for the frequencies of feature report as well as letter report. Four substantive visual feature-processing models are developed and tested against one another and against three models of a more descriptive nature. The substantive models predict the decisional letter report phase much better than they do the feature-sampling phase, but the best overall 4 X 4 letter confusion matrix fits are obtained with one of the descriptive models, the similarity choice model. The present and other recent results suggest that the assumption that features are sampled in a stochastically independent manner may not be generally valid. The traditional high-threshold conceptualization of feature sampling is also falsified by the frequent reporting by observers of features not contained in the stimulus letter.

Hollow Gaussian beams and their propagation properties

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Lu, Xuanhui; Lin, Qiang

2003-07-01

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.

Hollow Gaussian beams and their propagation properties.

PubMed

Cai, Yangjian; Lu, Xuanhui; Lin, Qiang

2003-07-01

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.

Space transportation system payload interface verification

NASA Technical Reports Server (NTRS)

Everline, R. T.

1977-01-01

The paper considers STS payload-interface verification requirements and the capability provided by STS to support verification. The intent is to standardize as many interfaces as possible, not only through the design, development, test and evaluation (DDT and E) phase of the major payload carriers but also into the operational phase. The verification process is discussed in terms of its various elements, such as the Space Shuttle DDT and E (including the orbital flight test program) and the major payload carriers DDT and E (including the first flights). Five tools derived from the Space Shuttle DDT and E are available to support the verification process: mathematical (structural and thermal) models, the Shuttle Avionics Integration Laboratory, the Shuttle Manipulator Development Facility, and interface-verification equipment (cargo-integration test equipment).

A PVS Prover Strategy Package for Common Manipulations

NASA Technical Reports Server (NTRS)

DiVito, Ben L.

2002-01-01

Sequent manipulations for an interactive prover such as PVS can often be labor intensive. We describe an approach to tactic-based proving for improved interactive deduction in specialized domains. An experimental package of strategies (tactics) and support functions has been developed for PVS to reduce the tedium of arithmetic manipulation. Included are strategies aimed at algebraic simplification of real-valued expressions as well as term-access techniques applicable in arbitrary settings. The approach is general enough to serve in other mathematical domains and for provers other than PVS. This report presents the full set of arithmetic strategies and discusses how they are invoked within the prover. Included is a description of the extended expression notation for accessing terms as well as a substitution technique provided for higher-order strategies. Several sample proofs are displayed in full to show how the strategies might be used in practice.

Study of design and control of remote manipulators. Part 2: Vibration considerations in manipulator design

NASA Technical Reports Server (NTRS)

Book, W. J.

1973-01-01

An investigation is reported involving a mathematical procedure using 4 x 4 transformation matrices for analyzing the vibrations of flexible manipulators. Previous studies with the procedure are summarized and the method is extended to include flexible joints as well as links, and to account for the effects of various power transmission schemes. A systematic study of the allocation of structural material and the placement of components such as motors and gearboxes was undertaken using the analytical tools developed. As one step in this direction the variables which relate the vibration parameters of the arm to the task and environment of the arm were isolated and nondimensionalized. The 4 x 4 transformation matrices were also used to develop analytical expressions for the terms of the complete 6 x 6 compliance matrix for the case of two flexible links joined by a rotating joint, flexible about its axis of rotation.

Spectrophotometric resolution of the severely overlapped spectra of clotrimazole with dexamethasone in cream dosage form by mathematical manipulation steps.

PubMed

Lotfy, Hayam Mahmoud; Fayez, Yasmin Mohammed; Tawakkol, Shereen Mostafa; Fahmy, Nesma Mahmoud; Shehata, Mostafa Abd El-Atty

2018-09-05

Several spectrophotometric techniques were recently conducted for the determination of binary mixtures of clotrimazole (CLT) and dexamethasone acetate (DA) without any separation procedure. The methods were based on generation of ratio spectra of mixture then applying simple mathematic manipulation. The zero order absorption spectra of both drugs could be obtained by the constant center (CC) method. The concentration of both CLT and DA could be obtained by constant value via amplitude difference (CV-AD) method depending on ratio spectra, Ratio difference (RD) method where the difference between the amplitudes at two wavelengths (ΔP) on the ratio spectra could eliminate the contribution of the interfering substance and bring the concentration of the other, and the derivative ratio (DD 1 ) method where the derivative of the ratio spectra was able to determine the drug of interest without any interference of the other one. While the concentration of DA could be measured after graphical manipulation as concentration using the novel advanced concentration value method (ACV). Calibration graphs were linear in the range of 75-550 μg/mL for CLT and 2-20 μg/mL for DA. The methods applied to the binary mixture under study were successfully applied for the simultaneous determination of the two drugs in synthetic mixtures and in their combined form Mycuten-D cream. The results obtained were compared statistically to each other and to the official methods. Copyright © 2018 Elsevier B.V. All rights reserved.

Modeling cortical circuits.

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

Rohrer, Brandon Robinson; Rothganger, Fredrick H.; Verzi, Stephen J.

2010-09-01

The neocortex is perhaps the highest region of the human brain, where audio and visual perception takes place along with many important cognitive functions. An important research goal is to describe the mechanisms implemented by the neocortex. There is an apparent regularity in the structure of the neocortex [Brodmann 1909, Mountcastle 1957] which may help simplify this task. The work reported here addresses the problem of how to describe the putative repeated units ('cortical circuits') in a manner that is easily understood and manipulated, with the long-term goal of developing a mathematical and algorithmic description of their function. The approachmore » is to reduce each algorithm to an enhanced perceptron-like structure and describe its computation using difference equations. We organize this algorithmic processing into larger structures based on physiological observations, and implement key modeling concepts in software which runs on parallel computing hardware.« less

Manipulating Traveling Brain Waves with Electric Fields: From Theory to Experiment.

NASA Astrophysics Data System (ADS)

Gluckman, Bruce J.

2004-03-01

Activity waves in disinhibited neocortical slices have been used as a biological model for epileptic seizure propagation [1]. Such waves have been mathematically modeled with integro-differential equations [2] representing non-local reaction diffusion dynamics of an excitable medium with an excitability threshold. Stability and propagation speed of traveling pulse solutions depend strongly on the threshold in the following manner: propagation speed should decrease with increased threshold over a finite range, beyond which the waves become unstable. Because populations of neurons can be polarized with an applied electric field that effectively shifts their threshold for action potential initiation [3], we predicted, and have experimentally verified, that electric fields could be used globally or locally to speed up, slow down and even block wave propagation. [1] Telfeian and Conners, Epilepsia, 40, 1499-1506, 1999. [2] Pinto and Ermentrout, SIAM J. App. Math, 62, 206-225, 2001. [3] Gluckman, et. al. J Neurophysiol. 76, 4202-5, 1996.

Integration of single-fiber reflectance spectroscopy into ultrasound-guided endoscopic lung cancer staging of mediastinal lymph nodes

NASA Astrophysics Data System (ADS)

Kanick, Stephen Chad; van der Leest, Cor; Aerts, Joachim G. J. V.; Hoogsteden, Henk C.; Kaščáková, Slávka; Sterenborg, Henricus J. C. M.; Amelink, Arjen

2010-01-01

We describe the incorporation of a single-fiber reflectance spectroscopy probe into the endoscopic ultrasound fine-needle aspiration (EUS-FNA) procedure utilized for lung cancer staging. A mathematical model is developed to extract information about the physiological and morphological properties of lymph tissue from single-fiber reflectance spectra, e.g., microvascular saturation, blood volume fraction, bilirubin concentration, average vessel diameter, and Mie slope. Model analysis of data from a clinical pilot study shows that the single-fiber reflectance measurement is capable of detecting differences in the physiology between normal and metastatic lymph nodes. Moreover, the clinical data show that probe manipulation within the lymph node can perturb the in vivo environment, a concern that must be carefully considered when developing a sampling strategy. The data show the feasibility of this novel technique; however, the potential clinical utility has yet to be determined.

A Feasibility Study on a Parallel Mechanism for Examining the Space Shuttle Orbiter Payload Bay Radiators

NASA Technical Reports Server (NTRS)

Roberts, Rodney G.; LopezdelCastillo, Eduardo

1996-01-01

The goal of the project was to develop the necessary analysis tools for a feasibility study of a cable suspended robot system for examining the space shuttle orbiter payload bay radiators These tools were developed to address design issues such as workspace size, tension requirements on the cable, the necessary accuracy and resolution requirements and the stiffness and movement requirements of the system. This report describes the mathematical models for studying the inverse kinematics, statics, and stiffness of the robot. Each model is described by a matrix. The manipulator Jacobian was also related to the stiffness matrix, which characterized the stiffness of the system. Analysis tools were then developed based on the singular value decomposition (SVD) of the corresponding matrices. It was demonstrated how the SVD can be used to quantify the robot's performance and to provide insight into different design issues.

Analysis of a minimal Rho-GTPase circuit regulating cell shape

NASA Astrophysics Data System (ADS)

Holmes, William R.; Edelstein-Keshet, Leah

2016-08-01

Networks of Rho-family GTPases regulate eukaryotic cell polarization and motility by controlling assembly and contraction of the cytoskeleton. The mutually inhibitory Rac-Rho circuit is emerging as a central, regulatory hub that can affect the shape and motility phenotype of eukaryotic cells. Recent experimental manipulation of the amounts of Rac and Rho or their regulators (guanine nucleotide-exchange factors, GTPase-activating proteins, guanine nucleotide dissociation inhibitors) have been shown to bias the prevalence of these different states and promote transitions between them. Here we show that part of this data can be understood in terms of inherent Rac-Rho mutually inhibitory dynamics. We analyze a spatio-temporal mathematical model of Rac-Rho dynamics to produce a detailed set of predictions of how parameters such as GTPase rates of activation and total amounts affect cell decisions (such as Rho-dominated contraction, Rac-dominated spreading, and spatially segregated Rac-Rho polarization). We find that in some parameter regimes, a cell can take on any of these three fates depending on its environment or stimuli. We also predict how experimental manipulations (corresponding to parameter variations) can affect cell shapes observed. Our methods are based on local perturbation analysis (a kind of nonlinear stability analysis), and an approximation of nonlinear feedback by sharp switches. We compare the Rac-Rho model to an even simpler single-GTPase (‘wave-pinning’) model and demonstrate that the overall behavior is inherent to GTPase properties, rather than stemming solely from network topology.

Modeling of Continuum Manipulators Using Pythagorean Hodograph Curves.

