Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Experiments in structural dynamics and control using a grid

NASA Technical Reports Server (NTRS)

Montgomery, R. C.

1985-01-01

Future spacecraft are being conceived that are highly flexible and of extreme size. The two features of flexibility and size pose new problems in control system design. Since large scale structures are not testable in ground based facilities, the decision on component placement must be made prior to full-scale tests on the spacecraft. Control law research is directed at solving problems of inadequate modelling knowledge prior to operation required to achieve peak performance. Another crucial problem addressed is accommodating failures in systems with smart components that are physically distributed on highly flexible structures. Parameter adaptive control is a method of promise that provides on-orbit tuning of the control system to improve performance by upgrading the mathematical model of the spacecraft during operation. Two specific questions are answered in this work. They are: What limits does on-line parameter identification with realistic sensors and actuators place on the ultimate achievable performance of a system in the highly flexible environment? Also, how well must the mathematical model used in on-board analytic redundancy be known and what are the reasonable expectations for advanced redundancy management schemes in the highly flexible and distributed component environment?

Asymmetrical booster ascent guidance and control system design study. Volume 2: SSFS math models - Ascent. [space shuttle development

NASA Technical Reports Server (NTRS)

Williams, F. E.; Lemon, R. S.

1974-01-01

The engineering equations and mathematical models developed for use in the space shuttle functional simulator (SSFS) are presented, and include extensive revisions and additions to earlier documentation. Definitions of coordinate systems used by the SSFS models and coordinate tranformations are given, along with documentation of the flexible body mathematical models. The models were incorporated in the SSFS and are in the checkout stage.

Spatial operator algebra for flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Jain, A.; Rodriguez, G.

1993-01-01

This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.

Cognitive Rationality and Its Logic-Mathematical Language

ERIC Educational Resources Information Center

Masalova, Svetlana

2012-01-01

The article deals with the cognitive (flexible) rationality, combining rational and irrational moments of the scientific search of the cognizing subject. Linguo-cognitive model of the concept as the flexible regulative rationality reveals the activity of the cognitive processes and the mentality of the epistemological-ontic subject, its leading…

Adult Students' Experiences of a Flipped Mathematics Classroom

ERIC Educational Resources Information Center

Larsen, Judy

2015-01-01

The flipped classroom is a flexible blended learning model that is growing in popularity due to the emergent accessibility to online content delivery technology. By delivering content outside of class time asynchronously, teachers are able to dedicate their face to face class time for student-centred teaching approaches. The flexibility in…

Acoustoelasticity. [sound-structure interaction

NASA Technical Reports Server (NTRS)

Dowell, E. H.

1977-01-01

Sound or pressure variations inside bounded enclosures are investigated. Mathematical models are given for determining: (1) the interaction between the sound pressure field and the flexible wall of a Helmholtz resonator; (2) coupled fluid-structural motion of an acoustic cavity with a flexible and/or absorbing wall; (3) acoustic natural modes in multiple connected cavities; and (4) the forced response of a cavity with a flexible and/or absorbing wall. Numerical results are discussed.

Evaluation of the effect of elastic joints on the auto-oscillation of spacecraft with gas-reactive direction systems

NASA Technical Reports Server (NTRS)

Sasin, G. G.

1979-01-01

A mathematical model was obtained, on the basis of the method of mixed coordinates, of a generalized flexible spacecraft at one end of which was appended the directive action of a system of gas reactive nozzles. Various structural forms were obtained functionally describing flexible spacecraft, as systems consisting of a solid central body with flexible structural elements joined to it.

The dynamics and control of large flexible space structures-V

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Diarra, C. M.; Kumar, V. K.

1982-01-01

A general survey of the progress made in the areas of mathematical modelling of the system dynamics, structural analysis, development of control algorithms, and simulation of environmental disturbances is presented. The use of graph theory techniques is employed to examine the effects of inherent damping associated with LSST systems on the number and locations of the required control actuators. A mathematical model of the forces and moments induced on a flexible orbiting beam due to solar radiation pressure is developed and typical steady state open loop responses obtained for the case when rotations and vibrations are limited to occur within the orbit plane. A preliminary controls analysis based on a truncated (13 mode) finite element model of the 122m. Hoop/Column antenna indicates that a minimum of six appropriately placed actuators is required for controllability. An algorithm to evaluate the coefficients which describe coupling between the rigid rotational and flexible modes and also intramodal coupling was developed and numerical evaluation based on the finite element model of Hoop/Column system is currently in progress.

Simple, Flexible, Trigonometric Taper Equations

Treesearch

Charles E. Thomas; Bernard R. Parresol

1991-01-01

There have been numerous approaches to modeling stem form in recent decades. The majority have concentrated on the simpler coniferous bole form and have become increasingly complex mathematical expressions. Use of trigonometric equations provides a simple expression of taper that is flexible enough to fit both coniferous and hard-wood bole forms. As an illustration, we...

Anticipatory Neurofuzzy Control

NASA Technical Reports Server (NTRS)

Mccullough, Claire L.

1994-01-01

Technique of feedback control, called "anticipatory neurofuzzy control," developed for use in controlling flexible structures and other dynamic systems for which mathematical models of dynamics poorly known or unknown. Superior ability to act during operation to compensate for, and adapt to, errors in mathematical model of dynamics, changes in dynamics, and noise. Also offers advantage of reduced computing time. Hybrid of two older fuzzy-logic control techniques: standard fuzzy control and predictive fuzzy control.

Basic mathematical rules are encoded by primate prefrontal cortex neurons

PubMed Central

Bongard, Sylvia; Nieder, Andreas

2010-01-01

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

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.

Unsymmetric Lanczos model reduction and linear state function observer for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1991-01-01

This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures.

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

PubMed

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

2016-06-01

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

Flexibility evaluation of multiechelon supply chains.

PubMed

Almeida, João Flávio de Freitas; Conceição, Samuel Vieira; Pinto, Luiz Ricardo; de Camargo, Ricardo Saraiva; Júnior, Gilberto de Miranda

2018-01-01

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution.

Flexibility evaluation of multiechelon supply chains

PubMed Central

Conceição, Samuel Vieira; Pinto, Luiz Ricardo; de Camargo, Ricardo Saraiva; Júnior, Gilberto de Miranda

2018-01-01

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution. PMID:29584755

Attitude dynamics and control of spacecraft with a partially filled liquid tank and flexible panels

NASA Astrophysics Data System (ADS)

Liu, Feng; Yue, Baozeng; Zhao, Liangyu

2018-02-01

A liquid-filled flexible spacecraft is essentially a time-variant fully-coupled system, whose dynamics characteristics are closely associated with its motion features. This paper focuses on the mathematical modelling and attitude control of the spacecraft coupled with fuel sloshing dynamics and flexible solar panels vibration. The slosh motion is represented by a spherical pendulum, whose motion description method is improved by using split variable operation. Benefiting from this improvement, the nonlinear lateral sloshing and the rotary sloshing as well as the rigid motion of a liquid respect to the spacecraft can be approximately described. The assumed modes discretization method has been adopted to approximate the elastic displacements of the attached panels, and the coupled dynamics is derived by using the Lagrangian formulation. A variable substitution method is proposed to obtain the apparently-uncoupled mathematical model of the rigid-flexible-liquid spacecraft. After linearization, this model can be directly used for designing Lyapunov output-feedback attitude controller (OFAC). With only torque actuators, and attitude and rate sensors installed, this kind of attitude controller, as simulation results show, is capable of not only bringing the spacecraft to the desired orientation, but also suppressing the effect of flex and slosh on the attitude motion of the spacecraft.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

A mathematical problem and a Spacecraft Control Laboratory Experiment (SCOLE) used to evaluate control laws for flexible spacecraft. NASA/IEEE design challenge

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Balakrishnan, A. V.

1988-01-01

The problen of controlling large, flexible space systems has been evaluated using computer simulation. In several cases, ground experiments have also been used to validate system performance under more realistic conditions. There remains a need, however, to test additional control laws for flexible spacecraft and to directly compare competing design techniques. A program is discussed which has been initiated to make direct comparisons of control laws for, first, a mathematical problem, then and experimental test article being assembled under the cognizance of the Spacecraft Control Branch at the NASA Langley Research Center with the advice and counsel of the IEEE Subcommittee on Large Space Structures. The physical apparatus will consist of a softly supported dynamic model of an antenna attached to the Shuttle by a flexible beam. The control objective will include the task of directing the line-of-sight of the Shuttle antenna configuration toward a fixed target, under conditions of noisy data, control authority and random disturbances.

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

2004-01-01

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

Mathematical Modeling for Inherited Diseases.

PubMed

Anis, Saima; Khan, Madad; Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

Impact of Online Flexible Games on Students' Attitude towards Mathematics

ERIC Educational Resources Information Center

Mavridis, Apostolos; Katmada, Aikaterini; Tsiatsos, Thrasyvoulos

2017-01-01

This study examined the effects of using an online flexible educational game on students' attitude towards mathematics as compared to the traditional method of solving mathematical problems. Moreover, the study assessed the learning effectiveness of the game and investigated potential gender differences in the game's effectiveness on changing…

Vibration sensing in flexible structures using a distributed-effect modal domain optical fiber sensor

NASA Technical Reports Server (NTRS)

Reichard, Karl M.; Lindner, Douglas K.; Claus, Richard O.

1991-01-01

Modal domain optical fiber sensors have recently been employed in the implementation of system identification algorithms and the closed-loop control of vibrations in flexible structures. The mathematical model of the modal domain optical fiber sensor used in these applications, however, only accounted for the effects of strain in the direction of the fiber's longitudinal axis. In this paper, we extend this model to include the effects of arbitrary stress. Using this sensor model, we characterize the sensor's sensitivity and dynamic range.

Handling Qualities of Large Flexible Aircraft. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Poopaka, S.

1980-01-01

The effects on handling qualities of elastic modes interaction with the rigid body dynamics of a large flexible aircraft are studied by a mathematical computer simulation. An analytical method to predict the pilot ratings when there is a severe modes interactions is developed. This is done by extending the optimal control model of the human pilot response to include the mode decomposition mechanism into the model. The handling qualities are determined for a longitudinal tracking task using a large flexible aircraft with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction.

Effects of structural flexibility of wings in flapping flight of butterfly.

PubMed

Senda, Kei; Obara, Takuya; Kitamura, Masahiko; Yokoyama, Naoto; Hirai, Norio; Iima, Makoto

2012-06-01

The objective of this paper is to clarify the effects of structural flexibility of wings of a butterfly in flapping flight. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. The panel method is employed to simulate the flow field and the aerodynamic forces acting on the wings. The mathematical model is validated by the agreement of the numerical result with the experimentally measured data. Then, periodic orbits of flapping-of-wings flights are parametrically searched in order to fly the butterfly models. Almost periodic orbits are found, but they are unstable. Deformation of the wings is modeled in two ways. One is bending and its effect on the aerodynamic forces is discussed. The other is passive wing torsion caused by structural flexibility. Numerical simulations demonstrate that flexible torsion reduces the flight instability.

Mathematical Modeling for Inherited Diseases

PubMed Central

Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra. PMID:28781606

Handling qualities of large flexible control-configured aircraft

NASA Technical Reports Server (NTRS)

Swaim, R. L.

1980-01-01

The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task.

Endoscope shaft-rigidity control mechanism: "FORGUIDE".

PubMed

Loeve, Arjo J; Plettenburg, Dick H; Breedveld, Paul; Dankelman, Jenny

2012-02-01

Recent developments in flexible endoscopy and other fields of medical technology have raised the need for compact slender shafts that can be made rigid and compliant at will. A novel compact mechanism, named FORGUIDE, with this functionality was developed. The FORGUIDE shaft rigidifies due to friction between a ring of cables situated between a spring and an inflated tube. A mathematical model for the FORGUIDE mechanism working principle was made and used to obtain understanding of this mechanism, predict the maximum rigidity of a FORGUIDE shaft design, and tune its design variables. The mathematical model gave suggestions for significant performance improvement by fine-tuning the design. A prototype FORGUIDE shaft was built and put to a series of bench tests. These tests showed that the FORGUIDE mechanism provides a reliable and simple way to control the rigidity of a flexible shaft. © 2011 IEEE

Unlocking the black box: teaching mathematical modeling with popular culture.

PubMed

Lofgren, Eric T

2016-10-01

Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Shift scheduling model considering workload and worker’s preference for security department

NASA Astrophysics Data System (ADS)

Herawati, A.; Yuniartha, D. R.; Purnama, I. L. I.; Dewi, LT

2018-04-01

Security department operates for 24 hours and applies shift scheduling to organize its workers as well as in hotel industry. This research has been conducted to develop shift scheduling model considering the workers physical workload using rating of perceived exertion (RPE) Borg’s Scale and workers’ preference to accommodate schedule flexibility. The mathematic model is developed in integer linear programming and results optimal solution for simple problem. Resulting shift schedule of the developed model has equally distribution shift allocation among workers to balance the physical workload and give flexibility for workers in working hours arrangement.

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.

Simulation of Dynamics of a Flexible Miniature Airplane

NASA Technical Reports Server (NTRS)

Waszak, Martin R.

2005-01-01

A short report discusses selected aspects of the development of the University of Florida micro-aerial vehicle (UFMAV) basically, a miniature airplane that has a flexible wing and is representative of a new class of airplanes that would operate autonomously or under remote control and be used for surveillance and/or scientific observation. The flexibility of the wing is to be optimized such that passive deformation of the wing in the presence of aerodynamic disturbances would reduce the overall response of the airplane to disturbances, thereby rendering the airplane more stable as an observation platform. The aspect of the development emphasized in the report is that of computational simulation of dynamics of the UFMAV in flight, for the purpose of generating mathematical models for use in designing control systems for the airplane. The simulations are performed by use of data from a wind-tunnel test of the airplane in combination with commercial software, in which are codified a standard set of equations of motion of an airplane, and a set of mathematical routines to compute trim conditions and extract linear state space models.

How preschool executive functioning predicts several aspects of math achievement in Grades 1 and 3: A longitudinal study.

PubMed

Viterbori, Paola; Usai, M Carmen; Traverso, Laura; De Franchis, Valentina

2015-12-01

This longitudinal study analyzes whether selected components of executive function (EF) measured during the preschool period predict several indices of math achievement in primary school. Six EF measures were assessed in a sample of 5-year-old children (N = 175). The math achievement of the same children was then tested in Grades 1 and 3 using both a composite math score and three single indices of written calculation, arithmetical facts, and problem solving. Using previous results obtained from the same sample of children, a confirmatory factor analysis examining the latent EF structure in kindergarten indicated that a two-factor model provided the best fit for the data. In this model, inhibition and working memory (WM)-flexibility were separate dimensions. A full structural equation model was then used to test the hypothesis that math achievement (the composite math score and single math scores) in Grades 1 and 3 could be explained by the two EF components comprising the kindergarten model. The results indicate that the WM-flexibility component measured during the preschool period substantially predicts mathematical achievement, especially in Grade 3. The math composite scores were predicted by the WM-flexibility factor at both grade levels. In Grade 3, both problem solving and arithmetical facts were predicted by the WM-flexibility component. The results empirically support interventions that target EF as an important component of early childhood mathematics education. Copyright © 2015 Elsevier Inc. All rights reserved.

Turning Potential Flexibility Into Flexible Performance: Moderating Effect of Self-Efficacy and Use of Flexible Cognition

PubMed Central

Liu, Ru-De; Wang, Jia; Star, Jon R.; Zhen, Rui; Jiang, Rong-Huan; Fu, Xin-Chen

2018-01-01

This study examined the relationship between two types of mathematical flexibility – potential flexibility, which indicates individuals’ knowledge of multiple strategies and strategy efficiency, and practical flexibility, which refers to individuals’ flexible performances when solving math problems. Both types of flexibility were assessed in the domain of linear equation solving. Furthermore, two types of beliefs – self-efficacy and use of flexible cognition (UFC) – were investigated as potential moderators between potential and practical flexibility. 121 8th grade students from China took part in this study. Results indicate that potential flexibility positively predicted practical flexibility. Additionally, self-efficacy and UFC might moderate the relationship between these two types of flexibility, suggesting that potential flexibility may lead to different degrees of practical flexibility depending on different levels of beliefs. Implications of these findings for research on mathematical flexibility and for educational practice are discussed. PMID:29780344

Bending induced electrical response variations in ultra-thin flexible chips and device modeling

NASA Astrophysics Data System (ADS)

Heidari, Hadi; Wacker, Nicoleta; Dahiya, Ravinder

2017-09-01

Electronics that conform to 3D surfaces are attracting wider attention from both academia and industry. The research in the field has, thus far, focused primarily on showcasing the efficacy of various materials and fabrication methods for electronic/sensing devices on flexible substrates. As the device response changes are bound to change with stresses induced by bending, the next step will be to develop the capacity to predict the response of flexible systems under various bending conditions. This paper comprehensively reviews the effects of bending on the response of devices on ultra-thin chips in terms of variations in electrical parameters such as mobility, threshold voltage, and device performance (static and dynamic). The discussion also includes variations in the device response due to crystal orientation, applied mechanics, band structure, and fabrication processes. Further, strategies for compensating or minimizing these bending-induced variations have been presented. Following the in-depth analysis, this paper proposes new mathematical relations to simulate and predict the device response under various bending conditions. These mathematical relations have also been used to develop new compact models that have been verified by comparing simulation results with the experimental values reported in the recent literature. These advances will enable next generation computer-aided-design tools to meet the future design needs in flexible electronics.

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.

Investigation of the torsional stiffness of flexible disc coupling

NASA Astrophysics Data System (ADS)

Buryy, A.; Simonovsky, V.; Obolonik, V.

2017-08-01

Calculation of flexible coupling torsional stiffness is required when analyzing the torsional vibrations of the reciprocating machinery train. While having the lowest torsional stiffness of all the elements of the train, flexible coupling has a significant influence on the natural frequencies of torsional vibration. However, considering structural complexity of coupling, precise definition of its torsional stiffness is quite a difficult task. The paper presents a method for calculating the torsional stiffness of flexible disc coupling based on the study of its finite element model response under the action of torque. The analysis of the basic parameters that quantitatively and qualitatively affect the coupling torsional stiffness has been also provided. The results of the calculation as well as model adequacy, sufficient for practical application, have been confirmed at the experimental measurement of flexible disc coupling torsional stiffness. The obtained elastic characteristics (dependences of applied torque and torsional stiffness versus twist angle) are nonlinear in the initial stage of loading. This feature should be taken into account when creating reliable mathematical models of torsional vibrations of reciprocating machinery trains containing flexible disc couplings.

Can goal-free problems facilitating students' flexible thinking?

NASA Astrophysics Data System (ADS)

Maulidya, Sity Rahmy; Hasanah, Rusi Ulfa; Retnowati, Endah

2017-08-01

Problem solving is the key of doing and also learning mathematics. It takes also the fundamental role of developing mathematical knowledge. Responding to the current reform movement in mathematics, students are expected to learn to be a flexible thinker. The ability to think flexible is challenged by the globalisation, hence influence mathematics education. A flexible thinking includes ability to apply knowledge in different contexts rather than simply use it in similar context when it is studied. Arguably problem solving activities can contribute to the development of the ability to apply skills to unfamiliar situations. Accordingly, an appropriate classroom instructional strategy must be developed. A cognitive load theory suggests that by reducing extraneous cognitive load during learning could enhance transfer learning. A goal-free problem strategy that is developed based in cognitive load theory have been showed to be effective for transfer learning. This strategy enables students to learn a large numbers of problem solving moves from a mathematics problem. The instruction in a goal-free problem directs students to `calculate as many solution as you can' rather than to calculate a single given goal. Many experiment research evident goal-free problem enhance learning. This literature review will discuss evidence goal-free problem facilitate students to solve problems flexibly and thus enhance their problem solving skills, including how its implication in the classroom.

Value of Flexibility - Phase 1

DTIC Science & Technology

2010-09-25

weaknesses of each approach. During this period, we also explored the development of an analytical framework based on sound mathematical constructs... mathematical constructs. A review of the current state-of-the-art showed that there is little unifying theory or guidance on best approaches to...research activities is in developing a coherent value based definition of flexibility that is based on an analytical framework that is mathematically

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.

The effect of mathematical model development on the instruction of acceleration to introductory physics students

NASA Astrophysics Data System (ADS)

Sauer, Tim Allen

The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

Application of Lanczos vectors to control design of flexible structures

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Su, Tzu-Jeng

1990-01-01

This report covers research conducted during the first year of the two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to obtain reduced-order mathematical models for use in dynamic response analyses and in control design studies. This report summarizes research described in several reports and papers that were written under this contract. Extended abstracts are presented for technical papers covering the following topics: controller reduction by preserving impulse response energy; substructuring decomposition and controller synthesis; model reduction methods for structural control design; and recent literature on structural modeling, identification, and analysis.

Vibration and Control of Flexible Rotor Supported by Magnetic Bearings

NASA Technical Reports Server (NTRS)

Nonami, Kenzou

1988-01-01

Active vibration control of flexible rotors supported by magnetic bearings is discussed. Using a finite-element method for a mathematical model of the flexible rotor, the eigenvalue problem is formulated taking into account the interaction between a mechanical system of the flexible rotor and an electrical system of the magnetic bearings and the controller. However, for the sake of simplicity, gyroscopic effects are disregarded. It is possible to adapt this formulation to a general flexible rotor-magnetic bearing system. Controllability with and without collocation sensors and actuators located at the same distance along the rotor axis is discussed for the higher order flexible modes of the test rig. In conclusion, it is proposed that it is necessary to add new active control loops for the higher flexible modes even in the case of collocation. Then it is possible to stabilize for the case of uncollocation by means of this method.