PubMed

Singh, Inderjeet; Amara, Yacine; Melingui, Achille; Mani Pathak, Pushparaj; Merzouki, Rochdi

2018-05-10

Research on continuum manipulators is increasingly developing in the context of bionic robotics because of their many advantages over conventional rigid manipulators. Due to their soft structure, they have inherent flexibility, which makes it a huge challenge to control them with high performances. Before elaborating a control strategy of such robots, it is essential to reconstruct first the behavior of the robot through development of an approximate behavioral model. This can be kinematic or dynamic depending on the conditions of operation of the robot itself. Kinematically, two types of modeling methods exist to describe the robot behavior; quantitative methods describe a model-based method, and qualitative methods describe a learning-based method. In kinematic modeling of continuum manipulator, the assumption of constant curvature is often considered to simplify the model formulation. In this work, a quantitative modeling method is proposed, based on the Pythagorean hodograph (PH) curves. The aim is to obtain a three-dimensional reconstruction of the shape of the continuum manipulator with variable curvature, allowing the calculation of its inverse kinematic model (IKM). It is noticed that the performances of the PH-based kinematic modeling of continuum manipulators are considerable regarding position accuracy, shape reconstruction, and time/cost of the model calculation, than other kinematic modeling methods, for two cases: free load manipulation and variable load manipulation. This modeling method is applied to the compact bionic handling assistant (CBHA) manipulator for validation. The results are compared with other IKMs developed in case of CBHA manipulator.

Young Children's Learning Performance and Efficiency When Using Virtual Manipulative Mathematics iPad Apps

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Shumway, Jessica F.; Bullock, Emma; Tucker, Stephen I.; Anderson-Pence, Katie L.; Westenskow, Arla; Boyer-Thurgood, Jennifer; Maahs-Fladung, Cathy; Symanzik, Juergen; Mahamane, Salif; MacDonald, Beth; Jordan, Kerry

2015-01-01

Part of a larger initiation mixed methods study (Greene, Caracelli, & Graham, 1989), this paper discusses the changes in young children's learning performance and efficiency (one element of the quantitative portion of the larger study) during clinical interviews in which each child interacted with a variety of virtual manipulative…

The Use of Physical and Virtual Manipulatives in an Undergraduate Mechanical Engineering (Dynamics) Course

ERIC Educational Resources Information Center

Pan, Edward A.

2013-01-01

Science, technology, engineering, and mathematics (STEM) education is a national focus. Engineering education, as part of STEM education, needs to adapt to meet the needs of the nation in a rapidly changing world. Using computer-based visualization tools and corresponding 3D printed physical objects may help nontraditional students succeed in…

Two Geo-Arithmetic Representations of n[superscript 3]: Sum of Hex Numbers

ERIC Educational Resources Information Center

Unal, Husan

2009-01-01

Studies have shown that students' understanding is typically analytic and not visual. Two possible reasons for this are when the analytic mode, instead of the graphic mode, is most frequently used in instruction or, when students or teachers hold the belief that mathematics consists simply of skillful manipulation of symbols and numbers. The…

Schema-Based Instruction with Concrete and Virtual Manipulatives to Teach Problem Solving to Students with Autism

ERIC Educational Resources Information Center

Root, Jenny R.; Browder, Diane M.; Saunders, Alicia F.; Lo, Ya-yu

2017-01-01

The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In…

Making Comparisons: Ratios. Topical Module for Use in a Mathematics Laboratory Setting.

ERIC Educational Resources Information Center

Andersen, Lyle; And Others

The objectives of this module on making comparisons and ratios include using ratios to compare sets of objects and expressing ratios as decimals or fractions in lowest terms. The module provides six experiments. An envelope of manipulatives accompanies each of the first three experiments. The fourth experiment requires a multispeed bicycle. The…

Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R

ERIC Educational Resources Information Center

Actuarial Foundation, 2013

2013-01-01

"Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…

Conditions for the Effectiveness of a Tablet-Based Algebra Program

ERIC Educational Resources Information Center

Jaciw, Andrew P.; Toby, Megan; Ma, Boya

2012-01-01

Tablets such as the iPad represent the next iteration of technologies that hold promise to facilitate learning, particularly in mathematics. In the case of algebra, tablets have the potential to bring the curriculum to life by easily linking to supporting materials and they allow an interactive experience whereby manipulation of one type of…

Something Drawn, Something Touched, Something Scrolled: An Exploratory Comparison of Perimeter and Area Interventions Including Kidspiration

ERIC Educational Resources Information Center

Sossi, Dino; Jamalian, Azadeh; Richardson, Shenetta

2011-01-01

This exploratory study compared a computer-based mathematics education intervention with two more traditional approaches with the purpose of improving instruction in perimeter and area. Kidspiration software, tile/stick manipulatives and pencil/paper-based copying/drawing of shapes were implemented in a 3rd Grade New York City public school…

Kinesthetic coupling between operator and remote manipulator

NASA Technical Reports Server (NTRS)

Bejczy, A. K.; Salisbury, J. K., Jr.

1980-01-01

A universal force-reflecting hand controller has been developed which allows the establishment of a kinesthetic coupling between the operator and a remote manipulator. The six-degree-of-freedom controller was designed to generate forces and torques on its three positional and three rotational axes in order to permit the operator to accurately feel the forces encountered by the manipulator and be as transparent to operate as possible. The universal controller has been used in an application involving a six-degree-of-freedom mechanical arm equipped with a six-dimensional force-torque sensor at its base. In this application, the hand controller acts as a position control input device to the arm, while forces and torques sensed at the base of the mechanical hand back drive the hand controller. The positional control relation and the back driving of the controller according to inputs experienced by the force-torque sensor are established through complex mathematical transformations performed by a minicomputer. The hand controller is intended as a development tool for investigating force-reflecting master-slave manipulator control technology.

Failure tolerance strategy of space manipulator for large load carrying tasks

NASA Astrophysics Data System (ADS)

Chen, Gang; Yuan, Bonan; Jia, Qingxuan; Sun, Hanxu; Guo, Wen

2018-07-01

During the execution of large load carrying tasks in long term service, there is a notable risk of space manipulator suffering from locked-joint failure, thus space manipulator should be with enough failure tolerance performance. A research on evaluating failure tolerance performance and re-planning feasible task trajectory for space manipulator performing large load carrying tasks is conducted in this paper. The effects of locked-joint failure on critical performance(reachability and load carrying capacity) of space manipulator are analyzed at first. According to the requirements of load carrying tasks, we further propose a new concept of failure tolerance workspace with load carrying capacity(FTWLCC) to evaluate failure tolerance performance, and improve the classic A* algorithm to search the feasible task trajectory. Through the normalized FTWLCC and the improved A* algorithm, the reachability and load carrying capacity of the degraded space manipulator are evaluated, and the reachable and capable trajectory can be obtained. The establishment of FTWLCC provides a novel idea that combines mathematical statistics with failure tolerance performance to illustrate the distribution of load carrying capacity in three-dimensional space, so multiple performance indices can be analyzed simultaneously and visually. And the full consideration of all possible failure situations and motion states makes FTWLCC and improved A* algorithm be universal and effective enough to be appropriate for random joint failure and variety of requirement of large load carrying tasks, so they can be extended to other types of manipulators.

Methodological Developments in Geophysical Assimilation Modeling

NASA Astrophysics Data System (ADS)

Christakos, George

2005-06-01

This work presents recent methodological developments in geophysical assimilation research. We revisit the meaning of the term "solution" of a mathematical model representing a geophysical system, and we examine its operational formulations. We argue that an assimilation solution based on epistemic cognition (which assumes that the model describes incomplete knowledge about nature and focuses on conceptual mechanisms of scientific thinking) could lead to more realistic representations of the geophysical situation than a conventional ontologic assimilation solution (which assumes that the model describes nature as is and focuses on form manipulations). Conceptually, the two approaches are fundamentally different. Unlike the reasoning structure of conventional assimilation modeling that is based mainly on ad hoc technical schemes, the epistemic cognition approach is based on teleologic criteria and stochastic adaptation principles. In this way some key ideas are introduced that could open new areas of geophysical assimilation to detailed understanding in an integrated manner. A knowledge synthesis framework can provide the rational means for assimilating a variety of knowledge bases (general and site specific) that are relevant to the geophysical system of interest. Epistemic cognition-based assimilation techniques can produce a realistic representation of the geophysical system, provide a rigorous assessment of the uncertainty sources, and generate informative predictions across space-time. The mathematics of epistemic assimilation involves a powerful and versatile spatiotemporal random field theory that imposes no restriction on the shape of the probability distributions or the form of the predictors (non-Gaussian distributions, multiple-point statistics, and nonlinear models are automatically incorporated) and accounts rigorously for the uncertainty features of the geophysical system. In the epistemic cognition context the assimilation concept may be used to investigate critical issues related to knowledge reliability, such as uncertainty due to model structure error (conceptual uncertainty).

Atmosphere stabilization and element recycle in an experimental mouse-algal system

NASA Technical Reports Server (NTRS)

Smernoff, David T.

1986-01-01

Life support systems based on bioregeneration rely on the control and manipulation of organisms. Experiments conducted with a gas-closed mouse-algal system designed to investigate principles of photosynthetic gas exchange focus primarily on observing gas exchange phenomena under varying algal environmental conditions and secondarily on studying element cycling through compartments of the experimental system. Inherent instabilities exit between the uptake and release of carbon dioxide CO2 and oxygen O2 by the mouse and algae. Variations in light intensity and cell density alter the photosynthetic rate of the algae and enable maintenance of physiologic concentrations of CO2 and O2. Different nitrogen sources (urea and nitrate) result in different algal assimilatory quotients (AQ). Combinations of photosynthetic rate and AQ ratio manipulations have been examined for their potential in stabilizing atmospheric gas concentrations in the gas-closed algal-mouse system. Elemental mass balances through the experimental systems compartments are being studied with the concurrent development of a mathematical simulation model. Element cycling experiments include quantification of elemental flows through system compartments and wet oxidation of system waste materials for use as an algal nutrient source. Oxidized waste products demonstrate inhibitory properties although dilution has been shown to allow normal growth.

Analysis of Peristaltic Waves & their Role in Migrating Physarum Plasmodia

NASA Astrophysics Data System (ADS)

Lewis, Owen; Guy, Robert

2017-11-01

The true slime mold Physarum polycephalum exhibits a vast array of sophisticated manipulations of its intracellular cytoplasm. Growing microplasmodia of physarum have been observed to adopt an elongated tadpole shape, then contract in a rhythmic, traveling wave pattern that resembles peristaltic pumping. This contraction drives a fast flow of non-gelated cytoplasm along the cell longitudinal axis. It has been hypothesized that this flow of cytoplasm is a driving factor in generating motility of the plasmodium. In this work, we use two different mathematical models to investigate how peristaltic pumping within physarum may be used to drive cellular motility. We compare the relative phase of flow and deformation waves predicted by both models to similar phase data collected from in vivo experiments using physarum plasmodia. Both models suggest that a mechanical asymmetry in the cell is required to reproduce the experimental observations. Such a mechanical asymmetry is also shown to increase the potential for cellular migration, as measured by both stress generation and migration velocity.

Adaptive hidden Markov model with anomaly States for price manipulation detection.

PubMed

Cao, Yi; Li, Yuhua; Coleman, Sonya; Belatreche, Ammar; McGinnity, Thomas Martin

2015-02-01

Price manipulation refers to the activities of those traders who use carefully designed trading behaviors to manually push up or down the underlying equity prices for making profits. With increasing volumes and frequency of trading, price manipulation can be extremely damaging to the proper functioning and integrity of capital markets. The existing literature focuses on either empirical studies of market abuse cases or analysis of particular manipulation types based on certain assumptions. Effective approaches for analyzing and detecting price manipulation in real time are yet to be developed. This paper proposes a novel approach, called adaptive hidden Markov model with anomaly states (AHMMAS) for modeling and detecting price manipulation activities. Together with wavelet transformations and gradients as the feature extraction methods, the AHMMAS model caters to price manipulation detection and basic manipulation type recognition. The evaluation experiments conducted on seven stock tick data from NASDAQ and the London Stock Exchange and 10 simulated stock prices by stochastic differential equation show that the proposed AHMMAS model can effectively detect price manipulation patterns and outperforms the selected benchmark models.

Modelling and Closed-Loop System Identification of a Quadrotor-Based Aerial Manipulator

NASA Astrophysics Data System (ADS)

Dube, Chioniso; Pedro, Jimoh O.

2018-05-01

This paper presents the modelling and system identification of a quadrotor-based aerial manipulator. The aerial manipulator model is first derived analytically using the Newton-Euler formulation for the quadrotor and Recursive Newton-Euler formulation for the manipulator. The aerial manipulator is then simulated with the quadrotor under Proportional Derivative (PD) control, with the manipulator in motion. The simulation data is then used for system identification of the aerial manipulator. Auto Regressive with eXogenous inputs (ARX) models are obtained from the system identification for linear accelerations \\ddot{X} and \\ddot{Y} and yaw angular acceleration \\ddot{\\psi }. For linear acceleration \\ddot{Z}, and pitch and roll angular accelerations \\ddot{θ } and \\ddot{φ }, Auto Regressive Moving Average with eXogenous inputs (ARMAX) models are identified.

Haptic Recreation of Elbow Spasticity

PubMed Central

Kim, Jonghyun; Damiano, Diane L.

2013-01-01

The aim of this paper is to develop a haptic device capable of presenting standardized recreation of elbow spasticity. Using the haptic device, clinicians will be able to repeatedly practice the assessment of spasticity without requiring patient involvement, and these practice opportunities will help improve accuracy and reliability of the assessment itself. Haptic elbow spasticity simulator (HESS) was designed and prototyped according to mechanical requirements to recreate the feel of elbow spasticity. Based on the data collected from subjects with elbow spasticity, a mathematical model representing elbow spasticity is proposed. As an attempt to differentiate the feel of each score in Modified Ashworth Scale (MAS), parameters of the model were obtained respectively for three different MAS scores 1, 1+, and 2. The implemented haptic recreation was evaluated by experienced clinicians who were asked to give MAS scores by manipulating the haptic device. The clinicians who participated in the study were blinded to each other’s scores and to the given models. They distinguished the three models and the MAS scores given to the recreated models matched 100% with the original MAS scores from the patients. PMID:22275660

Modeling Pilot State in Next Generation Aircraft Alert Systems

NASA Technical Reports Server (NTRS)

Carlin, Alan S.; Alexander, Amy L.; Schurr, Nathan

2011-01-01

The Next Generation Air Transportation System will introduce new, advanced sensor technologies into the cockpit that must convey a large number of potentially complex alerts. Our work focuses on the challenges associated with prioritizing aircraft sensor alerts in a quick and efficient manner, essentially determining when and how to alert the pilot This "alert decision" becomes very difficult in NextGen due to the following challenges: 1) the increasing number of potential hazards, 2) the uncertainty associated with the state of potential hazards as well as pilot slate , and 3) the limited time to make safely-critical decisions. In this paper, we focus on pilot state and present a model for anticipating duration and quality of pilot behavior, for use in a larger system which issues aircraft alerts. We estimate pilot workload, which we model as being dependent on factors including mental effort, task demands. and task performance. We perform a mathematically rigorous analysis of the model and resulting alerting plans. We simulate the model in software and present simulated results with respect to manipulation of the pilot measures.

Spatial panorama of malaria prevalence in Africa under climate change and interventions scenarios.

PubMed

Moukam Kakmeni, Francois M; Guimapi, Ritter Y A; Ndjomatchoua, Frank T; Pedro, Sansoa A; Mutunga, James; Tonnang, Henri E Z

2018-01-16

Malaria is highly sensitive to climatic variables and is strongly influenced by the presence of vectors in a region that further contribute to parasite development and sustained disease transmission. Mathematical analysis of malaria transmission through the use and application of the value of the basic reproduction number (R 0 ) threshold is an important and useful tool for the understanding of disease patterns. Temperature dependence aspect of R 0 obtained from dynamical mathematical network model was used to derive the spatial distribution maps for malaria transmission under different climatic and intervention scenarios. Model validation was conducted using MARA map and the Annual Plasmodium falciparum Entomological Inoculation Rates for Africa. The inclusion of the coupling between patches in dynamical model seems to have no effects on the estimate of the optimal temperature (about 25 °C) for malaria transmission. In patches environment, we were able to establish a threshold value (about α = 5) representing the ratio between the migration rates from one patch to another that has no effect on the magnitude of R 0 . Such findings allow us to limit the production of the spatial distribution map of R 0 to a single patch model. Future projections using temperature changes indicated a shift in malaria transmission areas towards the southern and northern areas of Africa and the application of the interventions scenario yielded a considerable reduction in transmission within malaria endemic areas of the continent. The approach employed here is a sole study that defined the limits of contemporary malaria transmission, using R 0 derived from a dynamical mathematical model. It has offered a unique prospect for measuring the impacts of interventions through simple manipulation of model parameters. Projections at scale provide options to visualize and query the results, when linked to the human population could potentially deliver adequate highlight on the number of individuals at risk of malaria infection across Africa. The findings provide a reasonable basis for understanding the fundamental effects of malaria control and could contribute towards disease elimination, which is considered as a challenge especially in the context of climate change.

Exploring the Earth System through online interactive models

NASA Astrophysics Data System (ADS)

Coogan, L. A.

2013-12-01

Upper level Earth Science students commonly have a strong background of mathematical training from Math courses, however their ability to use mathematical models to solve Earth Science problems is commonly limited. Their difficulty comes, in part, because of the nature of the subject matter. There is a large body of background ';conceptual' and ';observational' understanding and knowledge required in the Earth Sciences before in-depth quantification becomes useful. For example, it is difficult to answer questions about geological processes until you can identify minerals and rocks and understand the general geodynamic implications of their associations. However, science is fundamentally quantitative. To become scientists students have to translate their conceptual understanding into quantifiable models. Thus, it is desirable for students to become comfortable with using mathematical models to test hypotheses. With the aim of helping to bridging the gap between conceptual understanding and quantification I have started to build an interactive teaching website based around quantitative models of Earth System processes. The site is aimed at upper-level undergraduate students and spans a range of topics that will continue to grow as time allows. The mathematical models are all built for the students, allowing them to spend their time thinking about how the ';model world' changes in response to their manipulation of the input variables. The web site is divided into broad topics or chapters (Background, Solid Earth, Ocean and Atmosphere, Earth history) and within each chapter there are different subtopic (e.g. Solid Earth: Core, Mantle, Crust) and in each of these individual webpages. Each webpage, or topic, starts with an introduction to the topic, followed by an interactive model that the students can use sliders to control the input to and watch how the results change. This interaction between student and model is guided by a series of multiple choice questions that the student answers and immediately gets feedback whether the answer is correct or not. This way the students can ensure they understand the concepts before moving on. A discussion forum for the students to discuss the topics is in development and each page has a feedback option to allow both numerical (1-10) and written feedback on how useful the webpage was. By the end of exploring any given process students are expected to understand how the different parameters explored by the model interact to control the results. They should appreciate why the controlling equations look the way they do (all equations needed to develop the models are present in the introduction) and how these interact to control the results. While this is no substitute to students undertaking the calculations for themselves this approach allows a much wider range of topics to be explored quantitatively than if the students have to code all models themselves.

The human dynamic clamp as a paradigm for social interaction.

PubMed

Dumas, Guillaume; de Guzman, Gonzalo C; Tognoli, Emmanuelle; Kelso, J A Scott

2014-09-02

Social neuroscience has called for new experimental paradigms aimed toward real-time interactions. A distinctive feature of interactions is mutual information exchange: One member of a pair changes in response to the other while simultaneously producing actions that alter the other. Combining mathematical and neurophysiological methods, we introduce a paradigm called the human dynamic clamp (HDC), to directly manipulate the interaction or coupling between a human and a surrogate constructed to behave like a human. Inspired by the dynamic clamp used so productively in cellular neuroscience, the HDC allows a person to interact in real time with a virtual partner itself driven by well-established models of coordination dynamics. People coordinate hand movements with the visually observed movements of a virtual hand, the parameters of which depend on input from the subject's own movements. We demonstrate that HDC can be extended to cover a broad repertoire of human behavior, including rhythmic and discrete movements, adaptation to changes of pacing, and behavioral skill learning as specified by a virtual "teacher." We propose HDC as a general paradigm, best implemented when empirically verified theoretical or mathematical models have been developed in a particular scientific field. The HDC paradigm is powerful because it provides an opportunity to explore parameter ranges and perturbations that are not easily accessible in ordinary human interactions. The HDC not only enables to test the veracity of theoretical models, it also illuminates features that are not always apparent in real-time human social interactions and the brain correlates thereof.

Reflexive obstacle avoidance for kinematically-redundant manipulators

NASA Technical Reports Server (NTRS)

Karlen, James P.; Thompson, Jack M., Jr.; Farrell, James D.; Vold, Havard I.

1989-01-01

Dexterous telerobots incorporating 17 or more degrees of freedom operating under coordinated, sensor-driven computer control will play important roles in future space operations. They will also be used on Earth in assignments like fire fighting, construction and battlefield support. A real time, reflexive obstacle avoidance system, seen as a functional requirement for such massively redundant manipulators, was developed using arm-mounted proximity sensors to control manipulator pose. The project involved a review and analysis of alternative proximity sensor technologies for space applications, the development of a general-purpose algorithm for synthesizing sensor inputs, and the implementation of a prototypical system for demonstration and testing. A 7 degree of freedom Robotics Research K-2107HR manipulator was outfitted with ultrasonic proximity sensors as a testbed, and Robotics Research's standard redundant motion control algorithm was modified such that an object detected by sensor arrays located at the elbow effectively applies a force to the manipulator elbow, normal to the axis. The arm is repelled by objects detected by the sensors, causing the robot to steer around objects in the workspace automatically while continuing to move its tool along the commanded path without interruption. The mathematical approach formulated for synthesizing sensor inputs can be employed for redundant robots of any kinematic configuration.

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

NASA Astrophysics Data System (ADS)

Feriyanto

2018-01-01

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

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

PubMed Central

Spelke, Elizabeth S.