BehavePlus fire modeling system, version 5.0: Design and Features

Treesearch

Faith Ann Heinsch; Patricia L. Andrews

2010-01-01

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

BehavePlus fire modeling system, version 4.0: User's Guide

Treesearch

Patricia L. Andrews; Collin D. Bevins; Robert C. Seli

2005-01-01

The BehavePlus fire modeling system is a program for personal computers that is a collection of mathematical models that describe fire and the fire environment. It is a flexible system that produces tables, graphs, and simple diagrams. It can be used for a multitude of fire management applications including projecting the behavior of an ongoing fire, planning...

Digital controller design: Continuous and discrete describing function analysis of the IPS system

NASA Technical Reports Server (NTRS)

1977-01-01

The dynamic equations and the mathematical model of the continuous-data IPS control system are developed. The IPS model considered included one flexible body mode and was hardmounted to the Orbiter/Pallet. The model contains equations describing a torque feed-forward loop (using accelerometers as inputs) which will aid in reducing the pointing errors caused by Orbiter disturbances.

Strategic competence of senior secondary school students in solving mathematics problem based on cognitive style

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The purpose of this study was to explore the strategic competence of senior secondary school students in solving mathematics problems. Terdapat dua subjek, satu bergaya kognitif field-independent dan satu bergaya kognitif field-dependent tetapi keduanya memiliki tingkat prestasi belajar matematika yang setara. There were two subjects, one field-independent cognitive style and one field-dependent cognitive style. They had an equivalent high level of mathematics achievement. Keduanya dipilih berdasarkan hasil tes kompetensi matematika dan GEFT (Group Embedded Figures Test). Subjects were selected based on the test results of mathematics competence and GEFT (Group Embedded Figures Test). Kompetensi strategis dapat merangsang perkembangan otonomi dan fleksibilitas dalam diri siswa karena merupakan keterampilan yang sangat dibutuhkan di sepanjang abad 21. Gaya kognitif merupakan kecenderungan siswa dalam mengolah informasi sangat mempengaruhi performance dalam menyelesaikan masalah matematika. Strategic competence can stimulate the development of autonomy and flexibility of students and they are skills which are needed in the 21st century. Cognitive style is the tendency of students in processing informations and it greatly affects the performance in solving mathematics problems. Hasil penelitian menunjukkan bahwa subjek FI cenderung analitis baik pada pembentukan bayangannya maupun pada gambar yang dibuatnya untuk memproses informasi berdasarkan dengan struktur pengetahuannya sendiri (Internally directed). The research result showed that subject FI tended to be analytical both in forming the mental imagination and the picture to process information in accordance with his own knowledge structure (internally directed). Subjek FD kurang analitis dan tidak dapat mengenal bentuk sederhana (konsep matematika) dari bentuk yang kompleks (Exeternally directed) sehingga menerima ide sebagaimana yang disajikan. Subject FD was less analytical and unable to recognize simple form (mathematical concept) of a complex form (Externally directed), so he received the idea as presented. Hasil penelitian ini penting sebagai bahan masukan untuk guru dan pengembang ilmu pendidikan matematika untuk meningkatkan fleksibilitas (Flexibility) siswa dalam keberagaman karakteristiknya melalui penelitian terkait dengan pengembangan bahan instruksi, perangkat dan model pembelajaran matematika. The results of this research are important as input for teachers and mathematics education developers to increase the flexibility of students in the characteristics diversity through the research related to the development of instruction materials and mathematics learning model. Penelitian selanjutnya, sebaiknya melihat bagaimana FI dan FD dapat memberikan penjelasan dan pembenaran atas strategi yang telah diusahakan supaya terlihat lebih jelas bagaimana perbedaan FI dan FD dalam mengkontruksi konsep matematika pada pengalaman belajarnya Further research should study about how the explanation and justification for the strategy that has been attempted in order to look more clearly how constructing mathematical concepts in their learning experience.

Application of queuing theory in inventory systems with substitution flexibility

NASA Astrophysics Data System (ADS)

Seyedhoseini, S. M.; Rashid, Reza; Kamalpour, Iman; Zangeneh, Erfan

2015-03-01

Considering the competition in today's business environment, tactical planning of a supply chain becomes more complex than before. In many multi-product inventory systems, substitution flexibility can improve profits. This paper aims to prepare a comprehensive substitution inventory model, where an inventory system with two substitute products with ignorable lead time has been considered, and effects of simultaneous ordering have been examined. In this paper, demands of customers for both of the products have been regarded as stochastic parameters, and queuing theory has been used to construct a mathematical model. The model has been coded by C++, and it has been analyzed due to a real example, where the results indicate efficiency of proposed model.

[Influence of sample surface roughness on mathematical model of NIR quantitative analysis of wood density].

PubMed

Huang, An-Min; Fei, Ben-Hua; Jiang, Ze-Hui; Hse, Chung-Yun

2007-09-01

Near infrared spectroscopy is widely used as a quantitative method, and the main multivariate techniques consist of regression methods used to build prediction models, however, the accuracy of analysis results will be affected by many factors. In the present paper, the influence of different sample roughness on the mathematical model of NIR quantitative analysis of wood density was studied. The result of experiments showed that if the roughness of predicted samples was consistent with that of calibrated samples, the result was good, otherwise the error would be much higher. The roughness-mixed model was more flexible and adaptable to different sample roughness. The prediction ability of the roughness-mixed model was much better than that of the single-roughness model.

Meta-Modeling-Based Groundwater Remediation Optimization under Flexibility in Environmental Standard.

PubMed

He, Li; Xu, Zongda; Fan, Xing; Li, Jing; Lu, Hongwei

2017-05-01

  This study develops a meta-modeling based mathematical programming approach with flexibility in environmental standards. It integrates numerical simulation, meta-modeling analysis, and fuzzy programming within a general framework. A set of models between remediation strategies and remediation performance can well guarantee the mitigation in computational efforts in the simulation and optimization process. In order to prevent the occurrence of over-optimistic and pessimistic optimization strategies, a high satisfaction level resulting from the implementation of a flexible standard can indicate the degree to which the environmental standard is satisfied. The proposed approach is applied to a naphthalene-contaminated site in China. Results show that a longer remediation period corresponds to a lower total pumping rate and a stringent risk standard implies a high total pumping rate. The wells located near or in the down-gradient direction to the contaminant sources have the most significant efficiency among all of remediation schemes.

Characterization and modeling of an advanced flexible thermal protection material for space applications

NASA Technical Reports Server (NTRS)

Clayton, Joseph P.; Tinker, Michael L.

1991-01-01

This paper describes experimental and analytical characterization of a new flexible thermal protection material known as Tailorable Advanced Blanket Insulation (TABI). This material utilizes a three-dimensional ceramic fabric core structure and an insulation filler. TABI is the leading candidate for use in deployable aeroassisted vehicle designs. Such designs require extensive structural modeling, and the most significant in-plane material properties necessary for model development are measured and analytically verified in this study. Unique test methods are developed for damping measurements. Mathematical models are developed for verification of the experimental modulus and damping data, and finally, transverse properties are described in terms of the inplane properties through use of a 12-dof finite difference model of a simple TABI configuration.

Digital computer simulation of inductor-energy-storage dc-to-dc converters with closed-loop regulators

NASA Technical Reports Server (NTRS)

Ohri, A. K.; Owen, H. A.; Wilson, T. G.; Rodriguez, G. E.

1974-01-01

The simulation of converter-controller combinations by means of a flexible digital computer program which produces output to a graphic display is discussed. The procedure is an alternative to mathematical analysis of converter systems. The types of computer programming involved in the simulation are described. Schematic diagrams, state equations, and output equations are displayed for four basic forms of inductor-energy-storage dc to dc converters. Mathematical models are developed to show the relationship of the parameters.

NASA/Howard University Large Space Structures Institute

NASA Technical Reports Server (NTRS)

Broome, T. H., Jr.

1984-01-01

Basic research on the engineering behavior of large space structures is presented. Methods of structural analysis, control, and optimization of large flexible systems are examined. Topics of investigation include the Load Correction Method (LCM) modeling technique, stabilization of flexible bodies by feedback control, mathematical refinement of analysis equations, optimization of the design of structural components, deployment dynamics, and the use of microprocessors in attitude and shape control of large space structures. Information on key personnel, budgeting, support plans and conferences is included.

Application of Lanczos vectors to control design of flexible structures, part 2

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Su, Tzu-Jeng

1992-01-01

This report covers the period of the grant from January 1991 until its expiration in June 1992. Together with an Interim Report (Ref. 9), it summarizes the research conducted under NASA Grant NAG9-357 on the topic 'Application of Lanczos Vectors to Control Design of Flexible Structures.' The research concerns various ways to obtain reduced-order mathematical models of complex structures for use in dynamics analysis and in the design of control systems for these structures. This report summarizes the research.

An Improved Cochlea Model with a General User Interface

NASA Astrophysics Data System (ADS)

Duifhuis, H.; Kruseman, J. M.; van Hengel, P. W. J.

2003-02-01

We have developed a flexible 1D cochlea model to test hypotheses and data against physical and mathematical constraints. The model is flexible in the sense that several linear and nonlinear model characteristics can be selected, and different boundary conditions can be tested. The software model runs at a reasonable speed at a modern PC. As an example, we will show the results of the model in comparison with the systematic study of the phase behavior (group delay) of distortion product otoacoustic emissions (DPOAEs) in the guinea pig (S. Schneider, V. Prijs and R. Schoonhoven, [9]). We also will demonstrate the effects of some common non-physical boundary conditions. Finally, we briefly indicate that this model of the auditory periphery provides a superior front end for an ASR (automatic speech recognition)-system.

The dynamics and control of large flexible space structures. Part A: Discrete model and modal control

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Sellappan, R.

1978-01-01

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered.

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics.

PubMed

DeCaro, Marci S

2016-10-01

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

Educational Support for Low-Performing Students in Mathematics: The Three-Tier Support Model in Finnish Lower Secondary Schools

ERIC Educational Resources Information Center

Ekstam, Ulrika; Linnanmäki, Karin; Aunio, Pirjo

2015-01-01

In 2011, there was a legislative reform regarding educational support in Finland, with a focus on early identification, differentiation and flexible arrangement of support using a multi-professional approach, the three-tier support model. The main aim of this study was to investigate what educational support practices are used with low-performing…

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

PubMed

Braatz, Elise M; Coleman, Randolph A

2015-06-01

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

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

ERIC Educational Resources Information Center

Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

Latinas and Problem Solving: What They Say and What They Do

ERIC Educational Resources Information Center

Guerra, Paula; Lim, Woong

2014-01-01

In this article, the authors present three adolescent Latinas' perceptions of ideal mathematical competencies, their perception of their individual "abilities" in mathematics, and their work on a mathematics problem-solving task. Results indicate that these Latinas recognize flexible mathematics as the ideal mathematical competency in…

Linking LEGO and Algebra

ERIC Educational Resources Information Center

Özgün-Koca, S. Asli; Edwards, Thomas G.; Chelst, Kenneth R.

2015-01-01

In mathematics, students should represent, model, and work with such real-world situations as those found in the physical world, the public policy realm, and society (CCSSI 2010). Additionally, students need to make decisions and be flexible enough to improve their decisions after analyzing realistic situations. The LEGO® Pets activity does just…

Functional Specialization and Flexibility in Human Association Cortex

PubMed Central

Yeo, B. T. Thomas; Krienen, Fenna M.; Eickhoff, Simon B.; Yaakub, Siti N.; Fox, Peter T.; Buckner, Randy L.; Asplund, Christopher L.; Chee, Michael W.L.

2015-01-01

The association cortex supports cognitive functions enabling flexible behavior. Here, we explored the organization of human association cortex by mathematically formalizing the notion that a behavioral task engages multiple cognitive components, which are in turn supported by multiple overlapping brain regions. Application of the model to a large data set of neuroimaging experiments (N = 10 449) identified complex zones of frontal and parietal regions that ranged from being highly specialized to highly flexible. The network organization of the specialized and flexible regions was explored with an independent resting-state fMRI data set (N = 1000). Cortical regions specialized for the same components were strongly coupled, suggesting that components function as partially isolated networks. Functionally flexible regions participated in multiple components to different degrees. This heterogeneous selectivity was predicted by the connectivity between flexible and specialized regions. Functionally flexible regions might support binding or integrating specialized brain networks that, in turn, contribute to the ability to execute multiple and varied tasks. PMID:25249407

Modeling Individual Patient Preferences for Colorectal Cancer Screening Based on Their Tolerance for Complications Risk.

PubMed

Taksler, Glen B; Perzynski, Adam T; Kattan, Michael W

2017-04-01

Recommendations for colorectal cancer screening encourage patients to choose among various screening methods based on individual preferences for benefits, risks, screening frequency, and discomfort. We devised a model to illustrate how individuals with varying tolerance for screening complications risk might decide on their preferred screening strategy. We developed a discrete-time Markov mathematical model that allowed hypothetical individuals to maximize expected lifetime utility by selecting screening method, start age, stop age, and frequency. Individuals could choose from stool-based testing every 1 to 3 years, flexible sigmoidoscopy every 1 to 20 years with annual stool-based testing, colonoscopy every 1 to 20 years, or no screening. We compared the life expectancy gained from the chosen strategy with the life expectancy available from a benchmark strategy of decennial colonoscopy. For an individual at average risk of colorectal cancer who was risk neutral with respect to screening complications (and therefore was willing to undergo screening if it would actuarially increase life expectancy), the model predicted that he or she would choose colonoscopy every 10 years, from age 53 to 73 years, consistent with national guidelines. For a similar individual who was moderately averse to screening complications risk (and therefore required a greater increase in life expectancy to accept potential risks of colonoscopy), the model predicted that he or she would prefer flexible sigmoidoscopy every 12 years with annual stool-based testing, with 93% of the life expectancy benefit of decennial colonoscopy. For an individual with higher risk aversion, the model predicted that he or she would prefer 2 lifetime flexible sigmoidoscopies, 20 years apart, with 70% of the life expectancy benefit of decennial colonoscopy. Mathematical models may formalize how individuals with different risk attitudes choose between various guideline-recommended colorectal cancer screening strategies.

Epigenetics meets mathematics: towards a quantitative understanding of chromatin biology.

PubMed

Steffen, Philipp A; Fonseca, João P; Ringrose, Leonie

2012-10-01

How fast? How strong? How many? So what? Why do numbers matter in biology? Chromatin binding proteins are forever in motion, exchanging rapidly between bound and free pools. How do regulatory systems whose components are in constant flux ensure stability and flexibility? This review explores the application of quantitative and mathematical approaches to mechanisms of epigenetic regulation. We discuss methods for measuring kinetic parameters and protein quantities in living cells, and explore the insights that have been gained by quantifying and modelling dynamics of chromatin binding proteins. Copyright © 2012 WILEY Periodicals, Inc.

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

NASA Technical Reports Server (NTRS)

Kolb, Mark A.

1988-01-01

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

Modal analysis for Liapunov stability of rotating elastic bodies. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Colin, A. D.

1973-01-01

This study consisted of four parallel efforts: (1) modal analyses of elastic continua for Liapunov stability analysis of flexible spacecraft; (2) development of general purpose simulation equations for arbitrary spacecraft; (3) evaluation of alternative mathematical models for elastic components of spacecraft; and (4) examination of the influence of vehicle flexibility on spacecraft attitude control system performance. A complete record is given of achievements under tasks (1) and (3), in the form of technical appendices, and a summary description of progress under tasks two and four.

Generalized fluid impulse functions for oscillating marine structures

NASA Astrophysics Data System (ADS)

Janardhanan, K.; Price, W. G.; Wu, Y.

1992-03-01

A selection of generalized impulse response functions is presented for a variety of rigid and flexible marine structures (i.e. mono-hull, SWATH, floating drydock and twin dock, fixed flexible pile). These functions are determined from calculated and experimental frequency-dependent hydrodynamic data, and the characteristics of these data depend on the type of structure considered. This information is reflected in the shape and duration of the generalized impulse response functions which are pre-requisites for a generalized integro-differential mathematical model describing the dynamic behaviour of the structures to seaway excitation.

Pre-Service Secondary Mathematics Teachers Making Sense of Definitions of Functions

ERIC Educational Resources Information Center

Chesler, Joshua

2012-01-01

Definitions play an essential role in mathematics. As such, mathematics teachers and students need to flexibly and productively interact with mathematical definitions in the classroom. However, there has been little research about mathematics teachers' understanding of definitions. At an even more basic level, there is little clarity about what…

Giftedness and Aesthetics: Perspectives of Expert Mathematicians and Mathematically Gifted Students

ERIC Educational Resources Information Center

Tjoe, Hartono

2015-01-01

Giftedness in mathematics has been characterized by exceptional attributes including strong mathematical memory, formalizing perception, generalization, curtailment, flexibility, and elegance. Focusing on the last attribute, this study examined the following: (a) the criteria which expert mathematicians and mathematically gifted students fleshed…

Dynamic analysis of horizontal axis wind turbine by thin-walled beam theory

NASA Astrophysics Data System (ADS)

Wang, Jianhong; Qin, Datong; Lim, Teik C.

2010-08-01

A mixed flexible-rigid multi-body mathematical model is applied to predict the dynamic performance of a wind turbine system. Since the tower and rotor are both flexible thin-walled structures, a consistent expression for their deformations is applied, which employs a successive series of transformations to locate any point on the blade and tower relative to an inertial coordinate system. The kinetic and potential energy terms of each flexible body and rigid body are derived for use in the Lagrange approach to formulate the wind turbine system's governing equation. The mode shapes are then obtained from the free vibration solution, while the distributions of dynamic stress and displacement of the tower and rotor are computed from the forced vibration response analysis. Using this dynamic model, the influence of the tower's stiffness on the blade tip deformation is studied. From the analysis, it is evident that the proposed model not only inherits the simplicity of the traditional 1-D beam element, but also able to provide detailed information about the tower and rotor response due to the incorporation of the flexible thin-walled beam theory.

The Use of Flexible, Interactive, Situation-Focused Software for the E-Learning of Mathematics.

ERIC Educational Resources Information Center

Farnsworth, Ralph Edward

This paper discusses the classroom, home, and distance use of new, flexible, interactive, application-oriented software known as Active Learning Suite. The actual use of the software, not just a controlled experiment, is reported on. Designed for the e-learning of university mathematics, the program was developed by a joint U.S.-Russia team and…

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

ERIC Educational Resources Information Center

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

2016-01-01

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

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

A flexible framework for process-based hydraulic and water ...

EPA Pesticide Factsheets

Background Models that allow for design considerations of green infrastructure (GI) practices to control stormwater runoff and associated contaminants have received considerable attention in recent years. While popular, generally, the GI models are relatively simplistic. However, GI model predictions are being relied upon by many municipalities and State/Local agencies to make decisions about grey vs. green infrastructure improvement planning. Adding complexity to GI modeling frameworks may preclude their use in simpler urban planning situations. Therefore, the goal here was to develop a sophisticated, yet flexible tool that could be used by design engineers and researchers to capture and explore the effect of design factors and properties of the media used in the performance of GI systems at a relatively small scale. We deemed it essential to have a flexible GI modeling tool that is capable of simulating GI system components and specific biophysical processes affecting contaminants such as reactions, and particle-associated transport accurately while maintaining a high degree of flexibly to account for the myriad of GI alternatives. The mathematical framework for a stand-alone GI performance assessment tool has been developed and will be demonstrated.Framework Features The process-based model framework developed here can be used to model a diverse range of GI practices such as green roof, retention pond, bioretention, infiltration trench, permeable pavement and

Model of continual metabolism species for estimating stability of CELSS and natural ecosystems

NASA Astrophysics Data System (ADS)

Bartsev, S. I.

Estimation of stability range of natural and man-made ecosystems is necessary for effective control of them However traditional ecological models usually underestimate stability of real ecosystems It takes place due to the usage of fixed stoichiometry model of metabolism The objective is in creating theoretical and mathematical models for adequate description of both man-made and natural ecological systems A concept of genetically fixed but metabolically flexible species is considered in the paper According to the concept the total flow of matter through ecological system is supported at almost constant level depending on energy income by flexibility of metabolic organization of genetic species It is shown introducing continual metabolism species extends the range of stability making its estimation more adequate to real ecological systems

Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm

NASA Astrophysics Data System (ADS)

Li, Jia; Shen, Hua; Zhu, Rihong; Gao, Jinming; Sun, Yue; Wang, Jinsong; Li, Bo

2018-06-01

The precision of the measurements of aspheric and freeform surfaces remains the primary factor restrict their manufacture and application. One effective means of measuring such surfaces involves using reference or probe beams with angle modulation, such as tilted-wave-interferometer (TWI). It is necessary to improve the measurement efficiency by obtaining the optimum point source array for different pieces before TWI measurements. For purpose of forming a point source array based on the gradients of different surfaces under test, we established a mathematical model describing the relationship between the point source array and the test surface. However, the optimal point sources are irregularly distributed. In order to achieve a flexible point source array according to the gradient of test surface, a novel interference setup using fiber array is proposed in which every point source can be independently controlled on and off. Simulations and the actual measurement examples of two different surfaces are given in this paper to verify the mathematical model. Finally, we performed an experiment of testing an off-axis ellipsoidal surface that proved the validity of the proposed interference system.

Dynamic stability of an aerodynamically efficient motorcycle

NASA Astrophysics Data System (ADS)

Sharma, Amrit; Limebeer, David J. N.

2012-08-01

Motorcycles exhibit two potentially dangerous oscillatory modes known as 'wobble' and 'weave'. The former is reminiscent of supermarket castor shimmy, while the latter is a low frequency 'fish-tailing' motion that involves a combination of rolling, yawing, steering and side-slipping motions. These unwanted dynamic features, which can occur when two-wheeled vehicles are operated at speed, have been studied extensively. The aim of this paper is to use mathematical analysis to identify important stability trends in the on-going design of a novel aerodynamically efficient motorcycle known as the ECOSSE Spirit ES1. A mathematical model of the ES1 is developed using a multi-body dynamics software package called VehicleSim [Anon, VehicleSim Lisp Reference Manual Version 1.0, Mechanical Simulation Corporation, 2008. Available at http://www.carsim.com]. This high-fidelity motorcycle model includes realistic tyre-road contact geometry, a comprehensive tyre model, tyre relaxation and a flexible frame. A parameter set representative of a modern high-performance machine and rider is used. Local stability is investigated via the eigenvalues of the linearised models that are associated with equilibrium points of interest. A comprehensive study of the effects of frame flexibilities, acceleration, aerodynamics and tyre variations is presented, and an optimal passive steering compensator is derived. It is shown that the traditional steering damper cannot be used to stabilise the ES1 over its entire operating speed range. A simple passive compensator, involving an inerter is proposed. Flexibility can be introduced deliberately into various chassis components to change the stability characteristics of the vehicle; the implications of this idea are studied.

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

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

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

Foundations of mathematics and literacy: The role of executive functioning components.

PubMed

Purpura, David J; Schmitt, Sara A; Ganley, Colleen M

2017-01-01

The current study investigated the relations between the three cognitive processes that comprise executive functioning (EF)-response inhibition, working memory, and cognitive flexibility-and individual components of mathematics and literacy skills in preschool children. Participants were 125 preschool children ranging in age from 3.12 to 5.26years (M=4.17years, SD=0.58). Approximately 53.2% were female, and the sample was predominantly Caucasian (69.8%). Results suggest that the components of EF may be differentially related to the specific components of early mathematics and literacy. For mathematics, response inhibition was broadly related to most components. Working memory was related to more advanced mathematics skills that involve comparison or combination of numbers and quantities. Cognitive flexibility was related to more conceptual or abstract mathematics skills. For early literacy, response inhibition and cognitive flexibility were related to print knowledge, and working memory was related only to phonological awareness. None of the EF components was related to vocabulary. These findings provide initial evidence for better understanding the ways in which EF components and academic skills are related and measured. Furthermore, the findings provide a foundation for further study of the components of each domain using a broader and more diverse array of measures. Copyright © 2016 Elsevier Inc. All rights reserved.

Artificial retina model for the retinally blind based on wavelet transform

NASA Astrophysics Data System (ADS)

Zeng, Yan-an; Song, Xin-qiang; Jiang, Fa-gang; Chang, Da-ding

2007-01-01

Artificial retina is aimed for the stimulation of remained retinal neurons in the patients with degenerated photoreceptors. Microelectrode arrays have been developed for this as a part of stimulator. Design such microelectrode arrays first requires a suitable mathematical method for human retinal information processing. In this paper, a flexible and adjustable human visual information extracting model is presented, which is based on the wavelet transform. With the flexible of wavelet transform to image information processing and the consistent to human visual information extracting, wavelet transform theory is applied to the artificial retina model for the retinally blind. The response of the model to synthetic image is shown. The simulated experiment demonstrates that the model behaves in a manner qualitatively similar to biological retinas and thus may serve as a basis for the development of an artificial retina.

Analysis and experiments for delay compensation in attitude control of flexible spacecraft

NASA Astrophysics Data System (ADS)

Sabatini, Marco; Palmerini, Giovanni B.; Leonangeli, Nazareno; Gasbarri, Paolo

2014-11-01

Space vehicles are often characterized by highly flexible appendages, with low natural frequencies which can generate coupling phenomena during orbital maneuvering. The stability and delay margins of the controlled system are deeply affected by the presence of bodies with different elastic properties, assembled to form a complex multibody system. As a consequence, unstable behavior can arise. In this paper the problem is first faced from a numerical point of view, developing accurate multibody mathematical models, as well as relevant navigation and control algorithms. One of the main causes of instability is identified with the unavoidable presence of time delays in the GNC loop. A strategy to compensate for these delays is elaborated and tested using the simulation tool, and finally validated by means of a free floating platform, replicating the flexible spacecraft attitude dynamics (single axis rotation). The platform is equipped with thrusters commanded according to the on-off modulation of the Linear Quadratic Regulator (LQR) control law. The LQR is based on the estimate of the full state vector, i.e. including both rigid - attitude - and elastic variables, that is possible thanks to the on line measurement of the flexible displacements, realized by processing the images acquired by a dedicated camera. The accurate mathematical model of the system and the rigid and elastic measurements enable a prediction of the state, so that the control is evaluated taking the predicted state relevant to a delayed time into account. Both the simulations and the experimental campaign demonstrate that by compensating in this way the time delay, the instability is eliminated, and the maneuver is performed accurately.

A place for agent-based models. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Barbaro, Alethea

2015-03-01

Agent-based models have been widely applied in theoretical ecology to explain migrations and other collective animal movements [2,5,8]. As D'Orsogna and Perc have expertly highlighted in [6], the recent emergence of crime modeling has opened another interesting avenue for mathematical investigation. The area of crime modeling is particularly suited to agent-based models, because these models offer a great deal of flexibility within the model and also ease of communication among criminologist, law enforcement and modelers.

The Routine Fitting of Kinetic Data to Models

PubMed Central

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

1962-01-01

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

PharmML in Action: an Interoperable Language for Modeling and Simulation

PubMed Central

Bizzotto, R; Smith, G; Yvon, F; Kristensen, NR; Swat, MJ

2017-01-01

PharmML1 is an XML‐based exchange format2, 3, 4 created with a focus on nonlinear mixed‐effect (NLME) models used in pharmacometrics,5, 6 but providing a very general framework that also allows describing mathematical and statistical models such as single‐subject or nonlinear and multivariate regression models. This tutorial provides an overview of the structure of this language, brief suggestions on how to work with it, and use cases demonstrating its power and flexibility. PMID:28575551

Flexible multibody simulation of automotive systems with non-modal model reduction techniques

NASA Astrophysics Data System (ADS)

Shiiba, Taichi; Fehr, Jörg; Eberhard, Peter

2012-12-01

The stiffness of the body structure of an automobile has a strong relationship with its noise, vibration, and harshness (NVH) characteristics. In this paper, the effect of the stiffness of the body structure upon ride quality is discussed with flexible multibody dynamics. In flexible multibody simulation, the local elastic deformation of the vehicle has been described traditionally with modal shape functions. Recently, linear model reduction techniques from system dynamics and mathematics came into the focus to find more sophisticated elastic shape functions. In this work, the NVH-relevant states of a racing kart are simulated, whereas the elastic shape functions are calculated with modern model reduction techniques like moment matching by projection on Krylov-subspaces, singular value decomposition-based reduction techniques, and combinations of those. The whole elastic multibody vehicle model consisting of tyres, steering, axle, etc. is considered, and an excitation with a vibration characteristics in a wide frequency range is evaluated in this paper. The accuracy and the calculation performance of those modern model reduction techniques is investigated including a comparison of the modal reduction approach.

Gas Exchange Models for a Flexible Insect Tracheal System.

PubMed

Simelane, S M; Abelman, S; Duncan, F D

2016-06-01

In this paper two models for movement of respiratory gases in the insect trachea are presented. One model considers the tracheal system as a single flexible compartment while the other model considers the trachea as a single flexible compartment with gas exchange. This work represents an extension of Ben-Tal's work on compartmental gas exchange in human lungs and is applied to the insect tracheal system. The purpose of the work is to study nonlinear phenomena seen in the insect respiratory system. It is assumed that the flow inside the trachea is laminar, and that the air inside the chamber behaves as an ideal gas. Further, with the isothermal assumption, the expressions for the tracheal partial pressures of oxygen and carbon dioxide, rate of volume change, and the rates of change of oxygen concentration and carbon dioxide concentration are derived. The effects of some flow parameters such as diffusion capacities, reaction rates and air concentrations on net flow are studied. Numerical simulations of the tracheal flow characteristics are performed. The models developed provide a mathematical framework to further investigate gas exchange in insects.

Roll Damping Derivatives from Generalized Lifting-Surface Theory and Wind Tunnel Forced-Oscillation Tests

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S; Murphy, Patrick C.

2014-01-01

Improving aerodynamic models for adverse loss-of-control conditions in flight is an area being researched under the NASA Aviation Safety Program. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. As more general aerodynamic models are studied that include nonlinear higher order effects, the possibility of measurements that confound aerodynamic and structural responses are probable. In this study an initial step is taken to look at including structural flexibility in analysis of rigid-body forced-oscillation testing that accounts for dynamic rig, sting and balance flexibility. Because of the significant testing required and associated costs in a general study, it makes sense to capitalize on low cost analytical methods where possible, especially where structural flexibility can be accounted for by a low cost method. This paper provides an initial look at using linear lifting surface theory applied to rigid-body aircraft roll forced-oscillation tests.

Flexible Modes Control Using Sliding Mode Observers: Application to Ares I

NASA Technical Reports Server (NTRS)

Shtessel, Yuri B.; Hall, Charles E.; Baev, Simon; Orr, Jeb S.

2010-01-01

The launch vehicle dynamics affected by bending and sloshing modes are considered. Attitude measurement data that are corrupted by flexible modes could yield instability of the vehicle dynamics. Flexible body and sloshing modes are reconstructed by sliding mode observers. The resultant estimates are used to remove the undesirable dynamics from the measurements, and the direct effects of sloshing and bending modes on the launch vehicle are compensated by means of a controller that is designed without taking the bending and sloshing modes into account. A linearized mathematical model of Ares I launch vehicle was derived based on FRACTAL, a linear model developed by NASA/MSFC. The compensated vehicle dynamics with a simple PID controller were studied for the launch vehicle model that included two bending modes, two slosh modes and actuator dynamics. A simulation study demonstrated stable and accurate performance of the flight control system with the augmented simple PID controller without the use of traditional linear bending filters.

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…

Motivating Prospective Elementary School Teachers to Learn Mathematics by Focusing upon Children's Mathematical Thinking

ERIC Educational Resources Information Center

Philipp, Randolph A.

2008-01-01

Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Measures of Potential Flexibility and Practical Flexibility in Equation Solving.

PubMed

Xu, Le; Liu, Ru-De; Star, Jon R; Wang, Jia; Liu, Ying; Zhen, Rui

2017-01-01

Researchers interested in mathematical proficiency have recently begun to explore the development of strategic flexibility, where flexibility is defined as knowledge of multiple strategies for solving a problem and the ability to implement an innovative strategy for a given problem solving circumstance. However, anecdotal findings from this literature indicate that students do not consistently use an innovative strategy for solving a given problem, even when these same students demonstrate knowledge of innovative strategies. This distinction, sometimes framed in the psychological literature as competence vs. performance-has not been previously studied for flexibility. In order to explore the competence/performance distinction in flexibility, this study developed and validated measures for potential flexibility (e.g., competence, or knowledge of multiple strategies) and practical flexibility (e.g., performance, use of innovative strategies) for solving equations. The measures were administrated to a sample of 158 Chinese middle school students through a Tri-Phase Flexibility Assessment, in which the students were asked to solve each equation, generate additional strategies, and evaluate own multiple strategies. Confirmatory factor analysis supported a two-factor model of potential and practical flexibility. Satisfactory internal consistency was found for the measures. Additional validity evidence included the significant association with flexibility measured with the previous method. Potential flexibility and practical flexibility were found to be distinct but related. The theoretical and practical implications of the concepts and their measures of potential flexibility and practical flexibility are discussed.

Measures of Potential Flexibility and Practical Flexibility in Equation Solving

PubMed Central

Xu, Le; Liu, Ru-De; Star, Jon R.; Wang, Jia; Liu, Ying; Zhen, Rui

2017-01-01

Researchers interested in mathematical proficiency have recently begun to explore the development of strategic flexibility, where flexibility is defined as knowledge of multiple strategies for solving a problem and the ability to implement an innovative strategy for a given problem solving circumstance. However, anecdotal findings from this literature indicate that students do not consistently use an innovative strategy for solving a given problem, even when these same students demonstrate knowledge of innovative strategies. This distinction, sometimes framed in the psychological literature as competence vs. performance—has not been previously studied for flexibility. In order to explore the competence/performance distinction in flexibility, this study developed and validated measures for potential flexibility (e.g., competence, or knowledge of multiple strategies) and practical flexibility (e.g., performance, use of innovative strategies) for solving equations. The measures were administrated to a sample of 158 Chinese middle school students through a Tri-Phase Flexibility Assessment, in which the students were asked to solve each equation, generate additional strategies, and evaluate own multiple strategies. Confirmatory factor analysis supported a two-factor model of potential and practical flexibility. Satisfactory internal consistency was found for the measures. Additional validity evidence included the significant association with flexibility measured with the previous method. Potential flexibility and practical flexibility were found to be distinct but related. The theoretical and practical implications of the concepts and their measures of potential flexibility and practical flexibility are discussed. PMID:28848481

From puddles to planet: modeling approaches to vector-borne diseases at varying resolution and scale.

PubMed

Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A; Smith, David L

2015-08-01

Since the original Ross-Macdonald formulations of vector-borne disease transmission, there has been a broad proliferation of mathematical models of vector-borne disease, but many of these models retain most to all of the simplifying assumptions of the original formulations. Recently, there has been a new expansion of mathematical frameworks that contain explicit representations of the vector life cycle including aquatic stages, multiple vector species, host heterogeneity in biting rate, realistic vector feeding behavior, and spatial heterogeneity. In particular, there are now multiple frameworks for spatially explicit dynamics with movements of vector, host, or both. These frameworks are flexible and powerful, but require additional data to take advantage of these features. For a given question posed, utilizing a range of models with varying complexity and assumptions can provide a deeper understanding of the answers derived from models. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

NASA Astrophysics Data System (ADS)

Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.

2018-01-01

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Quantum-like dynamics applied to cognition: a consideration of available options

NASA Astrophysics Data System (ADS)

Broekaert, Jan; Basieva, Irina; Blasiak, Pawel; Pothos, Emmanuel M.

2017-10-01

Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Reconfiguration of broad leaves into cones

NASA Astrophysics Data System (ADS)

Miller, Laura

2013-11-01

Flexible plants, fungi, and sessile animals are thought to reconfigure in the wind and water to reduce the drag forces that act upon them. Simple mathematical models of a flexible beam immersed in a two-dimensional flow will also exhibit this behavior. What is less understood is how the mechanical properties of a leaf in a three-dimensional flow will passively allow roll up and reduce drag. This presentation will begin by examining how leaves roll up into drag reducing shapes in strong flow. The dynamics of the flow around the leaf of the wild ginger Hexastylis arifolia are described using particle image velocimetry. The flows around the leaves are compared with those of simplified sheets using 3D numerical simulations and physical models. For some reconfiguration shapes, large forces and oscillations due to strong vortex shedding are produced. In the actual leaf, a stable recirculation zone is formed within the wake of the reconfigured cone. In physical and numerical models that reconfigure into cones, a similar recirculation zone is observed with both rigid and flexible tethers. These results suggest that the three-dimensional cone structure in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced by the leaf.

Spatial transformation abilities and their relation to later mathematics performance.

PubMed

Frick, Andrea

2018-04-10

Using a longitudinal approach, this study investigated the relational structure of different spatial transformation skills at kindergarten age, and how these spatial skills relate to children's later mathematics performance. Children were tested at three time points, in kindergarten, first grade, and second grade (N = 119). Exploratory factor analyses revealed two subcomponents of spatial transformation skills: one representing egocentric transformations (mental rotation and spatial scaling), and one representing allocentric transformations (e.g., cross-sectioning, perspective taking). Structural equation modeling suggested that egocentric transformation skills showed their strongest relation to the part of the mathematics test tapping arithmetic operations, whereas allocentric transformations were strongly related to Numeric-Logical and Spatial Functions as well as geometry. The present findings point to a tight connection between early mental transformation skills, particularly the ones requiring a high level of spatial flexibility and a strong sense for spatial magnitudes, and children's mathematics performance at the beginning of their school career.

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

PubMed Central

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

2013-01-01

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

Identification of dynamic characteristics of flexible rotors as dynamic inverse problem

NASA Technical Reports Server (NTRS)

Roisman, W. P.; Vajingortin, L. D.

1991-01-01

The problem of dynamic and balancing of flexible rotors were considered, which were set and solved as the problem of the identification of flexible rotor systems, which is the same as the inverse problem of the oscillation theory dealing with the task of the identifying the outside influences and system parameters on the basis of the known laws of motion. This approach to the problem allows the disclosure the picture of disbalances throughout the rotor-under-test (which traditional methods of flexible rotor balancing, based on natural oscillations, could not provide), and identify dynamic characteristics of the system, which correspond to a selected mathematical model. Eventually, various methods of balancing were developed depending on the special features of the machines as to their design, technology, and operation specifications. Also, theoretical and practical methods are given for the flexible rotor balancing at far from critical rotation frequencies, which does not necessarily require the knowledge forms of oscillation, dissipation, and elasticity and inertia characteristics, and to use testing masses.

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

Several mathematical equations have been proposed to modeling nutrient-response curve for animal and human justified on the goodness of fit and/or on the biological mechanism. In this paper, a functional form of a generalized quantitative model based on Rayleigh distribution principle for description of nutrient-response phenomena is derived. The three parameters governing the curve a) has biological interpretation, b) may be used to calculate reliable estimates of nutrient response relationships, and c) provide the basis for deriving relationships between nutrient and physiological responses. The new function was successfully applied to fit the nutritional data obtained from 6 experiments including a wide range of nutrients and responses. An evaluation and comparison were also done based simulated data sets to check the suitability of new model and four-parameter logistic model for describing nutrient responses. This study indicates the usefulness and wide applicability of the new introduced, simple and flexible model when applied as a quantitative approach to characterizing nutrient-response curve. This new mathematical way to describe nutritional-response data, with some useful biological interpretations, has potential to be used as an alternative approach in modeling nutritional responses curve to estimate nutrient efficiency and requirements. PMID:29161271

On the Coupling Between a Supersonic Turbulent Boundary Layer and a Flexible Structure

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader

1996-01-01

A mathematical model and a computer code have been developed to fully couple the vibration of an aircraft fuselage panel to the surrounding flow field, turbulent boundary layer and acoustic fluid. The turbulent boundary layer model is derived using a triple decomposition of the flow variables and applying a conditional averaging to the resulting equations. Linearized panel and acoustic equations are used. Results from this model are in good agreement with existing experimental and numerical data. It is shown that in the supersonic regime, full coupling of the flexible panel leads to lower response and radiation from the panel. This is believed to be due to an increase in acoustic damping on the panel in this regime. Increasing the Mach number increases the acoustic damping, which is in agreement with earlier work.

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

University of Chicago School Mathematics Project (UCSMP). What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2016

2016-01-01

"University of Chicago School Mathematics Project" ("UCSMP") is a core mathematics curriculum that emphasizes problem solving, real-world applications, and the use of technology. The curriculum is based on a student-centered approach with a focus on active learning that incorporates reading and uses a flexible lesson…

Procuring load curtailment from local customers under uncertainty.

PubMed

Mijatović, Aleksandar; Moriarty, John; Vogrinc, Jure

2017-08-13

Demand side response (DSR) provides a flexible approach to managing constrained power network assets. This is valuable if future asset utilization is uncertain. However there may be uncertainty over the process of procurement of DSR from customers. In this context we combine probabilistic modelling, simulation and optimization to identify economically optimal procurement policies from heterogeneous customers local to the asset, under chance constraints on the adequacy of the procured DSR. Mathematically this gives rise to a search over permutations, and we provide an illustrative example implementation and case study.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

Computer aided flexible envelope designs

NASA Technical Reports Server (NTRS)

Resch, R. D.

1975-01-01

Computer aided design methods are presented for the design and construction of strong, lightweight structures which require complex and precise geometric definition. The first, flexible structures, is a unique system of modeling folded plate structures and space frames. It is possible to continuously vary the geometry of a space frame to produce large, clear spans with curvature. The second method deals with developable surfaces, where both folding and bending are explored with the observed constraint of available building materials, and what minimal distortion result in maximum design capability. Alternative inexpensive fabrication techniques are being developed to achieve computer defined enclosures which are extremely lightweight and mathematically highly precise.