2014-01-01

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics. PMID:24462713

Development of Computer Play Pedagogy Intervention for Children with Low Conceptual Understanding in Basic Mathematics Operation Using the Dyscalculia Feature Approach

ERIC Educational Resources Information Center

Mohd Syah, Nor Elleeiana; Hamzaid, Nur Azah; Murphy, Belinda Pingguan; Lim, Einly

2016-01-01

This study describes the development of a basic computer-based play pedagogy intervention using a dyscalculia-remedy-oriented approach such as repetition and number orientation manipulation, and the investigation of its effect on children displaying dyscalculia characteristics. This computer play was evaluated in a group of 50 seven-year-old…

Multimedia Network Design Study

DTIC Science & Technology

1989-09-30

manipulation and analysis of the equations involved, thereby providing the application of the great range of powerful mathematical optimization...be treated by this analysis. First, all arrivals to the network have the Poisson distribution, and separate traffic classes may have separate qrrival...different for open and closed networks, so these two situations will be treated separately in the following subsections. 2.3.1 The Computational Process in

Investigating Preservice Teachers' Understanding of Balance Concepts Utilizing a Clinical Interview Method and a Virtual Tool

ERIC Educational Resources Information Center

Wilhelm, Jennifer; Matteson, Shirley; She, Xiaobo

2013-01-01

Our study was enacted in university mathematics education classes in the USA with preservice teachers (PSTs). This research focused on PSTs' interview responses that were used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. Siegler's rules were used in analyzing PSTs' responses to…

Stereotype threat and group differences in test performance: a question of measurement invariance.

PubMed

Wicherts, Jelte M; Dolan, Conor V; Hessen, David J

2005-11-01

Studies into the effects of stereotype threat (ST) on test performance have shed new light on race and sex differences in achievement and intelligence test scores. In this article, the authors relate ST theory to the psychometric concept of measurement invariance and show that ST effects may be viewed as a source of measurement bias. As such, ST effects are detectable by means of multi-group confirmatory factor analysis. This enables research into the generalizability of ST effects to real-life or high-stakes testing. The modeling approach is described in detail and applied to 3 experiments in which the amount of ST for minorities and women was manipulated. Results indicate that ST results in measurement bias of intelligence and mathematics tests. ((c) 2005 APA, all rights reserved).

Single Vector Calibration System for Multi-Axis Load Cells and Method for Calibrating a Multi-Axis Load Cell

NASA Technical Reports Server (NTRS)

Parker, Peter A. (Inventor)

2003-01-01

A single vector calibration system is provided which facilitates the calibration of multi-axis load cells, including wind tunnel force balances. The single vector system provides the capability to calibrate a multi-axis load cell using a single directional load, for example loading solely in the gravitational direction. The system manipulates the load cell in three-dimensional space, while keeping the uni-directional calibration load aligned. The use of a single vector calibration load reduces the set-up time for the multi-axis load combinations needed to generate a complete calibration mathematical model. The system also reduces load application inaccuracies caused by the conventional requirement to generate multiple force vectors. The simplicity of the system reduces calibration time and cost, while simultaneously increasing calibration accuracy.

Tissue characterization using electrical impedance spectroscopy data: a linear algebra approach.

PubMed

Laufer, Shlomi; Solomon, Stephen B; Rubinsky, Boris

2012-06-01

In this study, we use a new linear algebra manipulation on electrical impedance spectroscopy measurements to provide real-time information regarding the nature of the tissue surrounding the needle in minimal invasive procedures. Using a Comsol Multiphysics three-dimensional model, a phantom based on ex vivo animal tissue and in vivo animal data, we demonstrate how tissue inhomogeneity can be characterized without any previous knowledge of the electrical properties of the different tissues, except that they should not be linearly dependent on a certain frequency range. This method may have applications in needle biopsies, radiation seeds, or minimally invasive surgery and can reduce the number of computer tomography or magnetic resonance imaging images. We conclude by demonstrating how this mathematical approach can be useful in other applications.

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

PubMed

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

2016-11-01

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

When is working memory important for arithmetic? The impact of strategy and age

PubMed Central

Richardson, Sophie; Hubber, Paula J.; Keeble, Sarah; Gilmore, Camilla

2017-01-01

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9–11 years, 12–14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition. PMID:29228008

Application of symbolic and algebraic manipulation software in solving applied mechanics problems

NASA Technical Reports Server (NTRS)

Tsai, Wen-Lang; Kikuchi, Noboru

1993-01-01

As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.

Motion sensors in mathematics teaching: learning tools for understanding general math concepts?

NASA Astrophysics Data System (ADS)

Urban-Woldron, Hildegard

2015-05-01

Incorporating technology tools into the mathematics classroom adds a new dimension to the teaching of mathematics concepts and establishes a whole new approach to mathematics learning. In particular, gathering data in a hands-on and real-time method helps classrooms coming alive. The focus of this paper is on bringing forward important mathematics concepts such as functions and rate of change with the motion detector. Findings from the author's studies suggest that the motion detector can be introduced from a very early age and used to enliven classes at any level. Using real-world data to present the main functions invites an experimental approach to mathematics and encourages students to engage actively in their learning. By emphasizing learning experiences with computer-based motion detectors and aiming to involve students in mathematical representations of real-world phenomena, six learning activities, which were developed in previous research studies, will be presented. Students use motion sensors to collect physical data that are graphed in real time and then manipulate and analyse them. Because data are presented in an immediately understandable graphical form, students are allowed to take an active role in their learning by constructing mathematical knowledge from observation of the physical world. By utilizing a predict-observe-explain format, students learn about slope, determining slope and distance vs. time graphs through motion-filled activities. Furthermore, exploring the meaning of slope, viewed as the rate of change, students acquire competencies for reading, understanding and interpreting kinematics graphs involving a multitude of mathematical representations. Consequently, the students are empowered to efficiently move among tabular, graphical and symbolic representation to analyse patterns and discover the relationships between different representations of motion. In fact, there is a need for further research to explore how mathematics teachers can integrate motion sensors into their classrooms.

Towards intelligent diagnostic system employing integration of mathematical and engineering model

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

Isa, Nor Ashidi Mat

The development of medical diagnostic system has been one of the main research fields during years. The goal of the medical diagnostic system is to place a nosological system that could ease the diagnostic evaluation normally performed by scientists and doctors. Efficient diagnostic evaluation is essentials and requires broad knowledge in order to improve conventional diagnostic system. Several approaches on developing the medical diagnostic system have been designed and tested since the earliest 60s. Attempts on improving their performance have been made which utilizes the fields of artificial intelligence, statistical analyses, mathematical model and engineering theories. With the availability ofmore » the microcomputer and software development as well as the promising aforementioned fields, medical diagnostic prototypes could be developed. In general, the medical diagnostic system consists of several stages, namely the 1) data acquisition, 2) feature extraction, 3) feature selection, and 4) classifications stages. Data acquisition stage plays an important role in converting the inputs measured from the real world physical conditions to the digital numeric values that can be manipulated by the computer system. One of the common medical inputs could be medical microscopic images, radiographic images, magnetic resonance image (MRI) as well as medical signals such as electrocardiogram (ECG) and electroencephalogram (EEG). Normally, the scientist or doctors have to deal with myriad of data and redundant to be processed. In order to reduce the complexity of the diagnosis process, only the significant features of the raw data such as peak value of the ECG signal or size of lesion in the mammogram images will be extracted and considered in the subsequent stages. Mathematical models and statistical analyses will be performed to select the most significant features to be classified. The statistical analyses such as principal component analysis and discriminant analysis as well as mathematical model of clustering technique have been widely used in developing the medical diagnostic systems. The selected features will be classified using mathematical models that embedded engineering theory such as artificial intelligence, support vector machine, neural network and fuzzy-neuro system. These classifiers will provide the diagnostic results without human intervention. Among many publishable researches, several prototypes have been developed namely NeuralPap, Neural Mammo, and Cervix Kit. The former system (NeuralPap) is an automatic intelligent diagnostic system for classifying and distinguishing between the normal and cervical cancerous cells. Meanwhile, the Cervix Kit is a portable Field-programmable gate array (FPGA)-based cervical diagnostic kit that could automatically diagnose the cancerous cell based on the images obtained during sampling test. Besides the cervical diagnostic system, the Neural Mammo system is developed to specifically aid the diagnosis of breast cancer using a fine needle aspiration image.« less

Towards intelligent diagnostic system employing integration of mathematical and engineering model

NASA Astrophysics Data System (ADS)

Isa, Nor Ashidi Mat

2015-05-01

The development of medical diagnostic system has been one of the main research fields during years. The goal of the medical diagnostic system is to place a nosological system that could ease the diagnostic evaluation normally performed by scientists and doctors. Efficient diagnostic evaluation is essentials and requires broad knowledge in order to improve conventional diagnostic system. Several approaches on developing the medical diagnostic system have been designed and tested since the earliest 60s. Attempts on improving their performance have been made which utilizes the fields of artificial intelligence, statistical analyses, mathematical model and engineering theories. With the availability of the microcomputer and software development as well as the promising aforementioned fields, medical diagnostic prototypes could be developed. In general, the medical diagnostic system consists of several stages, namely the 1) data acquisition, 2) feature extraction, 3) feature selection, and 4) classifications stages. Data acquisition stage plays an important role in converting the inputs measured from the real world physical conditions to the digital numeric values that can be manipulated by the computer system. One of the common medical inputs could be medical microscopic images, radiographic images, magnetic resonance image (MRI) as well as medical signals such as electrocardiogram (ECG) and electroencephalogram (EEG). Normally, the scientist or doctors have to deal with myriad of data and redundant to be processed. In order to reduce the complexity of the diagnosis process, only the significant features of the raw data such as peak value of the ECG signal or size of lesion in the mammogram images will be extracted and considered in the subsequent stages. Mathematical models and statistical analyses will be performed to select the most significant features to be classified. The statistical analyses such as principal component analysis and discriminant analysis as well as mathematical model of clustering technique have been widely used in developing the medical diagnostic systems. The selected features will be classified using mathematical models that embedded engineering theory such as artificial intelligence, support vector machine, neural network and fuzzy-neuro system. These classifiers will provide the diagnostic results without human intervention. Among many publishable researches, several prototypes have been developed namely NeuralPap, Neural Mammo, and Cervix Kit. The former system (NeuralPap) is an automatic intelligent diagnostic system for classifying and distinguishing between the normal and cervical cancerous cells. Meanwhile, the Cervix Kit is a portable Field-programmable gate array (FPGA)-based cervical diagnostic kit that could automatically diagnose the cancerous cell based on the images obtained during sampling test. Besides the cervical diagnostic system, the Neural Mammo system is developed to specifically aid the diagnosis of breast cancer using a fine needle aspiration image.

Mathematical foundations of the GraphBLAS

DOE PAGES

Kepner, Jeremy; Aaltonen, Peter; Bader, David; ...

2016-12-01

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This study provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, themore » two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Finally, performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.« less

Robot body self-modeling algorithm: a collision-free motion planning approach for humanoids.

PubMed

Leylavi Shoushtari, Ali

2016-01-01

Motion planning for humanoid robots is one of the critical issues due to the high redundancy and theoretical and technical considerations e.g. stability, motion feasibility and collision avoidance. The strategies which central nervous system employs to plan, signal and control the human movements are a source of inspiration to deal with the mentioned problems. Self-modeling is a concept inspired by body self-awareness in human. In this research it is integrated in an optimal motion planning framework in order to detect and avoid collision of the manipulated object with the humanoid body during performing a dynamic task. Twelve parametric functions are designed as self-models to determine the boundary of humanoid's body. Later, the boundaries which mathematically defined by the self-models are employed to calculate the safe region for box to avoid the collision with the robot. Four different objective functions are employed in motion simulation to validate the robustness of algorithm under different dynamics. The results also confirm the collision avoidance, reality and stability of the predicted motion.

Modeling systems-level dynamics: Understanding without mechanistic explanation in integrative systems biology.

PubMed

MacLeod, Miles; Nersessian, Nancy J

2015-02-01

In this paper we draw upon rich ethnographic data of two systems biology labs to explore the roles of explanation and understanding in large-scale systems modeling. We illustrate practices that depart from the goal of dynamic mechanistic explanation for the sake of more limited modeling goals. These processes use abstract mathematical formulations of bio-molecular interactions and data fitting techniques which we call top-down abstraction to trade away accurate mechanistic accounts of large-scale systems for specific information about aspects of those systems. We characterize these practices as pragmatic responses to the constraints many modelers of large-scale systems face, which in turn generate more limited pragmatic non-mechanistic forms of understanding of systems. These forms aim at knowledge of how to predict system responses in order to manipulate and control some aspects of them. We propose that this analysis of understanding provides a way to interpret what many systems biologists are aiming for in practice when they talk about the objective of a "systems-level understanding." Copyright © 2014 Elsevier Ltd. All rights reserved.

Non-classic multiscale modeling of manipulation based on AFM, in aqueous and humid ambient

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Homayooni, A.; Hefzabad, R. N.

2018-05-01

To achieve a precise manipulation, it is important that an accurate model consisting the size effect and environmental conditions be employed. In this paper, the non-classical multiscale modeling is developed to investigate the manipulation in a vacuum, aqueous and humid ambient. The manipulation structure is considered into two parts as a macro-field (MF) and a nano-field (NF). The governing equations of the AFM components (consist of the cantilever and tip) in the MF are derived based on the modified couple stress theory. The material length scale parameter is used to study the size effect. The fluid flow in the MF is assumed as the Couette and Creeping flows. Moreover, the NF is modeled using the molecular dynamics. The Electro-Based (ELBA) model is considered to model the ambient condition in the NF. The nanoparticle in the different conditions is taken into account to study the manipulation. The results of the manipulation indicate that the predicted deflection of the non-classical model is less than the classical one. Comparison of the nanoparticle travelled distance on substrate shows that the manipulation in the submerged condition is close to the ideal manipulation. The results of humid condition illustrate that by increasing the relative humidity (RH) the manipulation force decreases. Furthermore, Root Mean Square (RMS) as a criterion of damage demonstrates that the submerged nanoparticle has the minimum damage, however, the minimum manipulation force occurs in superlative humid ambient.

Identification of control targets in Boolean molecular network models via computational algebra.

PubMed

Murrugarra, David; Veliz-Cuba, Alan; Aguilar, Boris; Laubenbacher, Reinhard

2016-09-23

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

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…

Making Sense with Manipulatives: Developing Mathematical Experiences for Early Childhood Teachers

ERIC Educational Resources Information Center

Furman, Cara E.

2017-01-01

This paper is premised on the fact that math can be an important tool in helping people make sense of the world. Math offers a unique and particular lens, helping people to focus on a range of characteristics from shape and amount to the relationship between the general and the particular. To promote math as a tool for making sense, early…

Is It Worth Using CAS for Symbolic Algebra Manipulation in the Middle Secondary Years? Some Teachers' Views

ERIC Educational Resources Information Center

Pierce, Robyn; Ball, Lynda; Stacey, Kaye

2009-01-01

The use of Computer Algebra Systems (CAS) in years 9 and 10 classrooms as a tool to support learning or in preparation for senior secondary mathematics is controversial. This paper presents an analysis of the positive and negative aspects of using CAS identified in the literature related to these year levels, along with the perceptions of 12…

The Concept of Proportionality as a Predictor of Success at the University of Papua and New Guinea. E.R.U. Report 6.

ERIC Educational Resources Information Center

Jones, John

A main problem encountered by science and mathematics students at secondary and tertiary institutions throughout Papua New Guinea is that of dealing with ratio and proportion. The problem is most clearly defined in science, since this is the area in which the quantitative manipulation of physical variables is most frequently carried out. An…

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

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

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

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

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

Advanced surface design for logistics analysis

NASA Astrophysics Data System (ADS)

Brown, Tim R.; Hansen, Scott D.

The development of anthropometric arm/hand and tool models and their manipulation in a large system model for maintenance simulation are discussed. The use of Advanced Surface Design and s-fig technology in anthropometrics, and three-dimensional graphics simulation tools, are found to achieve a good balance between model manipulation speed and model accuracy. The present second generation models are shown to be twice as fast to manipulate as the first generation b-surf models, to be easier to manipulate into various configurations, and to more closely approximate human contours.

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

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

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

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

Functional brain organization of working memory in adolescents varies in relation to family income and academic achievement.

PubMed

Finn, Amy S; Minas, Jennifer E; Leonard, Julia A; Mackey, Allyson P; Salvatore, John; Goetz, Calvin; West, Martin R; Gabrieli, Christopher F O; Gabrieli, John D E

2017-09-01

Working memory (WM) capacity reflects executive functions associated with performance on a wide range of cognitive tasks and education outcomes, including mathematics achievement, and is associated with dorsolateral prefrontal and parietal cortices. Here we asked if family income is associated with variation in the functional brain organization of WM capacity among adolescents, and whether that variation is associated with performance on a statewide test of academic achievement in mathematics. Participants were classified into higher-income and lower-income groups based on family income, and performed a WM task with a parametric manipulation of WM load (N-back task) during functional magnetic resonance imaging (fMRI). Behaviorally, the higher-income group had greater WM capacity and higher mathematics achievement scores. Neurally, the higher-income group showed greater activation as a function of WM load in bilateral prefrontal, parietal, and other regions, although the lower-income group exhibited greater activation at the lowest load. Both groups exhibited positive correlations between parietal activations and mathematics achievement scores, but only the higher-income group exhibited a positive correlation between prefrontal activations and mathematics scores. Most of these findings were maintained when higher- and lower-income groups were matched on WM task performance or nonverbal IQ. Findings indicate that the functional neural architecture of WM varies with family income and is associated with education measures of mathematics achievement. © 2016 John Wiley & Sons Ltd.

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

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

The human dynamic clamp as a paradigm for social interaction

PubMed Central

Dumas, Guillaume; de Guzman, Gonzalo C.; Tognoli, Emmanuelle; Kelso, J. A. Scott

2014-01-01

Social neuroscience has called for new experimental paradigms aimed toward real-time interactions. A distinctive feature of interactions is mutual information exchange: One member of a pair changes in response to the other while simultaneously producing actions that alter the other. Combining mathematical and neurophysiological methods, we introduce a paradigm called the human dynamic clamp (HDC), to directly manipulate the interaction or coupling between a human and a surrogate constructed to behave like a human. Inspired by the dynamic clamp used so productively in cellular neuroscience, the HDC allows a person to interact in real time with a virtual partner itself driven by well-established models of coordination dynamics. People coordinate hand movements with the visually observed movements of a virtual hand, the parameters of which depend on input from the subject’s own movements. We demonstrate that HDC can be extended to cover a broad repertoire of human behavior, including rhythmic and discrete movements, adaptation to changes of pacing, and behavioral skill learning as specified by a virtual “teacher.” We propose HDC as a general paradigm, best implemented when empirically verified theoretical or mathematical models have been developed in a particular scientific field. The HDC paradigm is powerful because it provides an opportunity to explore parameter ranges and perturbations that are not easily accessible in ordinary human interactions. The HDC not only enables to test the veracity of theoretical models, it also illuminates features that are not always apparent in real-time human social interactions and the brain correlates thereof. PMID:25114256

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

From Genes to Networks: Characterizing Gene-Regulatory Interactions in Plants.

PubMed

Kaufmann, Kerstin; Chen, Dijun

2017-01-01

Plants, like other eukaryotes, have evolved complex mechanisms to coordinate gene expression during development, environmental response, and cellular homeostasis. Transcription factors (TFs), accompanied by basic cofactors and posttranscriptional regulators, are key players in gene-regulatory networks (GRNs). The coordinated control of gene activity is achieved by the interplay of these factors and by physical interactions between TFs and DNA. Here, we will briefly outline recent technological progress made to elucidate GRNs in plants. We will focus on techniques that allow us to characterize physical interactions in GRNs in plants and to analyze their regulatory consequences. Targeted manipulation allows us to test the relevance of specific gene-regulatory interactions. The combination of genome-wide experimental approaches with mathematical modeling allows us to get deeper insights into key-regulatory interactions and combinatorial control of important processes in plants.

Kinematics modeling and experimentation of the multi-manipulator tooth-arrangement robot for full denture manufacturing.

PubMed

Zhang, Yong-de; Jiang, Jin-gang; Liang, Ting; Hu, Wei-ping

2011-12-01

Artificial teeth are very complicated in shape, and not easy to be grasped and manipulated accurately by a single robot. The method of tooth-arrangement by multi-manipulator for complete denture manufacturing proposed in this paper. A novel complete denture manufacturing mechanism is designed based on multi-manipulator and dental arch generator. Kinematics model of the multi-manipulator tooth-arrangement robot is built by analytical method based on tooth-arrangement principle for full denture. Preliminary experiments on tooth-arrangement are performed using the multi-manipulator tooth-arrangement robot prototype system. The multi-manipulator tooth-arrangement robot prototype system can automatically design and manufacture a set of complete denture that is suitable for a patient according to the jaw arch parameters. The experimental results verified the validity of kinematics model of the multi-manipulator tooth-arrangement robot and the feasibility of the manufacture strategy of complete denture fulfilled by multi-manipulator tooth-arrangement robot.