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

Deng, Mingsen; Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Institute of Applied Physics, Guizhou Normal College, Guiyang, 550018; Ye, Gui

The probe of flexible molecular conformation is crucial for the electric application of molecular systems. We have developed a theoretical procedure to analyze the couplings of molecular local vibrations with the electron transportation process, which enables us to evaluate the structural fingerprints of some vibrational modes in the inelastic electron tunneling spectroscopy (IETS). Based on a model molecule of Bis-(4-mercaptophenyl)-ether with a flexible center angle, we have revealed and validated a simple mathematical relationship between IETS signals and molecular angles. Our results might open a route to quantitatively measure key geometrical parameters of molecular junctions, which helps to achieve precisemore » control of molecular devices.« less

The dynamics and control of large-flexible space structures, part 10

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R.

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

A new fractional nonlocal model and its application in free vibration of Timoshenko and Euler-Bernoulli beams

NASA Astrophysics Data System (ADS)

Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun

2017-11-01

The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.

Is DNA a worm-like chain in Couette flow? In search of persistence length, a critical review.

PubMed

Rittman, Martyn; Gilroy, Emma; Koohya, Hashem; Rodger, Alison; Richards, Adair

2009-01-01

Persistence length is the foremost measure of DNA flexibility. Its origins lie in polymer theory which was adapted for DNA following the determination of BDNA structure in 1953. There is no single definition of persistence length used, and the links between published definitions are based on assumptions which may, or may not be, clearly stated. DNA flexibility is affected by local ionic strength, solvent environment, bound ligands and intrinsic sequence-dependent flexibility. This article is a review of persistence length providing a mathematical treatment of the relationships between four definitions of persistence length, including: correlation, Kuhn length, bending, and curvature. Persistence length has been measured using various microscopy, force extension and solution methods such as linear dichroism and transient electric birefringence. For each experimental method a model of DNA is required to interpret the data. The importance of understanding the underlying models, along with the assumptions required by each definition to determine a value of persistence length, is highlighted for linear dichroism data, where it transpires that no model is currently available for long DNA or medium to high shear rate experiments.

A mathematical model of the human metabolic system and metabolic flexibility.

PubMed

Pearson, T; Wattis, J A D; King, J R; MacDonald, I A; Mazzatti, D J

2014-09-01

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

Monitoring apparatus and method for battery power supply

DOEpatents

Martin, Harry L.; Goodson, Raymond E.

1983-01-01

A monitoring apparatus and method are disclosed for monitoring and/or indicating energy that a battery power source has then remaining and/or can deliver for utilization purposes as, for example, to an electric vehicle. A battery mathematical model forms the basis for monitoring with a capacity prediction determined from measurement of the discharge current rate and stored battery parameters. The predicted capacity is used to provide a state-of-charge indication. Self-calibration over the life of the battery power supply is enacted through use of a feedback voltage based upon the difference between predicted and measured voltages to correct the battery mathematical model. Through use of a microprocessor with central information storage of temperature, current and voltage, system behavior is monitored, and system flexibility is enhanced.

Developing Procedural Flexibility: Are Novices Prepared to Learn from Comparing Procedures?

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Star, Jon R.; Durkin, Kelley

2012-01-01

Background: A key learning outcome in problem-solving domains is the development of procedural flexibility, where learners know multiple procedures and use them appropriately to solve a range of problems (e.g., Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009). However, students often fail to become flexible problem solvers in mathematics. To…

Electrical features of new DNC, CNC system viewed

NASA Astrophysics Data System (ADS)

Fritzsch, W.; Kochan, D.; Schaller, J.; Zander, H. J.

1985-03-01

Control structures capable of solving the problems of a flexible minial-labor manufacturing process are analyzed. The present state of development of equipment technology is described, and possible ways of modeling control processes are surveyed. Concepts which are frequently differently interpreted in various specialized disciplines are systematized, with a view toward creating the prerequisites for interdisciplinary cooperation. Problems and information flow during the preparatory and performance phases of manufacturing are examined with respect to coupling CAD/CAM functions. Mathematical modeling for direct numerical control is explored.

Electromagnetic Thermography Nondestructive Evaluation: Physics-based Modeling and Pattern Mining

PubMed Central

Gao, Bin; Woo, Wai Lok; Tian, Gui Yun

2016-01-01

Electromagnetic mechanism of Joule heating and thermal conduction on conductive material characterization broadens their scope for implementation in real thermography based Nondestructive testing and evaluation (NDT&E) systems by imparting sensitivity, conformability and allowing fast and imaging detection, which is necessary for efficiency. The issue of automatic material evaluation has not been fully addressed by researchers and it marks a crucial first step to analyzing the structural health of the material, which in turn sheds light on understanding the production of the defects mechanisms. In this study, we bridge the gap between the physics world and mathematical modeling world. We generate physics-mathematical modeling and mining route in the spatial-, time-, frequency-, and sparse-pattern domains. This is a significant step towards realizing the deeper insight in electromagnetic thermography (EMT) and automatic defect identification. This renders the EMT a promising candidate for the highly efficient and yet flexible NDT&E. PMID:27158061

Determination of the mass transfer limiting step of dye adsorption onto commercial adsorbent by using mathematical models.

PubMed

Marin, Pricila; Borba, Carlos Eduardo; Módenes, Aparecido Nivaldo; Espinoza-Quiñones, Fernando R; de Oliveira, Silvia Priscila Dias; Kroumov, Alexander Dimitrov

2014-01-01

Reactive blue 5G dye removal in a fixed-bed column packed with Dowex Optipore SD-2 adsorbent was modelled. Three mathematical models were tested in order to determine the limiting step of the mass transfer of the dye adsorption process onto the adsorbent. The mass transfer resistance was considered to be a criterion for the determination of the difference between models. The models contained information about the external, internal, or surface adsorption limiting step. In the model development procedure, two hypotheses were applied to describe the internal mass transfer resistance. First, the mass transfer coefficient constant was considered. Second, the mass transfer coefficient was considered as a function of the dye concentration in the adsorbent. The experimental breakthrough curves were obtained for different particle diameters of the adsorbent, flow rates, and feed dye concentrations in order to evaluate the predictive power of the models. The values of the mass transfer parameters of the mathematical models were estimated by using the downhill simplex optimization method. The results showed that the model that considered internal resistance with a variable mass transfer coefficient was more flexible than the other ones and this model described the dynamics of the adsorption process of the dye in the fixed-bed column better. Hence, this model can be used for optimization and column design purposes for the investigated systems and similar ones.

Mental Mathematics, Emergence of Strategies, and the Enactivist Theory of Cognition

ERIC Educational Resources Information Center

Proulx, Jérôme

2013-01-01

In this article, I present and build on the ideas of John Threlfall ("Educational Studies in Mathematics" 50:29-47, 2002) about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition,…

Active vibration suppression of self-excited structures using an adaptive LMS algorithm

NASA Astrophysics Data System (ADS)

Danda Roy, Indranil

The purpose of this investigation is to study the feasibility of an adaptive feedforward controller for active flutter suppression in representative linear wing models. The ability of the controller to suppress limit-cycle oscillations in wing models having root springs with freeplay nonlinearities has also been studied. For the purposes of numerical simulation, mathematical models of a rigid and a flexible wing structure have been developed. The rigid wing model is represented by a simple three-degree-of-freedom airfoil while the flexible wing is modelled by a multi-degree-of-freedom finite element representation with beam elements for bending and rod elements for torsion. Control action is provided by one or more flaps attached to the trailing edge and extending along the entire wing span for the rigid model and a fraction of the wing span for the flexible model. Both two-dimensional quasi-steady aerodynamics and time-domain unsteady aerodynamics have been used to generate the airforces in the wing models. An adaptive feedforward controller has been designed based on the filtered-X Least Mean Squares (LMS) algorithm. The control configuration for the rigid wing model is single-input single-output (SISO) while both SISO and multi-input multi-output (MIMO) configurations have been applied on the flexible wing model. The controller includes an on-line adaptive system identification scheme which provides the LMS controller with a reasonably accurate model of the plant. This enables the adaptive controller to track time-varying parameters in the plant and provide effective control. The wing models in closed-loop exhibit highly damped responses at airspeeds where the open-loop responses are destructive. Simulations with the rigid and the flexible wing models in a time-varying airstream show a 63% and 53% increase, respectively, over their corresponding open-loop flutter airspeeds. The ability of the LMS controller to suppress wing store flutter in the two models has also been investigated. With 10% measurement noise introduced in the flexible wing model, the controller demonstrated good robustness to the extraneous disturbances. In the examples studied it is found that adaptation is rapid enough to successfully control flutter at accelerations in the airstream of up to 15 ft/sec2 for the rigid wing model and 9 ft/sec2 for the flexible wing model.

PharmML in Action: an Interoperable Language for Modeling and Simulation.

PubMed

Bizzotto, R; Comets, E; Smith, G; Yvon, F; Kristensen, N R; Swat, M J

2017-10-01

PharmML is an XML-based exchange format created with a focus on nonlinear mixed-effect (NLME) models used in pharmacometrics, but providing a very general framework that also allows describing mathematical and statistical models such as single-subject or nonlinear and multivariate regression models. This tutorial provides an overview of the structure of this language, brief suggestions on how to work with it, and use cases demonstrating its power and flexibility. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.

Chang'E-3 data pre-processing system based on scientific workflow

NASA Astrophysics Data System (ADS)

tan, xu; liu, jianjun; wang, yuanyuan; yan, wei; zhang, xiaoxia; li, chunlai

2016-04-01

The Chang'E-3(CE3) mission have obtained a huge amount of lunar scientific data. Data pre-processing is an important segment of CE3 ground research and application system. With a dramatic increase in the demand of data research and application, Chang'E-3 data pre-processing system(CEDPS) based on scientific workflow is proposed for the purpose of making scientists more flexible and productive by automating data-driven. The system should allow the planning, conduct and control of the data processing procedure with the following possibilities: • describe a data processing task, include:1)define input data/output data, 2)define the data relationship, 3)define the sequence of tasks,4)define the communication between tasks,5)define mathematical formula, 6)define the relationship between task and data. • automatic processing of tasks. Accordingly, Describing a task is the key point whether the system is flexible. We design a workflow designer which is a visual environment for capturing processes as workflows, the three-level model for the workflow designer is discussed:1) The data relationship is established through product tree.2)The process model is constructed based on directed acyclic graph(DAG). Especially, a set of process workflow constructs, including Sequence, Loop, Merge, Fork are compositional one with another.3)To reduce the modeling complexity of the mathematical formulas using DAG, semantic modeling based on MathML is approached. On top of that, we will present how processed the CE3 data with CEDPS.

A flexible tool for hydraulic and water quality performance analysis of green infrastructure

NASA Astrophysics Data System (ADS)

Massoudieh, A.; Alikhani, J.

2017-12-01

Models that allow for design considerations of green infrastructure (GI) practices to control stormwater runoff and associated contaminants have received considerable attention in recent years. To be used to evaluate the effect design configurations on the long-term performance of GIs, models should be able to consider processes within GIs with good fidelity. In this presentation, a sophisticated, yet flexible tool for hydraulic and water quality assessment of GIs will be introduced. The tool can be used by design engineers and researchers to capture and explore the effect of design factors and properties of the media employed in the performance of GI systems at a relatively small scale. We deemed it essential to have a flexible GI modeling tool that is capable of simulating GI system components and specific biogeochemical processes affecting contaminants such as evapotranspiration, plant uptake, reactions, and particle-associated transport accurately while maintaining a high degree of flexibility to account for the myriad of GI alternatives. The mathematical framework for a stand-alone GI performance assessment tool has been developed and will be demonstrated. The process-based model framework developed here can be used to model a diverse range of GI practices such as stormwater ponds, green roofs, retention ponds, bioretention systems, infiltration trench, permeable pavement and other custom-designed combinatory systems. An example of the application of the system to evaluate the performance of a rain-garden system will be demonstrated.

Creativity of Field-dependent and Field-independent Students in Posing Mathematical Problems

NASA Astrophysics Data System (ADS)

Azlina, N.; Amin, S. M.; Lukito, A.

2018-01-01

This study aims at describing the creativity of elementary school students with different cognitive styles in mathematical problem-posing. The posed problems were assessed based on three components of creativity, namely fluency, flexibility, and novelty. The free-type problem posing was used in this study. This study is a descriptive research with qualitative approach. Data collections were conducted through written task and task-based interviews. The subjects were two elementary students. One of them is Field Dependent (FD) and the other is Field Independent (FI) which were measured by GEFT (Group Embedded Figures Test). Further, the data were analyzed based on creativity components. The results show thatFD student’s posed problems have fulfilled the two components of creativity namely fluency, in which the subject posed at least 3 mathematical problems, and flexibility, in whichthe subject posed problems with at least 3 different categories/ideas. Meanwhile,FI student’s posed problems have fulfilled all three components of creativity, namely fluency, in which thesubject posed at least 3 mathematical problems, flexibility, in which thesubject posed problems with at least 3 different categories/ideas, and novelty, in which the subject posed problems that are purely the result of her own ideas and different from problems they have known.

Making Sense of Math: How to Help Every Student become a Mathematical Thinker and Problem Solver (ASCD Arias)

ERIC Educational Resources Information Center

Seeley, Cathy L.

2016-01-01

In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…

A Case Study Using CRA to Teach Students with Disabilities to Count Using Flexible Numbers: Applying Skip Counting to Multiplication

ERIC Educational Resources Information Center

Gibbs, Anna S.; Hinton, Vanessa M.; Flores, Margaret M.

2018-01-01

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

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.

A case study of cost-efficient staffing under annualized hours.

PubMed

van der Veen, Egbert; Hans, Erwin W; Veltman, Bart; Berrevoets, Leo M; Berden, Hubert J J M

2015-09-01

We propose a mathematical programming formulation that incorporates annualized hours and shows to be very flexible with regard to modeling various contract types. The objective of our model is to minimize salary cost, thereby covering workforce demand, and using annualized hours. Our model is able to address various business questions regarding tactical workforce planning problems, e.g., with regard to annualized hours, subcontracting, and vacation planning. In a case study for a Dutch hospital two of these business questions are addressed, and we demonstrate that applying annualized hours potentially saves up to 5.2% in personnel wages annually.

Acoustoelasticity

NASA Technical Reports Server (NTRS)

Dowell, E. H.

1976-01-01

Internal sound fields are considered. Specifically, the interaction between the (acoustic) sound pressure field and the (elastic) flexible wall of an enclosure is discussed. Such problems frequently arise when the vibrating walls of a transportation vehicle induce a significant internal sound field. Cabin noise in various flight vehicles and the internal sound field in an automobile are representative examples. A mathematical model, simplified solutions, and numerical results and comparisons with representative experimental data are briefly considered. An overall conclusion is that reasonable grounds for optimism exist with respect to available theoretical models and their predictive capability.

RT-18: Value of Flexibility. Phase 1

DTIC Science & Technology

2010-09-25

an analytical framework based on sound mathematical constructs. A review of the current state-of-the-art showed that there is little unifying theory...framework that is mathematically consistent, domain independent and applicable under varying information levels. This report presents our advances in...During this period, we also explored the development of an analytical framework based on sound mathematical constructs. A review of the current state

Promoting middle school students’ mathematical creative thinking ability using scientific approach

NASA Astrophysics Data System (ADS)

Istiqomah, A.; Perbowo, K. S.; Purwanto, S. E.

2018-01-01

This research aims to identify the strength of scientific approach in order to develop mathematical creative thinking in junior high school. Descriptive qualitative method is used in this research. 34 students in 7th grade are chosen using purposive sampling. For collecting data, this research uses test, observation, and interview. The test consists of 6 items which have been tested for their validity and reliability and used in pre-test and post-test. The pre-test shows that students average score in mathematical creative thinking is 43 (low), while in post-test it is 69 (middle). The N-gain in mathematical creative thinking point is 0.461, which is classified in the middle grade. Furthermore, the N-gain for each indicator, they score 0.438 for fluency; 0.568 for flexibility; and 0.382 for novelty. The N-gain for those indicators falls under middle grade. The research shows that scientific approach develops more flexibility, and, on the other hand, it develops less novelty.

Dynamic Fuzzy Model Development for a Drum-type Boiler-turbine Plant Through GK Clustering

NASA Astrophysics Data System (ADS)

Habbi, Ahcène; Zelmat, Mimoun

2008-10-01

This paper discusses a TS fuzzy model identification method for an industrial drum-type boiler plant using the GK fuzzy clustering approach. The fuzzy model is constructed from a set of input-output data that covers a wide operating range of the physical plant. The reference data is generated using a complex first-principle-based mathematical model that describes the key dynamical properties of the boiler-turbine dynamics. The proposed fuzzy model is derived by means of fuzzy clustering method with particular attention on structure flexibility and model interpretability issues. This may provide a basement of a new way to design model based control and diagnosis mechanisms for the complex nonlinear plant.

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

NASA Technical Reports Server (NTRS)

Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.

1971-01-01

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

A Flexible framework for forward and inverse modeling of stormwater control measures

NASA Astrophysics Data System (ADS)

Aflaki, S.; Massoudieh, A.

2016-12-01

Models that allow for design considerations of green infrastructure (GI) practices to control stormwater runoff and associated contaminants have received considerable attention in recent years. While popular, generally, the GI models are relatively simplistic. However, GI model predictions are being relied upon by many municipalities and State/Local agencies to make decisions about grey vs. green infrastructure improvement planning. Adding complexity to GI modeling frameworks may preclude their use in simpler urban planning situations. Therefore, the goal here was to develop a sophisticated, yet flexible tool that could be used by design engineers and researchers to capture and explore the effect of design factors and properties of the media used in the performance of GI systems at a relatively small scale. We deemed it essential to have a flexible GI modeling tool that is capable of simulating GI system components and specific biophysical processes affecting contaminants such as reactions, and particle-associated transport accurately while maintaining a high degree of flexibly to account for the myriad of GI alternatives. The mathematical framework for a stand-alone GI performance assessment tool has been developed and will be demonstrated. The process-based model framework developed here can be used to model a diverse range of GI practices such as green roof, retention pond, bioretention, infiltration trench, permeable pavement and other custom-designed combinatory systems. Four demonstration applications covering a diverse range of systems will be presented. The example applications include a evaluating hydraulic performance of a complex bioretention system, hydraulic analysis of porous pavement system, flow colloid-facilitated transport, reactive transport and groundwater recharge underneath an infiltration pond and finally reactive transport and bed-sediment interactions in a wetland system will be presented.

The brian simulator.

PubMed

Goodman, Dan F M; Brette, Romain

2009-09-01

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

A new pneumatic suspension system with independent stiffness and ride height tuning capabilities

NASA Astrophysics Data System (ADS)

Yin, Zhihong; Khajepour, Amir; Cao, Dongpu; Ebrahimi, Babak; Guo, Konghui

2012-12-01

This paper introduces a new pneumatic spring for vehicle suspension systems, allowing independent tuning of stiffness and ride height according to different vehicle operating conditions and driver preferences. The proposed pneumatic spring comprises a double-acting pneumatic cylinder, two accumulators and a tuning subsystem. This paper presents a detailed description of the pneumatic spring and its working principle. The mathematical model is established based on principles of thermo and fluid dynamics. An experimental setup has been designed and fabricated for testing and evaluating the proposed pneumatic spring. The analytical and experimental results confirm the capability of the new pneumatic spring system for independent tuning of stiffness and ride height. The mathematical model is verified and the capabilities of the pneumatic spring are further proved. It is concluded that this new pneumatic spring provides a more flexible suspension design alternative for meeting various conflicting suspension requirements for ride comfort and performance.

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.

Large Deformation of an Elastic Rod with Structural Anisotropy Subjected to Fluid Flow

NASA Astrophysics Data System (ADS)

Hassani, Masoud; Mureithi, Njuki; Gosselin, Frederick

2015-11-01

In the present work, we seek to understand the fundamental mechanisms of three-dimensional reconfiguration of plants by studying the large deformation of a flexible rod in fluid flow. Flexible rods made of Polyurethane foam and reinforced with Nylon fibers are tested in a wind tunnel. The rods have bending-torsion coupling which induces a torsional deformation during asymmetric bending. A mathematical model is also developed by coupling the Kirchhoff rod theory with a semi-empirical drag formulation. Different alignments of the material frame with respect to the flow direction and a range of structural properties are considered to study their effect on the deformation of the flexible rod and its drag scaling. Results show that twisting causes the flexible rods to reorient and bend with the minimum bending rigidity. It is also found that the drag scaling of the rod in the large deformation regime is not affected by torsion. Finally, using a proper set of dimensionless numbers, the state of a bending and twisting rod is characterized as a beam undergoing a pure bending deformation.

A Flexible, Extensible Online Testing System for Mathematics

ERIC Educational Resources Information Center

Passmore, Tim; Brookshaw, Leigh; Butler, Harry

2011-01-01

An online testing system developed for entry-skills testing of first-year university students in algebra and calculus is described. The system combines the open-source computer algebra system "Maxima" with computer scripts to parse student answers, which are entered using standard mathematical notation and conventions. The answers can…

Learning about the Benetic Code via Programming: Representing the Process of Translation.

ERIC Educational Resources Information Center

Ploger, Don

1991-01-01

This study examined the representations that a 16-year-old student made using the flexible computer system, "Boxer," in learning the genetic code. Results indicated that programing made it easier to build and explore flexible and useful representations and encouraged interdisciplinary collaboration between mathematics and biology…

Computer Programs For Automated Welding System

NASA Technical Reports Server (NTRS)

Agapakis, John E.