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Modeling oscillations and spiral waves in Dictyostelium populations

NASA Astrophysics Data System (ADS)

Noorbakhsh, Javad; Schwab, David J.; Sgro, Allyson E.; Gregor, Thomas; Mehta, Pankaj

2015-06-01

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales—from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Opportunities and Challenges of Implementing Instructional Games in Mathematics Classrooms: Examining the Quality of Teacher-Student Interactions during the Cover-Up and Un-Cover Games

ERIC Educational Resources Information Center

Heshmati, Saeideh; Kersting, Nicole; Sutton, Taliesin

2018-01-01

This study explored the design and implementation of the Cover-up and Un-cover games, two manipulative-based fraction games, in 14 fifth-grade classrooms. We examined how the fraction concepts were integrated into the game design and explored the nature of teacher-student interactions during games using lesson videos. Our examination showed that…

The 1980 summer research fellowship program

NASA Technical Reports Server (NTRS)

Darden, G. C. (Compiler)

1980-01-01

The problem of incorporating visual input into robot systems is described. The photochemistry of the stratosphere, particularly possible permutations of the ozone layer, is discussed. Photoelectrochemical properties of metal thio-hypodiphosphates are investigated. Extreme eigenvalues are computed by the Lancqos approach. The rotational Raman spectra of the molecular atmosphere is studied. A computer operated mathematical symbolic manipulation system is described. Preparation of polycrystalline semiconductor electrodes of tungsten and molybdenum dichalcogenides is received.

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

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

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

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

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

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

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

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

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

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

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

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

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

A number sense intervention for low-income kindergartners at risk for mathematics difficulties.

PubMed

Dyson, Nancy I; Jordan, Nancy C; Glutting, Joseph

2013-01-01

Early number sense is a strong predictor of later success in school mathematics. A disproportionate number of children from low-income families come to first grade with weak number competencies, leaving them at risk for a cycle of failure. The present study examined the effects of an 8-week number sense intervention to develop number competencies of low-income kindergartners (N = 121). The intervention purposefully targeted whole number concepts related to counting, comparing, and manipulating sets. Children were randomly assigned to either a number sense intervention or a business as usual contrast group. The intervention was carried out in small-group, 30-min sessions, 3 days per week, for a total of 24 sessions. Controlling for number sense at pretest, the intervention group made meaningful gains relative to the control group at immediate as well delayed posttest on a measure of early numeracy. Intervention children also performed better than controls on a standardized test of mathematics calculation at immediate posttest.

A Number Sense Intervention for Low-Income Kindergartners at Risk for Mathematics Difficulties

PubMed Central

Dyson, Nancy I.; Jordan, Nancy C.; Glutting, Joseph

2012-01-01

Early number sense is a strong predictor of later success in school mathematics. A disproportionate number of children from low-income families come to first grade with weak number competencies, leaving them at-risk for a cycle of failure. The present study examined the effects of an 8-week number sense intervention to develop number competencies of low-income kindergartners (n = 121). The intervention purposefully targeted whole number concepts related to counting, comparing, and manipulating sets. Children were randomly assigned either to a number sense intervention or a business as usual contrast group. The intervention was carried out in small group, 30-minute sessions, 3 days per week for a total of 24 sessions. Controlling for number sense at pretest, the intervention group made meaningful gains relative to the control group at immediate as well delayed posttest on a measure of early numeracy. Intervention children also performed better than controls on a standardized test of mathematics calculation at immediate posttest. PMID:21685346

Post-16 update

NASA Astrophysics Data System (ADS)

1999-03-01

Post-16 Initiative logo Physics in Mathematical Mood Later this year, as part of the post-16 initiative of the Institute of Physics, a booklet with the above title will be published. In draft form, the booklet was discussed at the ASE conference in January. Some of the issues raised are briefly set out here. If you have any views to contribute, please write to Simon Carson at the Institute of Physics or e-mail simon.carson@physics.org. A mathematical view of the world is intrinsically a part of physics and therefore physics should be studied in an appropriately mathematical way. However, we all know that, to some students at least, mathematics proves to be a stumbling block rather than a powerful aid to understanding. So how can we help? Realizing that as physics teachers we need to deliver the mathematics necessary to an understanding of our subject is a start. Its corollary is that we need to find the space within the physics core. We may wish to use supplementary courses such as AS mathematics or QCA's new free-standing mathematics units, but requiring additional courses as a prerequisite to a study of A-level physics may deter students. Teaching the mathematics in context may aid understanding but we also must ensure that techniques are seen in a variety of contexts and that at some point the tool is abstracted from the background. As teachers we need to be aware of the very basic mathematical difficulties that students bring with them: the use of calculators, standard form, simple algebraic manipulation, for example. Mathematical arguments need to be developed fully and carefully. Encouraging cooperation and discussion between students may help the less able to understand and the more able to appreciate and develop their own understanding through making explicit their reasoning by explaining it to others. And what of new technology? Software tools allow students to develop their understanding about graphs, for example, enabling them to investigate the characteristics of particular functions. Modelling tools allow teachers or students to build models or more simply to create animations to demonstrate the properties of mathematical entities such as vectors. Graphical calculators mean that all students can have cheap access to such tools and it may be that some of the analytical mathematical tools we hold so dear are obsolete. Other issues are discussed in the booklet and were aired at the ASE conference: the situation in HE, the approach to mathematics taken by the Salters Horners approach, ways to introduce special functions such as exponentials, ways of thinking about the relationships between variables as expressed in equations. Many practical suggestions are made in the booklet about how we can help and support students and, most importantly, how we can communicate to them some of the beauty and pleasure of Physics in Mathematical Mood. Simon Carson A perspective on apparatus The effective deployment of apparatus is one technique available in physics that does not exist in some other areas of teaching. We should capitalize on this. Apparatus is a tool that can be used to enable thinking and learning. There are a number of purposes to be served by the effective use of apparatus. It is no more likely that apparatus will `teach' any more than nature `teaches' physics in the first place. Discussion and the creative interpretation of observation are both necessary to the sense-making process. Apparatus must be chosen with these opportunities in mind. In a demonstration we are trying to persuade students that the world behaves in a particular way. An attempt is being made to persuade students that a particular conception of the world is worth considering and that this conception is a fruitful and truthful picture of the world. Apparatus chosen for this purpose must have clear links between what is to be measured and the representations of that measurement. The art of demonstration is very much like a magician's show, in that it must all be well rehearsed and produce surprising and convincing results with apparently little effort. Students will be asked to engage in exploration and explanation using apparatus. Apparatus chosen for this purpose must not look as if it has been designed to give one specific answer. Students must feel confident that they can manipulate apparatus in such a way that the apparatus can serve to express their thoughts and be shaped to try out their hypotheses. Students will also be asked to engage in more traditional laboratory work that requires precision and a careful approach. Here the apparatus must be of sufficient quality and perceived modernity to allow the students to take the tasks seriously so that they will produce work of the expected quality. A final use for apparatus is to allow students to engage in genuine open-ended investigation where their knowledge of physics both informs their plans before work is carried out and interprets the observations and measurements from that work. Here apparatus that measures well is at a premium. The connection between manipulating the system to be measured and the resultant measurement must involve short-term feedback loops: the students must see how the system is behaving. A necessary consequence of this requirement is that the measurements are presented in a form that makes physical sense. This may imply a good deal of processing of the raw data before the number is displayed. It is in this area of measurement that we see the greatest potential for the integration of IT into laboratory practice. Apparatus worth developing. From this analysis and from the experience of trying to make its current practicals work it seems that we need to concentrate our development of apparatus in two areas. The first is to ensure that equipment which provides a range of a high quality, attractive and effective measurement tools is in place. In this area we can expect to see the exploitation of developments in information and sensor technology lead to new approaches which open up many possibilities. The second thrust must be to have a good supply of apparatus which can be can assembled and manipulated by students to suit their thoughts and purposes. This apparatus may well be rather simple and need not to be very expensive. This may compensate for some of the implied expense of the first thrust above. Alongside these two there will continue to be steady development of traditional apparatus, often used for a demonstration. Affording apparatus. The key to developing the apparatus within a department must be to look towards fewer items, each of which can perform more tasks, deployed as measurement tools. In this the increasing computing power available, often at a small cost, can be deployed intelligently. Following a practice elsewhere we must expect most of this development to take place in software, not the hardware. This has clear implications for the apparatus manufacturers. Low costs in computing have followed from the adoption of the widespread standards that enable one device to be used for many purposes. A similar development seems likely in the provision of apparatus. Some elements are likely to prove expensive. Compensating for the use of these expensive elements will then prove to be the challenge which makes the whole package affordable. Building up a department. Out of the post-16 initiative will come some thoughts developed from Advancing Physics that show how we can move from the current provision. New and effectively deployed apparatus can lead to an improvement in teaching and learning and in students' perceptions of physics. Ian Lawrence

Analytical investigation of different mathematical approaches utilizing manipulation of ratio spectra

NASA Astrophysics Data System (ADS)

Osman, Essam Eldin A.

2018-01-01

This work represents a comparative study of different approaches of manipulating ratio spectra, applied on a binary mixture of ciprofloxacin HCl and dexamethasone sodium phosphate co-formulated as ear drops. The proposed new spectrophotometric methods are: ratio difference spectrophotometric method (RDSM), amplitude center method (ACM), first derivative of the ratio spectra (1DD) and mean centering of ratio spectra (MCR). The proposed methods were checked using laboratory-prepared mixtures and were successfully applied for the analysis of pharmaceutical formulation containing the cited drugs. The proposed methods were validated according to the ICH guidelines. A comparative study was conducted between those methods regarding simplicity, limitations and sensitivity. The obtained results were statistically compared with those obtained from the reported HPLC method, showing no significant difference with respect to accuracy and precision.

Modeling and simulation of three dimensional manipulations of biological micro/nanoparticles by applying cylindrical contact mechanics models by means of AFM

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Saraee, M. B.; Mahmoodi, Z.; Dehghani, S.

2015-11-01

This paper has attempted to investigate the effective forces in 3D manipulation of biological micro/nano particles. Most of the recent researches have only examined 2D spherical geometries but in this paper, the cylindrical geometries, which are much closer to the real geometries, were considered. For achieving a more accurate modeling, manipulation dynamics was also considered to be three dimensional which have been done for the first time. Because of the sensibility to the amount of endurable applied forces, manipulation process of biological micro/nano particles has some restrictions. Therefore, applied forces exerted on the particles in all different directions were simulated in order to restrict all those possible damages cause by operator of the AFM. Those data from simulated forces will bring a more accurate and sensible understanding for the operator to operate. For the validation of results, the proposed model was compared with the model presented for manipulation of gold nanoparticle and then, by reducing the effective parameters in the 3D manipulation, the results were compared with those obtained for the 2D cylindrical model and with the experimental results of spherical nanoparticle in the 2D manipulation.

Extension of D-H parameter method to hybrid manipulators used in robot-assisted surgery.

PubMed

Singh, Amanpreet; Singla, Ashish; Soni, Sanjeev

2015-10-01

The main focus of this work is to extend the applicability of D-H parameter method to develop a kinematic model of a hybrid manipulator. A hybrid manipulator is a combination of open- and closed-loop chains and contains planar and spatial links. It has been found in the literature that D-H parameter method leads to ambiguities, when dealing with closed-loop chains. In this work, it has been observed that the D-H parameter method, when applied to a hybrid manipulator, results in an orientational inconsistency, because of which the method cannot be used to develop the kinematic model. In this article, the concept of dummy frames is proposed to resolve the orientational inconsistency and to develop the kinematic model of a hybrid manipulator. Moreover, the prototype of 7-degree-of-freedom hybrid manipulator, known as a surgeon-side manipulator to assist the surgeon during a medical surgery, is also developed to validate the kinematic model derived in this work. © IMechE 2015.