1993-01-01

Computer programs developed for use in controlling automated welding system described in MFS-28578. Together with control computer, computer input and output devices and control sensors and actuators, provide flexible capability for planning and implementation of schemes for automated welding of specific workpieces. Developed according to macro- and task-level programming schemes, which increases productivity and consistency by reducing amount of "teaching" of system by technician. System provides for three-dimensional mathematical modeling of workpieces, work cells, robots, and positioners.

Flexibility of Bricard's linkages and other structures via resultants and computer algebra.

PubMed

Lewis, Robert H; Coutsias, Evangelos A

2016-07-01

Flexibility of structures is extremely important for chemistry and robotics. Following our earlier work, we study flexibility using polynomial equations, resultants, and a symbolic algorithm of our creation that analyzes the resultant. We show that the software solves a classic arrangement of quadrilaterals in the plane due to Bricard. We fill in several gaps in Bricard's work and discover new flexible arrangements that he was apparently unaware of. This provides strong evidence for the maturity of the software, and is a wonderful example of mathematical discovery via computer assisted experiment.

Investigation of a vibration-damping unit for reduction in low-frequency vibrations of electric motors

NASA Technical Reports Server (NTRS)

Grigoryey, N. V.; Fedorovich, M. A.

1973-01-01

The vibroacoustical characteristics of different types of electric motors are discussed. It is shown that the basic source of low frequency vibrations is rotor unbalance. A flexible damping support, with an antivibrator, is used to obtain the vibroacoustical effect of reduction in the basic harmonic of the electric motor. A model of the electric motor and the damping apparatus is presented. Mathematical models are developed to show the relationships of the parameters. The basic purpose in using a calculation model id the simultaneous replacement of the exciting force created by the rotor unbalance and its inertial rigidity characteristics by a limiting kinematic disturbance.

Hybrid computational phantoms representing the reference adult male and adult female: construction and applications for retrospective dosimetry.

PubMed

Hurtado, Jorge L; Lee, Choonsik; Lodwick, Daniel; Goede, Timothy; Williams, Jonathan L; Bolch, Wesley E

2012-03-01

Currently, two classes of computational phantoms have been developed for dosimetry calculation: (1) stylized (or mathematical) and (2) voxel (or tomographic) phantoms describing human anatomy through mathematical surface equations and 3D voxel matrices, respectively. Mathematical surface equations in stylized phantoms are flexible, but the resulting anatomy is not as realistic. Voxel phantoms display far better anatomical realism, but they are limited in terms of their ability to alter organ shape, position, and depth, as well as body posture. A new class of computational phantoms called hybrid phantoms takes advantage of the best features of stylized and voxel phantoms-flexibility and anatomical realism, respectively. In the current study, hybrid computational phantoms representing the adult male and female reference anatomy and anthropometry are presented. These phantoms serve as the starting framework for creating patient or worker sculpted whole-body phantoms for retrospective dose reconstruction. Contours of major organs and tissues were converted or segmented from computed tomography images of a 36-y-old Korean volunteer and a 25-y-old U.S. female patient, respectively, with supplemental high-resolution CT images of the cranium. Polygon mesh models for the major organs and tissues were reconstructed and imported into Rhinoceros™ for non-uniform rational B-spline (NURBS) surface modeling. The resulting NURBS/polygon mesh models representing body contour and internal anatomy were matched to anthropometric data and reference organ mass data provided by Centers for Disease Control and Prevention and International Commission on Radiation Protection, respectively. Finally, two hybrid adult male and female phantoms were completed where a total of eight anthropometric data categories were matched to standard values within 4% and organ volumes matched to ICRP data within 1% with the exception of total skin. The hybrid phantoms were voxelized from the NURBS phantoms at resolutions of 0.158 × 0.158 × 0.158 cm and 0.126 × 0.126 × 0.126 cm for the male and female, respectively. To highlight the flexibility of the hybrid phantoms, graphical displays are given of (1) underweight and overweight adult male phantoms, (2) a sitting position for the adult female phantom, and (3) extraction and higher-resolution voxelization of the small intestine for localized dosimetry of mucosal and stem cell layers. These phantoms are used to model radioactively contaminated individuals and to then assess time-dependent detector count rate thresholds corresponding to 50, 250, and 500 mSv effective dose, as might be needed during in-field radiological triage by first responders or first receivers.

Intelligent modelling of bioprocesses: a comparison of structured and unstructured approaches.

PubMed

Hodgson, Benjamin J; Taylor, Christopher N; Ushio, Misti; Leigh, J R; Kalganova, Tatiana; Baganz, Frank

2004-12-01

This contribution moves in the direction of answering some general questions about the most effective and useful ways of modelling bioprocesses. We investigate the characteristics of models that are good at extrapolating. We trained three fully predictive models with different representational structures (differential equations, differential equations with inheritance of rates and a network of reactions) on Saccharopolyspora erythraea shake flask fermentation data using genetic programming. The models were then tested on unseen data outside the range of the training data and the resulting performances were compared. It was found that constrained models with mathematical forms analogous to internal mass balancing and stoichiometric relations were superior to flexible unconstrained models, even though no a priori knowledge of this fermentation was used.

Hot-bench simulation of the active flexible wing wind-tunnel model

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.; Houck, Jacob A.

1990-01-01

Two simulations, one batch and one real-time, of an aeroelastically-scaled wind-tunnel model were developed. The wind-tunnel model was a full-span, free-to-roll model of an advanced fighter concept. The batch simulation was used to generate and verify the real-time simulation and to test candidate control laws prior to implementation. The real-time simulation supported hot-bench testing of a digital controller, which was developed to actively control the elastic deformation of the wind-tunnel model. Time scaling was required for hot-bench testing. The wind-tunnel model, the mathematical models for the simulations, the techniques employed to reduce the hot-bench time-scale factors, and the verification procedures are described.

A systemic approach to explore the flexibility of energy stores at the cellular scale: Examples from muscle cells.

PubMed

Taghipoor, Masoomeh; van Milgen, Jaap; Gondret, Florence

2016-09-07

Variations in energy storage and expenditure are key elements for animals adaptation to rapidly changing environments. Because of the multiplicity of metabolic pathways, metabolic crossroads and interactions between anabolic and catabolic processes within and between different cells, the flexibility of energy stores in animal cells is difficult to describe by simple verbal, textual or graphic terms. We propose a mathematical model to study the influence of internal and external challenges on the dynamic behavior of energy stores and its consequence on cell energy status. The role of the flexibility of energy stores on the energy equilibrium at the cellular level is illustrated through three case studies: variation in eating frequency (i.e., glucose input), level of physical activity (i.e., ATP requirement), and changes in cell characteristics (i.e., maximum capacity of glycogen storage). Sensitivity analysis has been performed to highlight the most relevant parameters of the model; model simulations have then been performed to illustrate how variation in these key parameters affects cellular energy balance. According to this analysis, glycogen maximum accumulation capacity and homeostatic energy demand are among the most important parameters regulating muscle cell metabolism to ensure its energy equilibrium. Copyright © 2016 Elsevier Ltd. All rights reserved.

Power processing methodology. [computerized design of spacecraft electric power systems

NASA Technical Reports Server (NTRS)

Fegley, K. A.; Hansen, I. G.; Hayden, J. H.

1974-01-01

Discussion of the interim results of a program to investigate the feasibility of formulating a methodology for the modeling and analysis of aerospace electrical power processing systems. The object of the total program is to develop a flexible engineering tool which will allow the power processor designer to effectively and rapidly assess and analyze the tradeoffs available by providing, in one comprehensive program, a mathematical model, an analysis of expected performance, simulation, and a comparative evaluation with alternative designs. This requires an understanding of electrical power source characteristics and the effects of load control, protection, and total system interaction.

Implementing a Game for Supporting Learning in Mathematics

ERIC Educational Resources Information Center

Katmada, Aikaterini; Mavridis, Apostolos; Tsiatsos, Thrasyvoulos

2014-01-01

This paper focuses on the design, implementation and evaluation of an online game for elementary and middle school mathematics. Its aim is twofold: (a) the development of the prototype of a flexible and adaptable computer game, and (b) the evaluation of this prototype, as to its usability and technical aspects. The particular computer game was…

Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword

ERIC Educational Resources Information Center

Begolli, Kreshnik Nasi; Richland, Lindsey Engle

2016-01-01

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

Design of a Prototype Mobile Application to Make Mathematics Education More Realistic

ERIC Educational Resources Information Center

Jordaan, Dawid B.; Laubscher, Dorothy J.; Blignaut, A. Seugnet

2017-01-01

To enter the world of work, students require skills which include flexibility, critical thinking, problem solving, collaboration and communication. The use of mobile technologies which are specifically created for a context could stimulate motivation in students to recognise the relevance of Mathematics in the real world. South Africa in…

Generalized Full-Information Item Bifactor Analysis

PubMed Central

Cai, Li; Yang, Ji Seung; Hansen, Mark

2011-01-01

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than one group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker’s (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood only requires two-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy. PMID:21534682

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.

Modeling and analysis of pinhole occulter experiment: Initial study phase

NASA Technical Reports Server (NTRS)

Vandervoort, R. J.

1985-01-01

The feasibility of using a generic simulation, TREETOPS, to simulate the Pinhole/Occulter Facility (P/OF) to be tested on the space shuttle was demonstrated. The baseline control system was used to determine the pointing performance of the P/OF. The task included modeling the structure as a three body problem (shuttle-instrument pointing system- P/OP) including the flexibility of the 32 meter P/OF boom. Modeling of sensors, actuators, and control algorithms was also required. Detailed mathematical models for the structure, sensors, and actuators are presented, as well as the control algorithm and corresponding design procedure. Closed loop performance using this controller and computer listings for the simulator are also given.

FLBEIA : A simulation model to conduct Bio-Economic evaluation of fisheries management strategies

NASA Astrophysics Data System (ADS)

Garcia, Dorleta; Sánchez, Sonia; Prellezo, Raúl; Urtizberea, Agurtzane; Andrés, Marga

Fishery systems are complex systems that need to be managed in order to ensure a sustainable and efficient exploitation of marine resources. Traditionally, fisheries management has relied on biological models. However, in recent years the focus on mathematical models which incorporate economic and social aspects has increased. Here, we present FLBEIA, a flexible software to conduct bio-economic evaluation of fisheries management strategies. The model is multi-stock, multi-fleet, stochastic and seasonal. The fishery system is described as a sum of processes, which are internally assembled in a predetermined way. There are several functions available to describe the dynamic of each process and new functions can be added to satisfy specific requirements.

The Brian Simulator

PubMed Central

Goodman, Dan F. M.; Brette, Romain

2009-01-01

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

The mathematics of a successful deconvolution: a quantitative assessment of mixture-based combinatorial libraries screened against two formylpeptide receptors.

PubMed

Santos, Radleigh G; Appel, Jon R; Giulianotti, Marc A; Edwards, Bruce S; Sklar, Larry A; Houghten, Richard A; Pinilla, Clemencia

2013-05-30

In the past 20 years, synthetic combinatorial methods have fundamentally advanced the ability to synthesize and screen large numbers of compounds for drug discovery and basic research. Mixture-based libraries and positional scanning deconvolution combine two approaches for the rapid identification of specific scaffolds and active ligands. Here we present a quantitative assessment of the screening of 32 positional scanning libraries in the identification of highly specific and selective ligands for two formylpeptide receptors. We also compare and contrast two mixture-based library approaches using a mathematical model to facilitate the selection of active scaffolds and libraries to be pursued for further evaluation. The flexibility demonstrated in the differently formatted mixture-based libraries allows for their screening in a wide range of assays.

The Layer-Oriented Approach to Declarative Languages for Biological Modeling

PubMed Central

Raikov, Ivan; De Schutter, Erik

2012-01-01

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

The layer-oriented approach to declarative languages for biological modeling.

PubMed

Raikov, Ivan; De Schutter, Erik

2012-01-01

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

Measurement of irregularities in angular velocities of rotating assemblies in memory devices on magnetic carriers

NASA Technical Reports Server (NTRS)

Virakas, G. I.; Matsyulevichyus, R. A.; Minkevichyus, K. P.; Potsyus, Z. Y.; Shirvinskas, B. D.

1973-01-01

Problems in measurement of irregularities in angular velocity of rotating assemblies in memory devices with rigid and flexible magnetic data carriers are discussed. A device and method for determination of change in angular velocities in various frequency and rotation rate ranges are examined. A schematic diagram of a photoelectric sensor for recording the signal pulses is provided. Mathematical models are developed to show the amount of error which can result from misalignment of the test equipment.

Efficiency of geometric designs of flexible solar panels: mathematical simulation

NASA Astrophysics Data System (ADS)

Marciniak, Malgorzata; Hassebo, Yasser; Enriquez-Torres, Delfino; Serey-Roman, Maria Ignacia

2017-09-01

The purpose of this study is to analyze various surfaces of flexible solar panels and compare them to the traditional at panels mathematically. We evaluated the efficiency based on the integral formulas that involve flux. We performed calculations for flat panels with different positions, a cylindrical panel, conical panels with various opening angles and segments of a spherical panel. Our results indicate that the best efficiency per unit area belongs to particular segments of spherically-shaped panels. In addition, we calculated the optimal opening angle of a cone-shaped panel that maximizes the annual accumulation of the sun radiation per unit area. The considered shapes are presented below with a suggestion for connections of the cells.

Simultaneous prediction of binding free energy and specificity for PDZ domain-peptide interactions

NASA Astrophysics Data System (ADS)

Crivelli, Joseph J.; Lemmon, Gordon; Kaufmann, Kristian W.; Meiler, Jens

2013-12-01

Interactions between protein domains and linear peptides underlie many biological processes. Among these interactions, the recognition of C-terminal peptides by PDZ domains is one of the most ubiquitous. In this work, we present a mathematical model for PDZ domain-peptide interactions capable of predicting both affinity and specificity of binding based on X-ray crystal structures and comparative modeling with R osetta. We developed our mathematical model using a large phage display dataset describing binding specificity for a wild type PDZ domain and 91 single mutants, as well as binding affinity data for a wild type PDZ domain binding to 28 different peptides. Structural refinement was carried out through several R osetta protocols, the most accurate of which included flexible peptide docking and several iterations of side chain repacking and backbone minimization. Our findings emphasize the importance of backbone flexibility and the energetic contributions of side chain-side chain hydrogen bonds in accurately predicting interactions. We also determined that predicting PDZ domain-peptide interactions became increasingly challenging as the length of the peptide increased in the N-terminal direction. In the training dataset, predicted binding energies correlated with those derived through calorimetry and specificity switches introduced through single mutations at interface positions were recapitulated. In independent tests, our best performing protocol was capable of predicting dissociation constants well within one order of magnitude of the experimental values and specificity profiles at the level of accuracy of previous studies. To our knowledge, this approach represents the first integrated protocol for predicting both affinity and specificity for PDZ domain-peptide interactions.

The stationary flow in a heterogeneous compliant vessel network

NASA Astrophysics Data System (ADS)

Filoche, Marcel; Florens, Magali

2011-09-01

We introduce a mathematical model of the hydrodynamic transport into systems consisting in a network of connected flexible pipes. In each pipe of the network, the flow is assumed to be steady and one-dimensional. The fluid-structure interaction is described through tube laws which relate the pipe diameter to the pressure difference across the pipe wall. We show that the resulting one-dimensional differential equation describing the flow in the pipe can be exactly integrated if one is able to estimate averages of the Reynolds number along the pipe. The differential equation is then transformed into a non linear scalar equation relating pressures at both ends of the pipe and the flow rate in the pipe. These equations are coupled throughout the network with mass conservation equations for the flow and zero pressure losses at the branching points of the network. This allows us to derive a general model for the computation of the flow into very large inhomogeneous networks consisting of several thousands of flexible pipes. This model is then applied to perform numerical simulations of the human lung airway system at exhalation. The topology of the system and the tube laws are taken from morphometric and physiological data in the literature. We find good qualitative and quantitative agreement between the simulation results and flow-volume loops measured in real patients. In particular, expiratory flow limitation which is an essential characteristic of forced expiration is found to be well reproduced by our simulations. Finally, a mathematical model of a pathology (Chronic Obstructive Pulmonary Disease) is introduced which allows us to quantitatively assess the influence of a moderate or severe alteration of the airway compliances.

The Effects of Group Monitoring on Fatigue-Related Einstellung during Mathematical Problem Solving

ERIC Educational Resources Information Center

Frings, Daniel

2011-01-01

Fatigue resulting from sleep deficit can lead to decreased performance in a variety of cognitive domains and can result in potentially serious accidents. The present study aimed to test whether fatigue leads to increased Einstellung (low levels of cognitive flexibility) in a series of mathematical problem-solving tasks. Many situations involving…

eWorkbooks for Mathematics: Mapping the Independent Learning Experiences of Elementary Students with Learning Disabilities

ERIC Educational Resources Information Center

Kaczorowski, Tara; Raimondi, Sharon

2014-01-01

In this paper, we describe a small case study exploring how four elementary students with mathematics learning disabilities utilized mobile technology (the eWorkbook) during core math instruction in a general education setting. The lead author designed the eWorkbook intervention to provide a flexible learning experience optimized for diverse…

Characterizing the Use of Mathematical Knowledge in Boundary-Crossing Situations at Work

ERIC Educational Resources Information Center

Kent, Phillip; Noss, Richard; Guile, David; Hoyles, Celia; Bakker, Arthur

2007-01-01

The first aim of this article is to present a characterization of the techno-mathematical literacies needed for effective practice in modern, technology-rich workplaces that are both highly automated and increasingly focused on flexible response to customer needs. The second aim is to introduce an epistemological dimension to activity theory,…

Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

PubMed

Adamson, M W; Morozov, A Y; Kuzenkov, O A

2016-09-01

Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.

System analysis through bond graph modeling

NASA Astrophysics Data System (ADS)

McBride, Robert Thomas

2005-07-01

Modeling and simulation form an integral role in the engineering design process. An accurate mathematical description of a system provides the design engineer the flexibility to perform trade studies quickly and accurately to expedite the design process. Most often, the mathematical model of the system contains components of different engineering disciplines. A modeling methodology that can handle these types of systems might be used in an indirect fashion to extract added information from the model. This research examines the ability of a modeling methodology to provide added insight into system analysis and design. The modeling methodology used is bond graph modeling. An investigation into the creation of a bond graph model using the Lagrangian of the system is provided. Upon creation of the bond graph, system analysis is performed. To aid in the system analysis, an object-oriented approach to bond graph modeling is introduced. A framework is provided to simulate the bond graph directly. Through object-oriented simulation of a bond graph, the information contained within the bond graph can be exploited to create a measurement of system efficiency. A definition of system efficiency is given. This measurement of efficiency is used in the design of different controllers of varying architectures. Optimal control of a missile autopilot is discussed within the framework of the calculated system efficiency.

Mathematical simulation of efficiency of various shapes of solar panels for NASA geostationary satellites

NASA Astrophysics Data System (ADS)

Pandya, Raaghav; Raja, Hammad; Enriquez-Torres, Delfino; Serey-Roman, Maria Ignacia; Hassebo, Yasser; Marciniak, Małgorzata

2018-02-01

The purpose of this research is to analyze mathematically cylindrical shapes of flexible solar panels and compare their efficiency to the flat panels. The efficiency is defined to be the flux density, which is the ratio of the mathematical flux and the surface area. In addition we describe the trajectory of the Sun at specific locations: the North Pole, The Equator and a geostationary satellite above the Equator. The calculations were performed with software: Maple, Mathematica, and MATLAB.

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

NASA Astrophysics Data System (ADS)

Brown, Michelle Cetner

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

The systems biology simulation core algorithm

PubMed Central

2013-01-01

Background With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases. Results This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database. Conclusions The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net. PMID:23826941

Mathematical modeling and simulation of aquatic and aerial animal locomotion

NASA Astrophysics Data System (ADS)

Hou, T. Y.; Stredie, V. G.; Wu, T. Y.

2007-08-01

In this paper, we investigate the locomotion of fish and birds by applying a new unsteady, flexible wing theory that takes into account the strong nonlinear dynamics semi-analytically. We also make extensive comparative study between the new approach and the modified vortex blob method inspired from Chorin's and Krasny's work. We first implement the modified vortex blob method for two examples and then discuss the numerical implementation of the nonlinear analytical mathematical model of Wu. We will demonstrate that Wu's method can capture the nonlinear effects very well by applying it to some specific cases and by comparing with the experiments available. In particular, we apply Wu's method to analyze Wagner's result for a wing abruptly undergoing an increase in incidence angle. Moreover, we study the vorticity generated by a wing in heaving, pitching and bending motion. In both cases, we show that the new method can accurately represent the vortex structure behind a flying wing and its influence on the bound vortex sheet on the wing.

HELIOGate, a Portal for the Heliophysics Community

NASA Astrophysics Data System (ADS)

Pierantoni; Gabriele; Carley, Eoin

2014-10-01

Heliophysics is the branch of physics that investigates the interactions between the Sun and the other bodies of the solar system. Heliophysicists rely on data collected from numerous sources scattered across the Solar System. The data collected from these sources is processed to extract metadata and the metadata extracted in this fashion is then used to build indexes of features and events called catalogues. Heliophysicists also develop conceptual and mathematical models of the phenomena and the environment of the Solar System. More specifically, they investigate the physical characteristics of the phenomena and they simulate how they propagate throughout the Solar System with mathematical and physical abstractions called propagation models. HELIOGate aims at addressing the need to combine and orchestrate existing web services in a flexible and easily configurable fashion to tackle different scientific questions. HELIOGate also offers a tool capable of connecting to size! able computation and storage infrastructures to execute data processing codes that are needed to calibrate raw data and to extract metadata.

Robotics and neuroscience: a rhythmic interaction.

PubMed

Ronsse, Renaud; Lefèvre, Philippe; Sepulchre, Rodolphe

2008-05-01

At the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical modeling. The experiment is based on an impact juggling task, requiring the coordination of two upper-limb effectors and some phase-locking with the trajectories of one or several juggled objects. We describe the experiment, its implementation and the mathematical model used for the analysis. Our underlying research focuses on the role of sensory feedback in rhythmic tasks. In a robotic implementation of our experiment, we study the minimum feedback that is required to achieve robust control. A limited source of feedback, measuring only the impact times, is shown to give promising results. A second field of investigation concerns the human behavior in the same impact juggling task. We study how a variation of the tempo induces a transition between two distinct control strategies with different sensory feedback requirements. Analogies and differences between the robotic and human behaviors are obviously of high relevance in such a flexible setup.

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

Transient Cognitive Dynamics, Metastability, and Decision Making

PubMed Central

Rabinovich, Mikhail I.; Huerta, Ramón; Varona, Pablo; Afraimovich, Valentin S.

2008-01-01

The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. The main problem faced when using dynamical theory to describe transient cognitive processes is the fundamental contradiction between reproducibility and flexibility of transient behavior. In this paper, we propose a theoretical description of transient cognitive dynamics based on the interaction of functionally dependent metastable cognitive states. The mathematical image of such transient activity is a stable heteroclinic channel, i.e., a set of trajectories in the vicinity of a heteroclinic skeleton that consists of saddles and unstable separatrices that connect their surroundings. We suggest a basic mathematical model, a strongly dissipative dynamical system, and formulate the conditions for the robustness and reproducibility of cognitive transients that satisfy the competing requirements for stability and flexibility. Based on this approach, we describe here an effective solution for the problem of sequential decision making, represented as a fixed time game: a player takes sequential actions in a changing noisy environment so as to maximize a cumulative reward. As we predict and verify in computer simulations, noise plays an important role in optimizing the gain. PMID:18452000

Bifurcation and response analysis of a nonlinear flexible rotating disc immersed in bounded compressible fluid

NASA Astrophysics Data System (ADS)

Remigius, W. Dheelibun; Sarkar, Sunetra; Gupta, Sayan

2017-03-01

Use of heavy gases in centrifugal compressors for enhanced oil extraction have made the impellers susceptible to failures through acousto-elastic instabilities. This study focusses on understanding the dynamical behavior of such systems by considering the effects of the bounded fluid housed in a casing on a rotating disc. First, a mathematical model is developed that incorporates the interaction between the rotating impeller - modelled as a flexible disc - and the bounded compressible fluid medium in which it is immersed. The nonlinear effects arising due to large deformations of the disc have been included in the formulation so as to capture the post flutter behavior. A bifurcation analysis is carried out with the disc rotational speed as the bifurcation parameter to investigate the dynamical behavior of the coupled system and estimate the stability boundaries. Parametric studies reveal that the relative strengths of the various dissipation mechanisms in the coupled system play a significant role that affect the bifurcation route and the post flutter behavior in the acousto-elastic system.

A continuum model for dynamic analysis of the Space Station

NASA Technical Reports Server (NTRS)

Thomas, Segun

1989-01-01

Dynamic analysis of the International Space Station using MSC/NASTRAN had 1312 rod elements, 62 beam elements, 489 nodes and 1473 dynamic degrees of freedom. A realtime, man-in-the-loop simulation of such a model is impractical. This paper discusses the mathematical model for realtime dynamic simulation of the Space Station. Several key questions in structures and structural dynamics are addressed. First, to achieve a significant reduction in the number of dynamic degrees of freedom, a continuum equivalent representation of the Space Station truss structure which accounted for the unsymmetry of the basic configuration and resulted in the coupling of extensional and transverse deformation, is developed. Next, dynamic equations for the continuum equivalent of the Space Station truss structure are formulated using a matrix version of Kane's dynamical equations. Flexibility is accounted for by using a theory that accommodates extension, bending in two principal planes and shear displacement. Finally, constraint equations suitable for dynamic analysis of flexible bodies with closed loop configuration are developed and solution of the resulting system of equations is based on the zero eigenvalue theorem.

Enhancing student engagement to positively impact mathematics anxiety, confidence and achievement for interdisciplinary science subjects

NASA Astrophysics Data System (ADS)

Everingham, Yvette L.; Gyuris, Emma; Connolly, Sean R.

2017-11-01

Contemporary science educators must equip their students with the knowledge and practical know-how to connect multiple disciplines like mathematics, computing and the natural sciences to gain a richer and deeper understanding of a scientific problem. However, many biology and earth science students are prejudiced against mathematics due to negative emotions like high mathematical anxiety and low mathematical confidence. Here, we present a theoretical framework that investigates linkages between student engagement, mathematical anxiety, mathematical confidence, student achievement and subject mastery. We implement this framework in a large, first-year interdisciplinary science subject and monitor its impact over several years from 2010 to 2015. The implementation of the framework coincided with an easing of anxiety and enhanced confidence, as well as higher student satisfaction, retention and achievement. The framework offers interdisciplinary science educators greater flexibility and confidence in their approach to designing and delivering subjects that rely on mathematical concepts and practices.

The Mathematics of a Successful Deconvolution: A Quantitative Assessment of Mixture-Based Combinatorial Libraries Screened Against Two Formylpeptide Receptors

PubMed Central

Santos, Radleigh G.; Appel, Jon R.; Giulianotti, Marc A.; Edwards, Bruce S.; Sklar, Larry A.; Houghten, Richard A.; Pinilla, Clemencia

2014-01-01

In the past 20 years, synthetic combinatorial methods have fundamentally advanced the ability to synthesize and screen large numbers of compounds for drug discovery and basic research. Mixture-based libraries and positional scanning deconvolution combine two approaches for the rapid identification of specific scaffolds and active ligands. Here we present a quantitative assessment of the screening of 32 positional scanning libraries in the identification of highly specific and selective ligands for two formylpeptide receptors. We also compare and contrast two mixture-based library approaches using a mathematical model to facilitate the selection of active scaffolds and libraries to be pursued for further evaluation. The flexibility demonstrated in the differently formatted mixture-based libraries allows for their screening in a wide range of assays. PMID:23722730

High Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Lanteri, S.; Maman, N.; Piperno, S.; Gumaste, U.

1994-01-01

In order to predict the dynamic response of a flexible structure in a fluid flow, the equations of motion of the structure and the fluid must be solved simultaneously. In this paper, we present several partitioned procedures for time-integrating this focus coupled problem and discuss their merits in terms of accuracy, stability, heterogeneous computing, I/O transfers, subcycling, and parallel processing. All theoretical results are derived for a one-dimensional piston model problem with a compressible flow, because the complete three-dimensional aeroelastic problem is difficult to analyze mathematically. However, the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two-dimensional transient aeroelastic response of a flexible panel in a transonic nonlinear Euler flow regime.

Frost formation on an airfoil: A mathematical model 1

NASA Technical Reports Server (NTRS)

Dietenberger, M.; Kumar, P.; Luers, J.

1979-01-01

A computer model to predict the frost formation process on a flat plate was developed for application to most environmental conditions under which frost occurs. The model was analytically based on a generalized frost thermal conductivity expression, on frost density and thickness rate equations, and on modified heat and mass transfer coefficients designed to fit the available experimental data. The broad experimental ranges reflected by the extremes in ambient humidities, wall temperatures, and convective flow properties in the various publications which were examined served to severely test the flexibility of the model. An efficient numerical integration scheme was developed to solve for the frost surface temperature, density, and thickness under the changing environmental conditions. The comparison of results with experimental data was very encouraging.

Flexibility in Mathematics Problem Solving Based on Adversity Quotient

NASA Astrophysics Data System (ADS)

Dina, N. A.; Amin, S. M.; Masriyah

2018-01-01

Flexibility is an ability which is needed in problem solving. One of the ways in problem solving is influenced by Adversity Quotient (AQ). AQ is the power of facing difficulties. There are three categories of AQ namely climber, camper, and quitter. This research is a descriptive research using qualitative approach. The aim of this research is to describe flexibility in mathematics problem solving based on Adversity Quotient. The subjects of this research are climber student, camper student, and quitter student. This research was started by giving Adversity Response Profile (ARP) questioner continued by giving problem solving task and interviews. The validity of data measurement was using time triangulation. The results of this research shows that climber student uses two strategies in solving problem and doesn’t have difficulty. The camper student uses two strategies in solving problem but has difficulty to finish the second strategies. The quitter student uses one strategy in solving problem and has difficulty to finish it.

Foreign Military Sales Pricing Principles for Electronic Technical Manuals

DTIC Science & Technology

2004-06-01

companies provide benefits such as flexible hours, flexible days, and telecommuting . This information is useful because facilities costs and overhead can...personnel are listed below: Occupation Title Employment (1) Median Hourly Mean Hourly Mean Annual (2) Computer and Mathematical Science...be minimized or significantly reduced for companies providing this benefit . There was one disturbing statistic from this survey. Despite the

Robust Assignment Of Eigensystems For Flexible Structures

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Lim, Kyong B.; Junkins, John L.

1992-01-01

Improved method for placement of eigenvalues and eigenvectors of closed-loop control system by use of either state or output feedback. Applied to reduced-order finite-element mathematical model of NASA's MAST truss beam structure. Model represents deployer/retractor assembly, inertial properties of Space Shuttle, and rigid platforms for allocation of sensors and actuators. Algorithm formulated in real arithmetic for efficient implementation. Choice of open-loop eigenvector matrix and its closest unitary matrix believed suitable for generating well-conditioned eigensystem with small control gains. Implication of this approach is that element of iterative search for "optimal" unitary matrix appears unnecessary in practice for many test problems.

Quantitative Finance

NASA Astrophysics Data System (ADS)

James, Jessica

2017-01-01

Quantitative finance is a field that has risen to prominence over the last few decades. It encompasses the complex models and calculations that value financial contracts, particularly those which reference events in the future, and apply probabilities to these events. While adding greatly to the flexibility of the market available to corporations and investors, it has also been blamed for worsening the impact of financial crises. But what exactly does quantitative finance encompass, and where did these ideas and models originate? We show that the mathematics behind finance and behind games of chance have tracked each other closely over the centuries and that many well-known physicists and mathematicians have contributed to the field.

Historical mathematics in the French eighteenth century.

PubMed

Richards, Joan L

2006-12-01

At least since the seventeenth century, the strange combination of epistemological certainty and ontological power that characterizes mathematics has made it a major focus of philosophical, social, and cultural negotiation. In the eighteenth century, all of these factors were at play as mathematical thinkers struggled to assimilate and extend the analysis they had inherited from the seventeenth century. A combination of educational convictions and historical assumptions supported a humanistic mathematics essentially defined by its flexibility and breadth. This mathematics was an expression of l'esprit humain, which was unfolding in a progressive historical narrative. The French Revolution dramatically altered the historical and educational landscapes that had supported this eighteenth-century approach, and within thirty years Augustin Louis Cauchy had radically reconceptualized and restructured mathematics to be rigorous rather than narrative.

Towards a category theory approach to analogy: Analyzing re-representation and acquisition of numerical knowledge.

PubMed

Navarrete, Jairo A; Dartnell, Pablo

2017-08-01

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called "flexibility" whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena.

Diet expert subsystem for CELSS

NASA Technical Reports Server (NTRS)

Yendler, Boris S.; Nguyen, Thoi K.; Waleh, Ahmad

1991-01-01

An account is given of the mathematical basis of a diet-controlling expert system, designated 'Ceres' for the human crews of a Controlled Ecological Life Support System (CELSS). The Ceres methodology can furnish both steady-state and dynamic diet solutions; the differences between Ceres and a conventional nutritional-modeling method is illustrated by the case of a three-component, potato-wheat-soybean food system. Attention is given to the role of food processing in furnishing flexibility in diet-planning management. Crew diet solutions based on simple optimizations are not necessarily the most suitable for optimum CELSS operation.

Model verification of mixed dynamic systems. [POGO problem in liquid propellant rockets

NASA Technical Reports Server (NTRS)

Chrostowski, J. D.; Evensen, D. A.; Hasselman, T. K.

1978-01-01

A parameter-estimation method is described for verifying the mathematical model of mixed (combined interactive components from various engineering fields) dynamic systems against pertinent experimental data. The model verification problem is divided into two separate parts: defining a proper model and evaluating the parameters of that model. The main idea is to use differences between measured and predicted behavior (response) to adjust automatically the key parameters of a model so as to minimize response differences. To achieve the goal of modeling flexibility, the method combines the convenience of automated matrix generation with the generality of direct matrix input. The equations of motion are treated in first-order form, allowing for nonsymmetric matrices, modeling of general networks, and complex-mode analysis. The effectiveness of the method is demonstrated for an example problem involving a complex hydraulic-mechanical system.

Brian: a simulator for spiking neural networks in python.

PubMed

Goodman, Dan; Brette, Romain

2008-01-01

"Brian" is a new simulator for spiking neural networks, written in Python (http://brian. di.ens.fr). It is an intuitive and highly flexible tool for rapidly developing new models, especially networks of single-compartment neurons. In addition to using standard types of neuron models, users can define models by writing arbitrary differential equations in ordinary mathematical notation. Python scientific libraries can also be used for defining models and analysing data. Vectorisation techniques allow efficient simulations despite the overheads of an interpreted language. Brian will be especially valuable for working on non-standard neuron models not easily covered by existing software, and as an alternative to using Matlab or C for simulations. With its easy and intuitive syntax, Brian is also very well suited for teaching computational neuroscience.

Statistically generated weighted curve fit of residual functions for modal analysis of structures

NASA Technical Reports Server (NTRS)

Bookout, P. S.

1995-01-01

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure for modal testing large structures in an external constraint-free environment to measure the effects of higher order modes and interface stiffness. This test method is applicable to structures with distinct degree-of-freedom interfaces to other system components. A theoretical residual function in the displacement/force domain has the characteristics of a relatively flat line in the lower frequencies and a slight upward curvature in the higher frequency range. In the test residual function, the above-mentioned characteristics can be seen in the data, but due to the present limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of ragged data. A second order polynomial curve fit is required to obtain the residual flexibility term. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure. The residual flexibility modal test method is applied to a straight beam with a trunnion appendage and a space shuttle payload pallet simulator.

Flow noise of an underwater vector sensor embedded in a flexible towed array.

PubMed

Korenbaum, Vladimir I; Tagiltsev, Alexander A

2012-05-01

The objective of this work is to simulate the flow noise of a vector sensor embedded in a flexible towed array. The mathematical model developed, based on long-wavelength analysis of the inner space of a cylindrical multipole source, predicts the reduction of the flow noise of a vector sensor embedded in an underwater flexible towed array by means of intensimetric processing (cross-spectral density calculation of oscillatory velocity and sound-pressure-sensor responses). It is found experimentally that intensimetric processing results in flow noise reduction by 12-25 dB at mean levels and by 10-30 dB in fluctuations compared to a squared oscillatory velocity channel. The effect of flow noise suppression in the intensimetry channel relative to a squared sound pressure channel is observed, but only for frequencies above the threshold. These suppression values are 10-15 dB at mean noise levels and 3-6 dB in fluctuations. At towing velocities of 1.5-3 ms(-1) and an accumulation time of 98.3 s, the threshold frequency in fluctuations is between 30 and 45 Hz.

Tools or Crutches? Apparatus as a Sense-Making Aid in Mathematics Teaching with Children with Moderate Learning Difficulties

ERIC Educational Resources Information Center

Moscardini, Lio

2009-01-01

This paper challenges a view of concrete materials as artifacts used within a rigid instructional sequence that particular children are perceived to require or not, as the case may be. Focussing on mathematics teaching, it contends that it is more useful to consider the function of these materials as "tools," artefacts used flexibly and…

MCAT to XCAT: The Evolution of 4-D Computerized Phantoms for Imaging Research: Computer models that take account of body movements promise to provide evaluation and improvement of medical imaging devices and technology.

PubMed

Paul Segars, W; Tsui, Benjamin M W

2009-12-01

Recent work in the development of computerized phantoms has focused on the creation of ideal "hybrid" models that seek to combine the realism of a patient-based voxelized phantom with the flexibility of a mathematical or stylized phantom. We have been leading the development of such computerized phantoms for use in medical imaging research. This paper will summarize our developments dating from the original four-dimensional (4-D) Mathematical Cardiac-Torso (MCAT) phantom, a stylized model based on geometric primitives, to the current 4-D extended Cardiac-Torso (XCAT) and Mouse Whole-Body (MOBY) phantoms, hybrid models of the human and laboratory mouse based on state-of-the-art computer graphics techniques. This paper illustrates the evolution of computerized phantoms toward more accurate models of anatomy and physiology. This evolution was catalyzed through the introduction of nonuniform rational b-spline (NURBS) and subdivision (SD) surfaces, tools widely used in computer graphics, as modeling primitives to define a more ideal hybrid phantom. With NURBS and SD surfaces as a basis, we progressed from a simple geometrically based model of the male torso (MCAT) containing only a handful of structures to detailed, whole-body models of the male and female (XCAT) anatomies (at different ages from newborn to adult), each containing more than 9000 structures. The techniques we applied for modeling the human body were similarly used in the creation of the 4-D MOBY phantom, a whole-body model for the mouse designed for small animal imaging research. From our work, we have found the NURBS and SD surface modeling techniques to be an efficient and flexible way to describe the anatomy and physiology for realistic phantoms. Based on imaging data, the surfaces can accurately model the complex organs and structures in the body, providing a level of realism comparable to that of a voxelized phantom. In addition, they are very flexible. Like stylized models, they can easily be manipulated to model anatomical variations and patient motion. With the vast improvement in realism, the phantoms developed in our lab can be combined with accurate models of the imaging process (SPECT, PET, CT, magnetic resonance imaging, and ultrasound) to generate simulated imaging data close to that from actual human or animal subjects. As such, they can provide vital tools to generate predictive imaging data from many different subjects under various scanning parameters from which to quantitatively evaluate and improve imaging devices and techniques. From the MCAT to XCAT, we will demonstrate how NURBS and SD surface modeling have resulted in a major evolutionary advance in the development of computerized phantoms for imaging research.

A Study of Visualization for Mathematics Education

NASA Technical Reports Server (NTRS)

Daugherty, Sarah C.

2008-01-01

Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

Quasi-Langrangian models of nascent thermals

NASA Technical Reports Server (NTRS)

Rambaldi, S.; Randall, D. A.

1981-01-01

The motions in and around an isolated thermal were studied and rising motion in the core, and sinking motion on the outside were found; while the circulation resembled that of a vortex ring. In an entity cloud model, cloudy thermal is tracked, in a Lagrangian fashion, as a discrete entity; the field of motion in and around the thermal is not explicitly simulated. Field of motion cloud models, in which the equations of motion are numerically integrated on an Eulerian grid were developed. It is shown that the great potential of a hybrid cloud model can combine the simplicity of the entity models with the generality and flexibility of the field-of-motion models. A key problem to be overcome in the development of a hybrid model is the formulation of a mathematical framework within which the cloud dynamics can be represented.

A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

PubMed Central

2006-01-01

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

MCAT to XCAT: The Evolution of 4-D Computerized Phantoms for Imaging Research

PubMed Central

Paul Segars, W.; Tsui, Benjamin M. W.

2012-01-01

Recent work in the development of computerized phantoms has focused on the creation of ideal “hybrid” models that seek to combine the realism of a patient-based voxelized phantom with the flexibility of a mathematical or stylized phantom. We have been leading the development of such computerized phantoms for use in medical imaging research. This paper will summarize our developments dating from the original four-dimensional (4-D) Mathematical Cardiac-Torso (MCAT) phantom, a stylized model based on geometric primitives, to the current 4-D extended Cardiac-Torso (XCAT) and Mouse Whole-Body (MOBY) phantoms, hybrid models of the human and laboratory mouse based on state-of-the-art computer graphics techniques. This paper illustrates the evolution of computerized phantoms toward more accurate models of anatomy and physiology. This evolution was catalyzed through the introduction of nonuniform rational b-spline (NURBS) and subdivision (SD) surfaces, tools widely used in computer graphics, as modeling primitives to define a more ideal hybrid phantom. With NURBS and SD surfaces as a basis, we progressed from a simple geometrically based model of the male torso (MCAT) containing only a handful of structures to detailed, whole-body models of the male and female (XCAT) anatomies (at different ages from newborn to adult), each containing more than 9000 structures. The techniques we applied for modeling the human body were similarly used in the creation of the 4-D MOBY phantom, a whole-body model for the mouse designed for small animal imaging research. From our work, we have found the NURBS and SD surface modeling techniques to be an efficient and flexible way to describe the anatomy and physiology for realistic phantoms. Based on imaging data, the surfaces can accurately model the complex organs and structures in the body, providing a level of realism comparable to that of a voxelized phantom. In addition, they are very flexible. Like stylized models, they can easily be manipulated to model anatomical variations and patient motion. With the vast improvement in realism, the phantoms developed in our lab can be combined with accurate models of the imaging process (SPECT, PET, CT, magnetic resonance imaging, and ultrasound) to generate simulated imaging data close to that from actual human or animal subjects. As such, they can provide vital tools to generate predictive imaging data from many different subjects under various scanning parameters from which to quantitatively evaluate and improve imaging devices and techniques. From the MCAT to XCAT, we will demonstrate how NURBS and SD surface modeling have resulted in a major evolutionary advance in the development of computerized phantoms for imaging research. PMID:26472880

Development of a magnetic catheter with rotating multi-magnets to achieve unclogging motions with enhanced steering capability

NASA Astrophysics Data System (ADS)

Kim, N.; Lee, S.; Lee, W.; Jang, G.