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

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

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

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

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

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

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

NASA Technical Reports Server (NTRS)

Tesar, Delbert; Tosunoglu, Sabri; Lin, Shyng-Her

1990-01-01

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied.

A model-based investigation of manipulator characteristics and pilot/vehicle performance

NASA Technical Reports Server (NTRS)

Hess, R. A.

1983-01-01

Hess (1978, 1981) has introduced and discussed a structural model of the human pilot in which proprioceptive feedback plays a fundamental role in determining pilot equalization characteristics. It is pointed out that, on account of the feedback structure, this model may provide more insight into the effects of certain manipulator characteristics upon pilot equalization than would other modeling approaches. The model is briefly discussed, and an outline is presented concerning some of the implications of the model structure regarding the manipulator characteristics. Attention is given to some specific empirical examples of manipulator effects involving glide slope tracking in STOL aircraft, taking into account an employment of the model as a theoretical framework.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Theoretical linear approach to the combined man-manipulator system in manual control of an aircraft

NASA Technical Reports Server (NTRS)

Brauser, K.

1981-01-01

An approach to the calculation of the dynamic characteristics of the combined man manipulator system in manual aircraft control was derived from a model of the neuromuscular system. This model combines the neuromuscular properties of man with the physical properties of the manipulator system which is introduced as pilot manipulator model into the manual aircraft control. The assumption of man as a quasilinear and time invariant control operator adapted to operating states, depending on the flight phases, of the control system gives rise to interesting solutions of the frequency domain transfer functions of both the man manipulator system and the closed loop pilot aircraft control system. It is shown that it is necessary to introduce the complete precision pilot manipulator model into the closed loop pilot aircraft transfer function in order to understand the well known handling quality criteria, and to derive these criteria directly from human operator properties.

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

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

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

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

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

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

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

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

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

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

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

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

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

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

ERIC Educational Resources Information Center

Suppes, Patrick

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

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

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

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

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

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

Dynamics of local grid manipulations for internal flow problems

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Snyder, Aaron; Choo, Yung K.

1991-01-01

The control point method of algebraic grid generation is briefly reviewed. The review proceeds from the general statement of the method in 2-D unencumbered by detailed mathematical formulation. The method is supported by an introspective discussion which provides the basis for confidence in the approach. The more complex 3-D formulation is then presented as a natural generalization. Application of the method is carried out through 2-D examples which demonstrate the technique.

Defense AT and L, Volume 41, Number 5, September - October 2012

DTIC Science & Technology

2012-09-01

subtle differences confound us. In the insurance industry, years, decades, and centuries of historical data give actuaries high confidence in making...live another 23.26 years, it can declare with the utmost certainty that on average, all men in this category will. These actuaries bet their...variables are manipulated and data is collected. There are abundant sources of literature on DoE that describe the mathematical and statistical based tac

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

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

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

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

PubMed

Farrell, K; Wasser, T

1997-01-01

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

Kinship, parental manipulation and evolutionary origins of eusociality

PubMed Central

Kapheim, Karen M.; Nonacs, Peter; Smith, Adam R.; Wayne, Robert K.; Wcislo, William T.

2015-01-01

One of the hallmarks of eusociality is that workers forego their own reproduction to assist their mother in raising siblings. This seemingly altruistic behaviour may benefit workers if gains in indirect fitness from rearing siblings outweigh the loss of direct fitness. If worker presence is advantageous to mothers, however, eusociality may evolve without net benefits to workers. Indirect fitness benefits are often cited as evidence for the importance of inclusive fitness in eusociality, but have rarely been measured in natural populations. We compared inclusive fitness of alternative social strategies in the tropical sweat bee, Megalopta genalis, for which eusociality is optional. Our results show that workers have significantly lower inclusive fitness than females that found their own nests. In mathematical simulations based on M. genalis field data, eusociality cannot evolve with reduced intra-nest relatedness. The simulated distribution of alternative social strategies matched observed distributions of M. genalis social strategies when helping behaviour was simulated as the result of maternal manipulation, but not as worker altruism. Thus, eusociality in M. genalis is best explained through kin selection, but the underlying mechanism is likely maternal manipulation. PMID:25694620

Recursive Newton-Euler formulation of manipulator dynamics

NASA Technical Reports Server (NTRS)

Nasser, M. G.

1989-01-01

A recursive Newton-Euler procedure is presented for the formulation and solution of manipulator dynamical equations. The procedure includes rotational and translational joints and a topological tree. This model was verified analytically using a planar two-link manipulator. Also, the model was tested numerically against the Walker-Orin model using the Shuttle Remote Manipulator System data. The hinge accelerations obtained from both models were identical. The computational requirements of the model vary linearly with the number of joints. The computational efficiency of this method exceeds that of Walker-Orin methods. This procedure may be viewed as a considerable generalization of Armstrong's method. A six-by-six formulation is adopted which enhances both the computational efficiency and simplicity of the model.

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

The Cockroft and Gault formula for estimation of creatinine clearance: a friendly deconstruction.

PubMed

Millar, J Alasdair

2012-02-24

To review the derivation of the Cockroft and Gault formula for estimating creatinine clearance from serum creatinine in a historical context. The derivation described by Cockroft and Gault was reviewed, and an alternative formula was sought using the data reported in the paper. Cockroft and Gault used 24 hour urine creatinine data expressed as mg/kg body weight and mathematical manipulation of a linear regression equation which introduced body weight as an independent variable into the formula. This involved a circular logic and may have been mathematically invalid. A more logical equation not containing body weight was derived from the data. The Cockcroft and Gault formula has been validated by long usage but the derivation appears logically insecure. Nevertheless, its role in estimating renal function at the bedside is established.

Predicting the response of olfactory sensory neurons to odor mixtures from single odor response

NASA Astrophysics Data System (ADS)

Marasco, Addolorata; de Paris, Alessandro; Migliore, Michele

2016-04-01

The response of olfactory receptor neurons to odor mixtures is not well understood. Here, using experimental constraints, we investigate the mathematical structure of the odor response space and its consequences. The analysis suggests that the odor response space is 3-dimensional, and predicts that the dose-response curve of an odor receptor can be obtained, in most cases, from three primary components with specific properties. This opens the way to an objective procedure to obtain specific olfactory receptor responses by manipulating mixtures in a mathematically predictable manner. This result is general and applies, independently of the number of odor components, to any olfactory sensory neuron type with a response curve that can be represented as a sigmoidal function of the odor concentration.

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

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

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

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

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

2018-01-01

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

An oral exam model for teaching advanced "Batchelor-level" fluid mechanics in the US

NASA Astrophysics Data System (ADS)

Freund, Jonathan

2016-11-01

A teaching model is developed to meet the challenge of teaching fluid mechanics at what might be considered a high level, at least by the current norms in the US. The initial goal was to avoid loss of concepts amidst the challenge of particular mathematical manipulations on particular assignments. However, it evolved toward fostering facile working knowledge of challenging material, such as in the books by Batchelor (e.g. streaming flow), Whitham (e.g. ship waves), and van Dyke (e.g. second-order boundary layer). To this end, the course model forgoes traditional assigned problems to focus on completion, augmentation, and in-depth understanding of the lecture material. The lectures are relatively traditional in structure, albeit with somewhat more interactive examples. The main unusual feature-again, by modern US standards-was assessment via multiple half-hour oral exams. This model has now been successful over 8 semesters for 3 different graduate courses in 2 departments. For all, students were assume to have already completed a full course at a "Navier-Stokes level". The presentation will include specifics of the course and exam structure, impressions of positive outcomes from the instructor, and a summary of the overwhelmingly positive student feedback.

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

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

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

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

Mathematics Anxiety, Working Memory, and Mathematics Performance in Secondary-School Children.

PubMed

Passolunghi, Maria C; Caviola, Sara; De Agostini, Ruggero; Perin, Chiara; Mammarella, Irene C

2016-01-01

Mathematics anxiety (MA) has been defined as "a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations." Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA.

Mathematics Anxiety, Working Memory, and Mathematics Performance in Secondary-School Children

PubMed Central

Passolunghi, Maria C.; Caviola, Sara; De Agostini, Ruggero; Perin, Chiara; Mammarella, Irene C.

2016-01-01

Mathematics anxiety (MA) has been defined as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations.” Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA. PMID:26869951

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

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

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

PubMed

Ganusov, Vitaly V

2016-01-01

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

Summer Camp of Mathematical Modeling in China

ERIC Educational Resources Information Center

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

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

Rapid expulsion of microswimmers by a vortical flow

DOE PAGES

Sokolov, Andrey; Aranson, Igor S.

2016-03-23

Interactions of microswimmers with their fluid environment are exceptionally complex. Macroscopic shear flow alters swimming trajectories in a highly nontrivial way and results in dramatic reduction of viscosity and heterogeneous bacterial distributions. Here we report on experimental and theoretical studies of rapid expulsion of microswimmers, such as motile bacteria, by a vortical flow created by a rotating microparticle. We observe a formation of a macroscopic depletion area in a high-shear region, in the vicinity of a microparticle. The rapid migration of bacteria from the shear-rich area is caused by a vortical structure of the flow rather than intrinsic random fluctuationsmore » of bacteria orientations, in stark contrast to planar shear flow. Our mathematical model reveals that expulsion is a combined effect of motility and alignment by a vortical flow. Our findings offer a novel approach for manipulation of motile microorganisms and shed light on bacteria-flow interactions.« less

Dynamic optimization and adaptive controller design

NASA Astrophysics Data System (ADS)

Inamdar, S. R.

2010-10-01

In this work I present a new type of controller which is an adaptive tracking controller which employs dynamic optimization for optimizing current value of controller action for the temperature control of nonisothermal continuously stirred tank reactor (CSTR). We begin with a two-state model of nonisothermal CSTR which are mass and heat balance equations and then add cooling system dynamics to eliminate input multiplicity. The initial design value is obtained using local stability of steady states where approach temperature for cooling action is specified as a steady state and a design specification. Later we make a correction in the dynamics where material balance is manipulated to use feed concentration as a system parameter as an adaptive control measure in order to avoid actuator saturation for the main control loop. The analysis leading to design of dynamic optimization based parameter adaptive controller is presented. The important component of this mathematical framework is reference trajectory generation to form an adaptive control measure.

Genetic algorithm based fuzzy control of spacecraft autonomous rendezvous

NASA Technical Reports Server (NTRS)

Karr, C. L.; Freeman, L. M.; Meredith, D. L.

1990-01-01

The U.S. Bureau of Mines is currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy logic based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective decision. High performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions learned by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for learning fuzzy membership functions.

A Visual Basic simulation software tool for performance analysis of a membrane-based advanced water treatment plant.