2018-05-01

We developed a novel magnetic catheter structure that can selectively generate steering and unclogging motions. The proposed magnetic catheter is composed of a flexible tube and two modules with ring magnets that can axially rotate in a way that enables the catheter to independently steer and unclog blood clots by controlling external magnetic fields. We mathematically modeled the deflection of the catheter using the large deflection Euler-Bernoulli beam model and developed a design method to determine the optimal distance between magnets in order to maximize steering performance. Finally, we prototyped the proposed magnetic catheter and conducted several experiments to verify the theoretical model and assess its steering and unclogging capabilities.

Design Strategy for a Formally Verified Reliable Computing Platform

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Caldwell, James L.; DiVito, Ben L.

1991-01-01

This paper presents a high-level design for a reliable computing platform for real-time control applications. The design tradeoffs and analyses related to the development of a formally verified reliable computing platform are discussed. The design strategy advocated in this paper requires the use of techniques that can be completely characterized mathematically as opposed to more powerful or more flexible algorithms whose performance properties can only be analyzed by simulation and testing. The need for accurate reliability models that can be related to the behavior models is also stressed. Tradeoffs between reliability and voting complexity are explored. In particular, the transient recovery properties of the system are found to be fundamental to both the reliability analysis as well as the "correctness" models.

A Mathematical Model for Pathogen Cross-Contamination Dynamics during the Postharvest Processing of Leafy Greens.

PubMed

Mokhtari, Amir; Oryang, David; Chen, Yuhuan; Pouillot, Regis; Van Doren, Jane

2018-01-08

We developed a probabilistic mathematical model for the postharvest processing of leafy greens focusing on Escherichia coli O157:H7 contamination of fresh-cut romaine lettuce as the case study. Our model can (i) support the investigation of cross-contamination scenarios, and (ii) evaluate and compare different risk mitigation options. We used an agent-based modeling framework to predict the pathogen prevalence and levels in bags of fresh-cut lettuce and quantify spread of E. coli O157:H7 from contaminated lettuce to surface areas of processing equipment. Using an unbalanced factorial design, we were able to propagate combinations of random values assigned to model inputs through different processing steps and ranked statistically significant inputs with respect to their impacts on selected model outputs. Results indicated that whether contamination originated on incoming lettuce heads or on the surface areas of processing equipment, pathogen prevalence among bags of fresh-cut lettuce and batches was most significantly impacted by the level of free chlorine in the flume tank and frequency of replacing the wash water inside the tank. Pathogen levels in bags of fresh-cut lettuce were most significantly influenced by the initial levels of contamination on incoming lettuce heads or surface areas of processing equipment. The influence of surface contamination on pathogen prevalence or levels in fresh-cut bags depended on the location of that surface relative to the flume tank. This study demonstrates that developing a flexible yet mathematically rigorous modeling tool, a "virtual laboratory," can provide valuable insights into the effectiveness of individual and combined risk mitigation options. © 2018 The Authors Risk Analysis published by Wiley Periodicals, Inc. on behalf of Society for Risk Analysis.

Analysis of blocking probability for OFDM-based variable bandwidth optical network

NASA Astrophysics Data System (ADS)

Gong, Lei; Zhang, Jie; Zhao, Yongli; Lin, Xuefeng; Wu, Yuyao; Gu, Wanyi

2011-12-01

Orthogonal Frequency Division Multiplexing (OFDM) has recently been proposed as a modulation technique. For optical networks, because of its good spectral efficiency, flexibility, and tolerance to impairments, optical OFDM is much more flexible compared to traditional WDM systems, enabling elastic bandwidth transmissions, and optical networking is the future trend of development. In OFDM-based optical network the research of blocking rate has very important significance for network assessment. Current research for WDM network is basically based on a fixed bandwidth, in order to accommodate the future business and the fast-changing development of optical network, our study is based on variable bandwidth OFDM-based optical networks. We apply the mathematical analysis and theoretical derivation, based on the existing theory and algorithms, research blocking probability of the variable bandwidth of optical network, and then we will build a model for blocking probability.

Pressure distribution under flexible polishing tools. I - Conventional aspheric optics

NASA Astrophysics Data System (ADS)

Mehta, Pravin K.; Hufnagel, Robert E.

1990-10-01

The paper presents a mathematical model, based on Kirchoff's thin flat plate theory, developed to determine polishing pressure distribution for a flexible polishing tool. A two-layered tool in which bending and compressive stiffnesses are equal is developed, which is formulated as a plate on a linearly elastic foundation. An equivalent eigenvalue problem and solution for a free-free plate are created from the plate formulation. For aspheric, anamorphic optical surfaces, the tool misfit is derived; it is defined as the result of movement from the initial perfect fit on the optic to any other position. The Polisher Design (POD) software for circular tools on aspheric optics is introduced. NASTRAN-based finite element analysis results are compared with the POD software, showing high correlation. By employing existing free-free eigenvalues and eigenfunctions, the work may be extended to rectangular polishing tools as well.

A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter

NASA Technical Reports Server (NTRS)

Agrawal, Om P.

1988-01-01

A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis.

Multiporosity flow in fractured low-permeability rocks: Extension to shale hydrocarbon reservoirs

DOE PAGES

Kuhlman, Kristopher L.; Malama, Bwalya; Heath, Jason E.

2015-02-05

We presented a multiporosity extension of classical double and triple-porosity fractured rock flow models for slightly compressible fluids. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo steady state and transient interporosity flow double-porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probability mass function. Semianalytical cylindrically symmetric solutions to the multiporosity mathematical model are developed using the Laplace transform tomore » illustrate its behavior. Furthermore, the multiporosity model presented here is conceptually simple, yet flexible enough to simulate common conceptualizations of double and triple-porosity flow. This combination of generality and simplicity makes the multiporosity model a good choice for flow modelling in low-permeability fractured rocks.« less

An analytical and experimental investigation of flutter suppression via piezoelectric actuation

NASA Technical Reports Server (NTRS)

Heeg, Jennifer

1992-01-01

The objective of this research was to analytically and experimentally study the capabilities of adaptive material plate actuators for suppressing flutter. Piezoelectrics are materials which are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two degree of freedom wind-tunnel model was designed, analyzed, and tested. The model consisted of a rigid wing and a flexible mount system which permitted translational and rotational degrees of freedom. Actuators, made of piezoelectric material were affixed to leaf springs on the mount system. Command signals, applied to the piezoelectric actuators, exerted control over the closed-loop damping and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element methods, laminated plate theory, and aeroelastic analysis tools. A flutter suppression control law was designed, implemented on a digital control computer, and tested to conditions 20 percent above the passive flutter speed of the model. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. It demonstrates that small, carefully-placed actuating plates can be used effectively to control aeroelastic response.

The Trade-Off Mechanism in Mammalian Circadian Clock Model with Two Time Delays

NASA Astrophysics Data System (ADS)

Yan, Jie; Kang, Xiaxia; Yang, Ling

Circadian clock is an autonomous oscillator which orchestrates the daily rhythms of physiology and behaviors. This study is devoted to explore how a positive feedback loop affects the dynamics of mammalian circadian clock. We simplify an experimentally validated mathematical model in our previous work, to a nonlinear differential equation with two time delays. This simplified mathematical model incorporates the pacemaker of mammalian circadian clock, a negative primary feedback loop, and a critical positive auxiliary feedback loop, Rev-erbα/Cry1 loop. We perform analytical studies of the system. Delay-dependent conditions for the asymptotic stability of the nontrivial positive steady state of the model are investigated. We also prove the existence of Hopf bifurcation, which leads to self-sustained oscillation of mammalian circadian clock. Our theoretical analyses show that the oscillatory regime is reduced upon the participation of the delayed positive auxiliary loop. However, further simulations reveal that the auxiliary loop can enable the circadian clock gain widely adjustable amplitudes and robust period. Thus, the positive auxiliary feedback loop may provide a trade-off mechanism, to use the small loss in the robustness of oscillation in exchange for adaptable flexibility in mammalian circadian clock. The results obtained from the model may gain new insights into the dynamics of biological oscillators with interlocked feedback loops.

SYSTID - A flexible tool for the analysis of communication systems.

NASA Technical Reports Server (NTRS)

Dawson, C. T.; Tranter, W. H.

1972-01-01

Description of the System Time Domain Simulation (SYSTID) computer-aided analysis program which is specifically structured for communication systems analysis. The SYSTID program is user oriented so that very little knowledge of computer techniques and very little programming ability are required for proper application. The program is designed so that the user can go from a system block diagram to an accurate simulation by simply programming a single English language statement for each block in the system. The mathematical and functional models available in the SYSTID library are presented. An example problem is given which illustrates the ease of modeling communication systems. Examples of the outputs available are presented, and proposed improvements are summarized.

The impact of assumed knowledge entry standards on undergraduate mathematics teaching in Australia

NASA Astrophysics Data System (ADS)

King, Deborah; Cattlin, Joann

2015-10-01

Over the last two decades, many Australian universities have relaxed their selection requirements for mathematics-dependent degrees, shifting from hard prerequisites to assumed knowledge standards which provide students with an indication of the prior learning that is expected. This has been regarded by some as a positive move, since students who may be returning to study, or who are changing career paths but do not have particular prerequisite study, now have more flexible pathways. However, there is mounting evidence to indicate that there are also significant negative impacts associated with assumed knowledge approaches, with large numbers of students enrolling in degrees without the stated assumed knowledge. For students, there are negative impacts on pass rates and retention rates and limitations to pathways within particular degrees. For institutions, the necessity to offer additional mathematics subjects at a lower level than normal and more support services for under-prepared students impacts on workloads and resources. In this paper, we discuss early research from the First Year in Maths project, which begins to shed light on the realities of a system that may in fact be too flexible.

Mathematics and online learning experiences: a gateway site for engineering students

NASA Astrophysics Data System (ADS)

Masouros, Spyridon D.; Alpay, Esat

2010-03-01

This paper focuses on the preliminary design of a multifaceted computer-based mathematics resource for undergraduate and pre-entry engineering students. Online maths resources, while attractive in their flexibility of delivery, have seen variable interest from students and teachers alike. Through student surveys and wide consultations, guidelines have been developed for effectively collating and integrating learning, support, application and diagnostic tools to produce an Engineer's Mathematics Gateway. Specific recommendations include: the development of a shared database of engineering discipline-specific problems and examples; the identification of, and resource development for, troublesome mathematics topics which encompass ideas of threshold concepts and mastery components; the use of motivational and promotional material to raise student interest in learning mathematics in an engineering context; the use of general and lecture-specific concept maps and matrices to identify the needs and relevance of mathematics to engineering topics; and further exploration of the facilitation of peer-based learning through online resources.

A new flexible plug and play scheme for modeling, simulating, and predicting gastric emptying

PubMed Central

2014-01-01

Background In-silico models that attempt to capture and describe the physiological behavior of biological organisms, including humans, are intrinsically complex and time consuming to build and simulate in a computing environment. The level of detail of description incorporated in the model depends on the knowledge of the system’s behavior at that level. This knowledge is gathered from the literature and/or improved by knowledge obtained from new experiments. Thus model development is an iterative developmental procedure. The objective of this paper is to describe a new plug and play scheme that offers increased flexibility and ease-of-use for modeling and simulating physiological behavior of biological organisms. Methods This scheme requires the modeler (user) first to supply the structure of the interacting components and experimental data in a tabular format. The behavior of the components described in a mathematical form, also provided by the modeler, is externally linked during simulation. The advantage of the plug and play scheme for modeling is that it requires less programming effort and can be quickly adapted to newer modeling requirements while also paving the way for dynamic model building. Results As an illustration, the paper models the dynamics of gastric emptying behavior experienced by humans. The flexibility to adapt the model to predict the gastric emptying behavior under varying types of nutrient infusion in the intestine (ileum) is demonstrated. The predictions were verified with a human intervention study. The error in predicting the half emptying time was found to be less than 6%. Conclusions A new plug-and-play scheme for biological systems modeling was developed that allows changes to the modeled structure and behavior with reduced programming effort, by abstracting the biological system into a network of smaller sub-systems with independent behavior. In the new scheme, the modeling and simulation becomes an automatic machine readable and executable task. PMID:24917054

PRMS-IV, the precipitation-runoff modeling system, version 4

USGS Publications Warehouse

Markstrom, Steven L.; Regan, R. Steve; Hay, Lauren E.; Viger, Roland J.; Webb, Richard M.; Payn, Robert A.; LaFontaine, Jacob H.

2015-01-01

Computer models that simulate the hydrologic cycle at a watershed scale facilitate assessment of variability in climate, biota, geology, and human activities on water availability and flow. This report describes an updated version of the Precipitation-Runoff Modeling System. The Precipitation-Runoff Modeling System is a deterministic, distributed-parameter, physical-process-based modeling system developed to evaluate the response of various combinations of climate and land use on streamflow and general watershed hydrology. Several new model components were developed, and all existing components were updated, to enhance performance and supportability. This report describes the history, application, concepts, organization, and mathematical formulation of the Precipitation-Runoff Modeling System and its model components. This updated version provides improvements in (1) system flexibility for integrated science, (2) verification of conservation of water during simulation, (3) methods for spatial distribution of climate boundary conditions, and (4) methods for simulation of soil-water flow and storage.

Future Directions for The Math You Need, When You Need It: Adaptation and Implementation of Online Student-Centered Tutorials that Remediate Introductory Geoscience-Related Mathematical Skills

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Burn, H.; Baer, E. M.

2009-12-01

Requiring introductory geoscience students to apply mathematical concepts and solve quantitative problems can be an arduous task because these courses tend to attract students with diverse levels of mathematical preparedness. Perhaps more significantly, geoscience instructors grapple with quantitative content because of the difficulties students have transferring their prior mathematical learning to common geological problems. As a result, instructors can choose to eliminate the mathematics, spend valuable class time teaching basic mathematical skills or let students flounder in the hope that they will learn on their own. None of these choices are ideal. Instead, research suggests that introductory geoscience courses are opportune places to increase students’ quantitative abilities but that students need effective support at their own skill level. To provide such support, we developed The Math You Need, When You Need It (TMYN): a set of online geoscience context-rich tutorials that students complete just before they encounter a mathematical or numerical skill in their introductory course. The tutorials are modular; each mathematical topic has a set of pages that students work through toward a final assessment. The 11 modules currently available, including unit conversions, graphing, calculating density, and rearranging equations, touch on quantitative topics that cross a number of geologic contexts. TMYN modules are designed to be stand-alone and flexible - faculty members can choose modules appropriate for their courses and implement them at any time throughout the term. The flexible and adaptable nature of TMYN enables faculty to provide a supportive learning environment that remediates math for those who need it without taking significant classroom time. Since spring 2008, seven instructors at Highline Community College and University of Wisconsin Oshkosh successfully implemented TMYN in six geoscience courses with diverse student audiences. Evaluation of pilot implementations suggests that the flexibility of TYMN is one of its strengths. Specifically, faculty members responded positively to the ability to choose relevant topics and provide students with competence in pertinent mathematical concepts; students liked the supportive, contextual environment and the ability to work at their own pace. And, despite the fact that each implementation varied in the number and type of modules used, the timing of module use, grading stakes, and course size, pre/post test results consistently showed improvement in student skills associated with a given module, suggesting that all implementations were successful. Post-module surveys likewise revealed that both instructors and students found the experience valuable. We present the wide variety of successful implementations with an eye toward exploring future directions for the project, including soliciting new and diverse ways in which other institutions and instructors might adapt and apply TMYN to their own courses.

Calculations of flexibility module in measurements instruments

NASA Astrophysics Data System (ADS)

Wróbel, A.; Płaczek, M.; Baier, A.

2017-08-01

Piezoelectricity has found a lot of applications since it were discovered in 1880 by Pierre and Jacques Curie. There are many applications of the direct piezoelectric effect - the production of an electric potential when stress is applied to the piezoelectric material, as well as the reverse piezoelectric effect - the production of strain when an electric field is applied. This work presents a mathematical model of a new model of vibration sensor. The principle of operation of currently used sensors is based on the idea: changes in thickness of the piezoelectric plates cause the vibration of the mechanical element, so-called “fork”. If the “forks” are not buried by the material deformation of the full tiles broadcasting is transmitted to receiver piezoelectric plate. As a result of vibration of receiver plates the cladding is formed on the potential difference proportional to the force. The value of this voltage is processed by an electronic circuit. In the case of backfilling “forks” the electric signal is lower. At the same time is not generated the potential for cladding tiles. Such construction have a lot of drawbacks, for example: need to use several piezoelectric plates, with the increase in number of components is increased failure of sensors, sensors have now produced two forks resonance, using these sensors in moist materials is often the case that the material remains between the forks and at the same time causes a measurement error. Mentioned disadvantages do not appear in the new proposed sensor design. The Galerkin method of the analysis of considered systems will be presented started from development of the mathematical model, to determine the graphs of flexibility and confirm two methods: exact and approximate. Analyzed beam is a part of the vibration level sensor and the results will be used to identify the electrical parameters of the generator. Designing of technical systems containing piezoelectric transducers is a complex process, due to the phenomena occurring in them. A correct description of the given device in the form of a mathematical model, already in its design phase, is a fundamental condition for its proper functioning. The presented analyzes may be used in the study of any mechanism by piezoelectric sensor, including for the steering column examination.

Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.

PubMed

Koch, Gilbert; Krzyzanski, Wojciech; Pérez-Ruixo, Juan Jose; Schropp, Johannes

2014-08-01

In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.

Intelligent control of a planning system for astronaut training.

PubMed

Ortiz, J; Chen, G

1999-07-01

This work intends to design, analyze and solve, from the systems control perspective, a complex, dynamic, and multiconstrained planning system for generating training plans for crew members of the NASA-led International Space Station. Various intelligent planning systems have been developed within the framework of artificial intelligence. These planning systems generally lack a rigorous mathematical formalism to allow a reliable and flexible methodology for their design, modeling, and performance analysis in a dynamical, time-critical, and multiconstrained environment. Formulating the planning problem in the domain of discrete-event systems under a unified framework such that it can be modeled, designed, and analyzed as a control system will provide a self-contained theory for such planning systems. This will also provide a means to certify various planning systems for operations in the dynamical and complex environments in space. The work presented here completes the design, development, and analysis of an intricate, large-scale, and representative mathematical formulation for intelligent control of a real planning system for Space Station crew training. This planning system has been tested and used at NASA-Johnson Space Center.

A flexible motif search technique based on generalized profiles.

PubMed

Bucher, P; Karplus, K; Moeri, N; Hofmann, K

1996-03-01

A flexible motif search technique is presented which has two major components: (1) a generalized profile syntax serving as a motif definition language; and (2) a motif search method specifically adapted to the problem of finding multiple instances of a motif in the same sequence. The new profile structure, which is the core of the generalized profile syntax, combines the functions of a variety of motif descriptors implemented in other methods, including regular expression-like patterns, weight matrices, previously used profiles, and certain types of hidden Markov models (HMMs). The relationship between generalized profiles and other biomolecular motif descriptors is analyzed in detail, with special attention to HMMs. Generalized profiles are shown to be equivalent to a particular class of HMMs, and conversion procedures in both directions are given. The conversion procedures provide an interpretation for local alignment in the framework of stochastic models, allowing for clear, simple significance tests. A mathematical statement of the motif search problem defines the new method exactly without linking it to a specific algorithmic solution. Part of the definition includes a new definition of disjointness of alignments.

Slew maneuvers on the SCOLE Laboratory Facility

NASA Technical Reports Server (NTRS)

Williams, Jeffrey P.

1987-01-01

The Spacecraft Control Laboratory Experiment (SCOLE) was conceived to provide a physical test bed for the investigation of control techniques for large flexible spacecraft. The control problems studied are slewing maneuvers and pointing operations. The slew is defined as a minimum time maneuver to bring the antenna line-of-sight (LOS) pointing to within an error limit of the pointing target. The second objective is to rotate about the LOS within the 0.02 degree error limit. The SCOLE problem is defined as two design challenges: control laws for a mathematical model of a large antenna attached to the Space Shuttle by a long flexible mast; and a control scheme on a laboratory representation of the structure modelled on the control laws. Control sensors and actuators are typical of those which the control designer would have to deal with on an actual spacecraft. Computational facilities consist of microcomputer based central processing units with appropriate analog interfaces for implementation of the primary control system, and the attitude estimation algorithm. Preliminary results of some slewing control experiments are given.