PubMed

Pal, P; Kumar, R; Srivastava, N; Chaudhuri, J

2014-02-01

A Visual Basic simulation software (WATTPPA) has been developed to analyse the performance of an advanced wastewater treatment plant. This user-friendly and menu-driven software is based on the dynamic mathematical model for an industrial wastewater treatment scheme that integrates chemical, biological and membrane-based unit operations. The software-predicted results corroborate very well with the experimental findings as indicated in the overall correlation coefficient of the order of 0.99. The software permits pre-analysis and manipulation of input data, helps in optimization and exhibits performance of an integrated plant visually on a graphical platform. It allows quick performance analysis of the whole system as well as the individual units. The software first of its kind in its domain and in the well-known Microsoft Excel environment is likely to be very useful in successful design, optimization and operation of an advanced hybrid treatment plant for hazardous wastewater.

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

PubMed Central

Ganusov, Vitaly V.

2016-01-01

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

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

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

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

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

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

Definition and verification of a complex aircraft for aerodynamic calculations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1986-01-01

Techniques are reviewed which are of value in CAD/CAM CFD studies of the geometries of new fighter aircraft. In order to refine the computations of the flows to take advantage of the computing power available from supercomputers, it is often necessary to interpolate the geometry of the mesh selected for the numerical analysis of the aircraft shape. Interpolating the geometry permits a higher level of detail in calculations of the flow past specific regions of a design. A microprocessor-based mathematics engine is described for fast image manipulation and rotation to verify that the interpolated geometry will correspond to the design geometry in order to ensure that the flow calculations will remain valid through the interpolation. Applications of the image manipulation system to verify geometrical representations with wire-frame and shaded-surface images are described.

Chiropractic biophysics technique: a linear algebra approach to posture in chiropractic.

PubMed

Harrison, D D; Janik, T J; Harrison, G R; Troyanovich, S; Harrison, D E; Harrison, S O

1996-10-01

This paper discusses linear algebra as applied to human posture in chiropractic, specifically chiropractic biophysics technique (CBP). Rotations, reflections and translations are geometric functions studied in vector spaces in linear algebra. These mathematical functions are termed rigid body transformations and are applied to segmental spinal movement in the literature. Review of the literature indicates that these linear algebra concepts have been used to describe vertebral motion. However, these rigid body movers are presented here as applying to the global postural movements of the head, thoracic cage and pelvis. The unique inverse functions of rotations, reflections and translations provide a theoretical basis for making postural corrections in neutral static resting posture. Chiropractic biophysics technique (CBP) uses these concepts in examination procedures, manual spinal manipulation, instrument assisted spinal manipulation, postural exercises, extension traction and clinical outcome measures.

Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo

NASA Astrophysics Data System (ADS)

Schön, Thomas B.; Svensson, Andreas; Murray, Lawrence; Lindsten, Fredrik

2018-05-01

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state-space models. There is no closed-form solution available for this problem, implying that we are forced to use approximations. In this tutorial we will provide a self-contained introduction to one of the state-of-the-art methods-the particle Metropolis-Hastings algorithm-which has proven to offer a practical approximation. This is a Monte Carlo based method, where the particle filter is used to guide a Markov chain Monte Carlo method through the parameter space. One of the key merits of the particle Metropolis-Hastings algorithm is that it is guaranteed to converge to the "true solution" under mild assumptions, despite being based on a particle filter with only a finite number of particles. We will also provide a motivating numerical example illustrating the method using a modeling language tailored for sequential Monte Carlo methods. The intention of modeling languages of this kind is to open up the power of sophisticated Monte Carlo methods-including particle Metropolis-Hastings-to a large group of users without requiring them to know all the underlying mathematical details.

Closed-loop model identification of cooperative manipulators holding deformable objects

NASA Astrophysics Data System (ADS)

Alkathiri, A. A.; Akmeliawati, R.; Azlan, N. Z.

2017-11-01

This paper presents system identification to obtain the closed-loop models of a couple of cooperative manipulators in a system, which function to hold deformable objects. The system works using the master-slave principle. In other words, one of the manipulators is position-controlled through encoder feedback, while a force sensor gives feedback to the other force-controlled manipulator. Using the closed-loop input and output data, the closed-loop models, which are useful for model-based control design, are estimated. The criteria for model validation are a 95% fit between the measured and simulated output of the estimated models and residual analysis. The results show that for both position and force control respectively, the fits are 95.73% and 95.88%.

Mathematical modeling of tumor-associated macrophage interactions with the cancer microenvironment.

PubMed

Mahlbacher, Grace; Curtis, Louis T; Lowengrub, John; Frieboes, Hermann B

2018-01-30

Immuno-oncotherapy has emerged as a promising means to target cancer. In particular, therapeutic manipulation of tumor-associated macrophages holds promise due to their various and sometimes opposing roles in tumor progression. It is established that M1-type macrophages suppress tumor progression while M2-types support it. Recently, Tie2-expressing macrophages (TEM) have been identified as a distinct sub-population influencing tumor angiogenesis and vascular remodeling as well as monocyte differentiation. This study develops a modeling framework to evaluate macrophage interactions with the tumor microenvironment, enabling assessment of how these interactions may affect tumor progression. M1, M2, and Tie2 expressing variants are integrated into a model of tumor growth representing a metastatic lesion in a highly vascularized organ, such as the liver. Behaviors simulated include M1 release of nitric oxide (NO), M2 release of growth-promoting factors, and TEM facilitation of angiogenesis via Angiopoietin-2 and promotion of monocyte differentiation into M2 via IL-10. The results show that M2 presence leads to larger tumor growth regardless of TEM effects, implying that immunotherapeutic strategies that lead to TEM ablation may fail to restrain growth when the M2 represents a sizeable population. As TEM pro-tumor effects are less pronounced and on a longer time scale than M1-driven tumor inhibition, a more nuanced approach to influence monocyte differentiation taking into account the tumor state (e.g., under chemotherapy) may be desirable. The results highlight the dynamic interaction of macrophages within a growing tumor, and, further, establish the initial feasibility of a mathematical framework that could longer term help to optimize cancer immunotherapy.

Changing restoration rules: exotic bivalves interact with residence time and depth to control phytoplankton productivity

USGS Publications Warehouse

Lucas, Lisa V.; Thompson, Janet K.

2012-01-01

Non-native species are a prevalent ecosystem stressor that can interact with other stressors to confound resource management and restoration. We examine how interactions between physical habitat attributes and a particular category of non-native species (invasive bivalves) influence primary production in aquatic ecosystems. Using mathematical models, we show how intuitive relationships between phytoplankton productivity and controllable physical factors (water depth, hydraulic transport time) that hold in the absence of bivalves can be complicated—and even reversed—by rapid bivalve grazing. In light-limited environments without bivalves, shallow, hydrodynamically “slow” habitats should generally have greater phytoplankton biomass and productivity than deeper, “faster” habitats. But shallower, slower environments can be less productive than deeper, faster ones if benthic grazing is strong. Moreover, shallower and slower waters exhibit a particularly broad range of possible productivity outcomes that can depend on whether bivalves are present. Since it is difficult to predict the response of non-native bivalves to habitat restoration, outcomes for new shallow, slow environments can be highly uncertain. Habitat depth and transport time should therefore not be used as indicators of phytoplankton biomass and production where bivalve colonization is possible. This study provides for ecosystem management a particular example of a broad lesson: abiotic ecosystem stressors should be managed with explicit consideration of interactions with other major (including biotic) stressors. We discuss the applicability and management implications of our models and results for a range of aquatic system types, with a case study focused on the Sacramento-San Joaquin Delta (California, USA). Simple mathematical models like those used here can illuminate interactions between ecosystem stressors and provide process-based guidance for resource managers as they develop strategies to augment valued populations, restore habitats, and manipulate ecosystem functions.

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

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

Kinematics Modelling of Tendon-Driven Continuum Manipulator with Crossed Notches

NASA Astrophysics Data System (ADS)

Yang, Z. X.; Yang, W. L.; Du, Z. J.

2018-03-01

Single port surgical robot (SPSR) is a giant leap in the development of minimally invasive surgical robot. An innovative manipulator with high control accuracy and good kinematic dexterity can reduce wound, expedite recovery, and improve the success rate. This paper presents a tendon-driven continuum manipulator with crossed notches. This manipulator has two degrees of freedom (DOF), which possesses good flexibility and high capacity. Then based on cantilever beam theory, a mechanics model is proposed, which connects external force and deformation of a single flexible ring (SFR). By calculating the deformation of each SFR, the manipulator is considered as a series robot whose joint numbers is equal to SFR numbers, and the kinematics model is established through Denavit-Hartenberg (D-H) procedure. In this paper, the total manipulator is described as a curve tube whose curvature is increased from tip to base. Experiments were conducted and the comparison between theoretical and actual results proved the rationality of the models.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

ERIC Educational Resources Information Center

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

2011-01-01

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

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

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

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

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

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

Model-based analysis of N-glycosylation in Chinese hamster ovary cells

PubMed Central

Krambeck, Frederick J.; Bennun, Sandra V.; Betenbaugh, Michael J.

2017-01-01

The Chinese hamster ovary (CHO) cell is the gold standard for manufacturing of glycosylated recombinant proteins for production of biotherapeutics. The similarity of its glycosylation patterns to the human versions enable the products of this cell line favorable pharmacokinetic properties and lower likelihood of causing immunogenic responses. Because glycan structures are the product of the concerted action of intracellular enzymes, it is difficult to predict a priori how the effects of genetic manipulations alter glycan structures of cells and therapeutic properties. For that reason, quantitative models able to predict glycosylation have emerged as promising tools to deal with the complexity of glycosylation processing. For example, an earlier version of the same model used in this study was used by others to successfully predict changes in enzyme activities that could produce a desired change in glycan structure. In this study we utilize an updated version of this model to provide a comprehensive analysis of N-glycosylation in ten Chinese hamster ovary (CHO) cell lines that include a wild type parent and nine mutants of CHO, through interpretation of previously published mass spectrometry data. The updated N-glycosylation mathematical model contains up to 50,605 glycan structures. Adjusting the enzyme activities in this model to match N-glycan mass spectra produces detailed predictions of the glycosylation process, enzyme activity profiles and complete glycosylation profiles of each of the cell lines. These profiles are consistent with biochemical and genetic data reported previously. The model-based results also predict glycosylation features of the cell lines not previously published, indicating more complex changes in glycosylation enzyme activities than just those resulting directly from gene mutations. The model predicts that the CHO cell lines possess regulatory mechanisms that allow them to adjust glycosylation enzyme activities to mitigate side effects of the primary loss or gain of glycosylation function known to exist in these mutant cell lines. Quantitative models of CHO cell glycosylation have the potential for predicting how glycoengineering manipulations might affect glycoform distributions to improve the therapeutic performance of glycoprotein products. PMID:28486471

Controlling Flexible Manipulators, an Experimental Investigation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Hastings, Gordon Greene

1986-01-01

Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.