Modeling biochemical transformation processes and information processing with Narrator.

PubMed

Mandel, Johannes J; Fuss, Hendrik; Palfreyman, Niall M; Dubitzky, Werner

2007-03-27

Software tools that model and simulate the dynamics of biological processes and systems are becoming increasingly important. Some of these tools offer sophisticated graphical user interfaces (GUIs), which greatly enhance their acceptance by users. Such GUIs are based on symbolic or graphical notations used to describe, interact and communicate the developed models. Typically, these graphical notations are geared towards conventional biochemical pathway diagrams. They permit the user to represent the transport and transformation of chemical species and to define inhibitory and stimulatory dependencies. A critical weakness of existing tools is their lack of supporting an integrative representation of transport, transformation as well as biological information processing. Narrator is a software tool facilitating the development and simulation of biological systems as Co-dependence models. The Co-dependence Methodology complements the representation of species transport and transformation together with an explicit mechanism to express biological information processing. Thus, Co-dependence models explicitly capture, for instance, signal processing structures and the influence of exogenous factors or events affecting certain parts of a biological system or process. This combined set of features provides the system biologist with a powerful tool to describe and explore the dynamics of life phenomena. Narrator's GUI is based on an expressive graphical notation which forms an integral part of the Co-dependence Methodology. Behind the user-friendly GUI, Narrator hides a flexible feature which makes it relatively easy to map models defined via the graphical notation to mathematical formalisms and languages such as ordinary differential equations, the Systems Biology Markup Language or Gillespie's direct method. This powerful feature facilitates reuse, interoperability and conceptual model development. Narrator is a flexible and intuitive systems biology tool. It is specifically intended for users aiming to construct and simulate dynamic models of biology without recourse to extensive mathematical detail. Its design facilitates mappings to different formal languages and frameworks. The combined set of features makes Narrator unique among tools of its kind. Narrator is implemented as Java software program and available as open-source from http://www.narrator-tool.org.

Modeling biochemical transformation processes and information processing with Narrator

PubMed Central

Mandel, Johannes J; Fuß, Hendrik; Palfreyman, Niall M; Dubitzky, Werner

2007-01-01

Background Software tools that model and simulate the dynamics of biological processes and systems are becoming increasingly important. Some of these tools offer sophisticated graphical user interfaces (GUIs), which greatly enhance their acceptance by users. Such GUIs are based on symbolic or graphical notations used to describe, interact and communicate the developed models. Typically, these graphical notations are geared towards conventional biochemical pathway diagrams. They permit the user to represent the transport and transformation of chemical species and to define inhibitory and stimulatory dependencies. A critical weakness of existing tools is their lack of supporting an integrative representation of transport, transformation as well as biological information processing. Results Narrator is a software tool facilitating the development and simulation of biological systems as Co-dependence models. The Co-dependence Methodology complements the representation of species transport and transformation together with an explicit mechanism to express biological information processing. Thus, Co-dependence models explicitly capture, for instance, signal processing structures and the influence of exogenous factors or events affecting certain parts of a biological system or process. This combined set of features provides the system biologist with a powerful tool to describe and explore the dynamics of life phenomena. Narrator's GUI is based on an expressive graphical notation which forms an integral part of the Co-dependence Methodology. Behind the user-friendly GUI, Narrator hides a flexible feature which makes it relatively easy to map models defined via the graphical notation to mathematical formalisms and languages such as ordinary differential equations, the Systems Biology Markup Language or Gillespie's direct method. This powerful feature facilitates reuse, interoperability and conceptual model development. Conclusion Narrator is a flexible and intuitive systems biology tool. It is specifically intended for users aiming to construct and simulate dynamic models of biology without recourse to extensive mathematical detail. Its design facilitates mappings to different formal languages and frameworks. The combined set of features makes Narrator unique among tools of its kind. Narrator is implemented as Java software program and available as open-source from . PMID:17389034

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

Analysis of laser remote fusion cutting based on a mathematical model

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

Matti, R. S.; Department of Mechanical Engineering, College of Engineering, University of Mosul, Mosul; Ilar, T.

Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, lasermore » remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.« less

Analysis of laser remote fusion cutting based on a mathematical model

NASA Astrophysics Data System (ADS)

Matti, R. S.; Ilar, T.; Kaplan, A. F. H.

2013-12-01

Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.

Mathematical computer programs: A compilation

NASA Technical Reports Server (NTRS)

1972-01-01

Computer programs, routines, and subroutines for aiding engineers, scientists, and mathematicians in direct problem solving are presented. Also included is a group of items that affords the same users greater flexibility in the use of software.

Asymmetrical booster ascent guidance and control system design study. Volume 1: Summary. [space shuttle development

NASA Technical Reports Server (NTRS)

Williams, F. E.; Lemon, R. S.; Jaggers, R. F.; Wilson, J. L.

1974-01-01

Dynamics and control, stability, and guidance analyses are summarized for the asymmetrical booster ascent guidance and control system design studies, performed in conjunction with space shuttle planning. The mathematical models developed for use in rigid body and flexible body versions of the NASA JSC space shuttle functional simulator are briefly discussed, along with information on the following: (1) space shuttle stability analysis using equations of motion for both pitch and lateral axes; (2) the computer program used to obtain stability margin; and (3) the guidance equations developed for the space shuttle powered flight phases.

Artificial neural network does better spatiotemporal compressive sampling

NASA Astrophysics Data System (ADS)

Lee, Soo-Young; Hsu, Charles; Szu, Harold

2012-06-01

Spatiotemporal sparseness is generated naturally by human visual system based on artificial neural network modeling of associative memory. Sparseness means nothing more and nothing less than the compressive sensing achieves merely the information concentration. To concentrate the information, one uses the spatial correlation or spatial FFT or DWT or the best of all adaptive wavelet transform (cf. NUS, Shen Shawei). However, higher dimensional spatiotemporal information concentration, the mathematics can not do as flexible as a living human sensory system. The reason is obviously for survival reasons. The rest of the story is given in the paper.

Simulation of swimming strings immersed in a viscous fluid flow

NASA Astrophysics Data System (ADS)

Huang, Wei-Xi; Sung, Hyung Jin

2006-11-01

In nature, many phenomena involve interactions between flexible bodies and their surrounding viscous fluid, such as a swimming fish or a flapping flag. The intrinsic dynamics is complicate and not well understood. A flexible string can be regarded as a one-dimensional flag model. Many similarities can be found between the flapping string and swimming fish, although different wake speed results in a drag force for the flapping string and a propulsion force for the swimming fish. In the present study, we propose a mathematical formulation for swimming strings immersed in a viscous fluid flow. Fluid motion is governed by the Navier-Stokes equations and a momentum forcing is added in order to bring the fluid to move at the same velocity with the immersed surface. A flexible inextensible string model is described by another set of equations with an additional momentum forcing which is a result of the fluid viscosity and the pressure difference across the string. The momentum forcing is calculated by a feedback loop. Simulations of several numerical examples are carried out, including a hanging string which starts moving under gravity without ambient fluid, a swinging string immersed in a quiescent viscous fluid, a string swimming within a uniform surrounding flow, and flow over two side-by-side strings. The numerical results agree well with the theoretical analysis and previous experimental observations. Further simulation of a swimming fish is under consideration.

The dynamics and control of large flexible space structures, part 11

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R; Diarra, Cheick M.; Li, Feiyue

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed Spacecraft Control Laboratory Experiment during the stationkeeping phase. The Shuttle and reflector are assumed to be rigid, while the mass connecting the Shuttle to the reflector is assumed to be flexible with elastic deformations small as compared with its length. It is seen that in the presence of gravity-gradient torques, the system assumes a new equilibrium position primarily due to the offset in the mass attachment point to the reflector from the reflector's mass center. Control is assumed to be provided through the Shuttle's three torquers and throught six actuators located by painrs at two points on the mass and at the reflector mass center. Numerical results confirm the robustness of an LQR derived control strategy during stationkeeping with maximum control efforts significantly below saturation levels. The linear regulator theory is also used to derive control laws for the linearized model of the rigidized SCOLE configuration where the mast flexibility is not included. It is seen that this same type of control strategy can be applied for the rapid single axis slewing of the SCOLE through amplitudes as large as 20 degrees. These results provide a definite trade-off between the slightly larger slewing times with the considerable reduction in over-all control effort as compared with the results of the two point boundary value problem application of Pontryagin's Maximum Principle.

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

NASA Astrophysics Data System (ADS)

Park, Sang Chul

1989-09-01

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

A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility.

PubMed

Moore, Jason H; Gilbert, Joshua C; Tsai, Chia-Ti; Chiang, Fu-Tien; Holden, Todd; Barney, Nate; White, Bill C

2006-07-21

Detecting, characterizing, and interpreting gene-gene interactions or epistasis in studies of human disease susceptibility is both a mathematical and a computational challenge. To address this problem, we have previously developed a multifactor dimensionality reduction (MDR) method for collapsing high-dimensional genetic data into a single dimension (i.e. constructive induction) thus permitting interactions to be detected in relatively small sample sizes. In this paper, we describe a comprehensive and flexible framework for detecting and interpreting gene-gene interactions that utilizes advances in information theory for selecting interesting single-nucleotide polymorphisms (SNPs), MDR for constructive induction, machine learning methods for classification, and finally graphical models for interpretation. We illustrate the usefulness of this strategy using artificial datasets simulated from several different two-locus and three-locus epistasis models. We show that the accuracy, sensitivity, specificity, and precision of a naïve Bayes classifier are significantly improved when SNPs are selected based on their information gain (i.e. class entropy removed) and reduced to a single attribute using MDR. We then apply this strategy to detecting, characterizing, and interpreting epistatic models in a genetic study (n = 500) of atrial fibrillation and show that both classification and model interpretation are significantly improved.

Fast generation of sparse random kernel graphs

DOE PAGES

Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

2015-09-10

The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less

A biologically inspired network design model.

PubMed

Zhang, Xiaoge; Adamatzky, Andrew; Chan, Felix T S; Deng, Yong; Yang, Hai; Yang, Xin-She; Tsompanas, Michail-Antisthenis I; Sirakoulis, Georgios Ch; Mahadevan, Sankaran

2015-06-04

A network design problem is to select a subset of links in a transport network that satisfy passengers or cargo transportation demands while minimizing the overall costs of the transportation. We propose a mathematical model of the foraging behaviour of slime mould P. polycephalum to solve the network design problem and construct optimal transport networks. In our algorithm, a traffic flow between any two cities is estimated using a gravity model. The flow is imitated by the model of the slime mould. The algorithm model converges to a steady state, which represents a solution of the problem. We validate our approach on examples of major transport networks in Mexico and China. By comparing networks developed in our approach with the man-made highways, networks developed by the slime mould, and a cellular automata model inspired by slime mould, we demonstrate the flexibility and efficiency of our approach.

A Biologically Inspired Network Design Model

PubMed Central

Zhang, Xiaoge; Adamatzky, Andrew; Chan, Felix T.S.; Deng, Yong; Yang, Hai; Yang, Xin-She; Tsompanas, Michail-Antisthenis I.; Sirakoulis, Georgios Ch.; Mahadevan, Sankaran

2015-01-01

A network design problem is to select a subset of links in a transport network that satisfy passengers or cargo transportation demands while minimizing the overall costs of the transportation. We propose a mathematical model of the foraging behaviour of slime mould P. polycephalum to solve the network design problem and construct optimal transport networks. In our algorithm, a traffic flow between any two cities is estimated using a gravity model. The flow is imitated by the model of the slime mould. The algorithm model converges to a steady state, which represents a solution of the problem. We validate our approach on examples of major transport networks in Mexico and China. By comparing networks developed in our approach with the man-made highways, networks developed by the slime mould, and a cellular automata model inspired by slime mould, we demonstrate the flexibility and efficiency of our approach. PMID:26041508

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter; Wells, Garth N.

2011-09-01

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.

Strategies for the coupling of global and local crystal growth models

NASA Astrophysics Data System (ADS)

Derby, Jeffrey J.; Lun, Lisa; Yeckel, Andrew

2007-05-01

The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

NASA Astrophysics Data System (ADS)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Using statistical and artificial neural network models to forecast potentiometric levels at a deep well in South Texas

NASA Astrophysics Data System (ADS)

Uddameri, V.

2007-01-01

Reliable forecasts of monthly and quarterly fluctuations in groundwater levels are necessary for short- and medium-term planning and management of aquifers to ensure proper service of seasonal demands within a region. Development of physically based transient mathematical models at this time scale poses considerable challenges due to lack of suitable data and other uncertainties. Artificial neural networks (ANN) possess flexible mathematical structures and are capable of mapping highly nonlinear relationships. Feed-forward neural network models were constructed and trained using the back-percolation algorithm to forecast monthly and quarterly time-series water levels at a well that taps into the deeper Evangeline formation of the Gulf Coast aquifer in Victoria, TX. Unlike unconfined formations, no causal relationships exist between water levels and hydro-meteorological variables measured near the vicinity of the well. As such, an endogenous forecasting model using dummy variables to capture short-term seasonal fluctuations and longer-term (decadal) trends was constructed. The root mean square error, mean absolute deviation and correlation coefficient ( R) were noted to be 1.40, 0.33 and 0.77 m, respectively, for an evaluation dataset of quarterly measurements and 1.17, 0.46, and 0.88 m for an evaluative monthly dataset not used to train or test the model. These statistics were better for the ANN model than those developed using statistical regression techniques.

On the accuracy of modelling the dynamics of large space structures

NASA Technical Reports Server (NTRS)

Diarra, C. M.; Bainum, P. M.

1985-01-01

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Faculty career flexibility: Why we need it and how best to achieve it

NASA Astrophysics Data System (ADS)

Quinn, Kate

2010-02-01

Research conducted over the last decade provides compelling evidence that higher education institutions have a strong business case for providing flexibility for their tenure-track and tenured faculty. Flexibility constitutes an effective tool for recruiting and retaining talented faculty. Career flexibility is especially critical to retaining some of the most qualified female PhDs in academic science, engineering, and mathematics. Acquiring the best talent is essential to an institution's ability to achieve excellence and maintain its competitive advantage in a global environment. In an effort to increase the flexibility of faculty careers, the American Council on Education partnered with the Alfred P. Sloan Foundation to create the Award for Faculty Career Flexibility. This presentation will address the origins of the award and share findings from the awards process. Fairly simple and cost effective strategies have been successful in accelerating the cultural change necessary to increase the flexibility of faculty careers. This presentation shares these strategies in addition to information about the types of policies and practices being adopted to support faculty work-life balance through career flexibility. )

Live lectures or online videos: students' resource choices in a first-year university mathematics module

NASA Astrophysics Data System (ADS)

Howard, Emma; Meehan, Maria; Parnell, Andrew

2018-05-01

In Maths for Business, a mathematics module for non-mathematics specialists, students are given the choice of completing the module content via short online videos, live lectures or a combination of both. In this study, we identify students' specific usage patterns with both of these resources and discuss their reasons for the preferences they exhibit. In 2015-2016, we collected quantitative data on each student's resource usage (attendance at live lectures and access of online videos) for the entire class of 522 students and employed model-based clustering which identified four distinct resource usage patterns with lectures and/or videos. We also collected qualitative data on students' perceptions of resource usage through a survey administered at the end of the semester, to which 161 students responded. The 161 survey responses were linked to each cluster and analysed using thematic analysis. Perceived benefits of videos include flexibility of scheduling and pace, and avoidance of large, long lectures. In contrast, the main perceived advantages of lectures are the ability to engage in group tasks, to ask questions, and to learn 'gradually'. Students in the two clusters with high lecture attendance achieved, on average, higher marks in the module.

Thermal stress in flexible interdigital transducers with anisotropic electroactive cellulose substrates

NASA Astrophysics Data System (ADS)

Yoon, Sean J.; Kim, Jung Woong; Kim, Hyun Chan; Kang, Jinmo; Kim, Jaehwan

2017-12-01

Thermal stress in flexible interdigital transducers a reliability concern in the development of flexible devices, which may lead to interface delamination, stress voiding and plastic deformation. In this paper, a mathematical model is presented to investigate the effect of material selections on the thermal stress in interdigital transducers. We modified the linear relationships in the composite materials theory with the effect of high curvature, anisotropic substrate and small substrate thickness. We evaluated the thermal stresses of interdigital transducers, fabricated with various electrodes, insulators and substrate materials for the comparison. The results show that, among various insulators, organic polymer developed the highest stress level while oxide showed the lowest stress level. Aluminium shows a higher stress level and curvature as an electrode than gold. As substrate materials, polyimide and electroactive cellulose show similar stress levels except the opposite sign convention to each other. Polyimide shows positive curvatures while electroactive cellulose shows negative curvatures, which is attributed to the stress and thermal expansion state of the metal/insulator composite. The results show that the insulator is found to be responsible for the confinement across the metal lines while the substrate is responsible for the confinement along the metal lines.

Magic in the machine: a computational magician's assistant.

PubMed

Williams, Howard; McOwan, Peter W

2014-01-01

A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required. The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced. Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact. In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect. We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London.

An investigation of constraint-based component-modeling for knowledge representation in computer-aided conceptual design

NASA Technical Reports Server (NTRS)

Kolb, Mark A.

1990-01-01

Originally, computer programs for engineering design focused on detailed geometric design. Later, computer programs for algorithmically performing the preliminary design of specific well-defined classes of objects became commonplace. However, due to the need for extreme flexibility, it appears unlikely that conventional programming techniques will prove fruitful in developing computer aids for engineering conceptual design. The use of symbolic processing techniques, such as object-oriented programming and constraint propagation, facilitate such flexibility. Object-oriented programming allows programs to be organized around the objects and behavior to be simulated, rather than around fixed sequences of function- and subroutine-calls. Constraint propagation allows declarative statements to be understood as designating multi-directional mathematical relationships among all the variables of an equation, rather than as unidirectional assignments to the variable on the left-hand side of the equation, as in conventional computer programs. The research has concentrated on applying these two techniques to the development of a general-purpose computer aid for engineering conceptual design. Object-oriented programming techniques are utilized to implement a user-extensible database of design components. The mathematical relationships which model both geometry and physics of these components are managed via constraint propagation. In addition, to this component-based hierarchy, special-purpose data structures are provided for describing component interactions and supporting state-dependent parameters. In order to investigate the utility of this approach, a number of sample design problems from the field of aerospace engineering were implemented using the prototype design tool, Rubber Airplane. The additional level of organizational structure obtained by representing design knowledge in terms of components is observed to provide greater convenience to the program user, and to result in a database of engineering information which is easier both to maintain and to extend.

Modeling error distributions of growth curve models through Bayesian methods.

PubMed

Zhang, Zhiyong

2016-06-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

Statistical ecology comes of age.

PubMed

Gimenez, Olivier; Buckland, Stephen T; Morgan, Byron J T; Bez, Nicolas; Bertrand, Sophie; Choquet, Rémi; Dray, Stéphane; Etienne, Marie-Pierre; Fewster, Rachel; Gosselin, Frédéric; Mérigot, Bastien; Monestiez, Pascal; Morales, Juan M; Mortier, Frédéric; Munoz, François; Ovaskainen, Otso; Pavoine, Sandrine; Pradel, Roger; Schurr, Frank M; Thomas, Len; Thuiller, Wilfried; Trenkel, Verena; de Valpine, Perry; Rexstad, Eric

2014-12-01

The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1-4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.

Statistical ecology comes of age

PubMed Central

Gimenez, Olivier; Buckland, Stephen T.; Morgan, Byron J. T.; Bez, Nicolas; Bertrand, Sophie; Choquet, Rémi; Dray, Stéphane; Etienne, Marie-Pierre; Fewster, Rachel; Gosselin, Frédéric; Mérigot, Bastien; Monestiez, Pascal; Morales, Juan M.; Mortier, Frédéric; Munoz, François; Ovaskainen, Otso; Pavoine, Sandrine; Pradel, Roger; Schurr, Frank M.; Thomas, Len; Thuiller, Wilfried; Trenkel, Verena; de Valpine, Perry; Rexstad, Eric

2014-01-01

The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1–4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data. PMID:25540151

Physical Modeling of Activation Energy in Organic Semiconductor Devices based on Energy and Momentum Conservations

PubMed Central

Mao, Ling-Feng; Ning, H.; Hu, Changjun; Lu, Zhaolin; Wang, Gaofeng

2016-01-01

Field effect mobility in an organic device is determined by the activation energy. A new physical model of the activation energy is proposed by virtue of the energy and momentum conservation equations. The dependencies of the activation energy on the gate voltage and the drain voltage, which were observed in the experiments in the previous independent literature, can be well explained using the proposed model. Moreover, the expression in the proposed model, which has clear physical meanings in all parameters, can have the same mathematical form as the well-known Meyer-Neldel relation, which lacks of clear physical meanings in some of its parameters since it is a phenomenological model. Thus it not only describes a physical mechanism but also offers a possibility to design the next generation of high-performance optoelectronics and integrated flexible circuits by optimizing device physical parameter. PMID:27103586

The Effects of Brain Based Learning Approach on Motivation and Students Achievement in Mathematics Learning

NASA Astrophysics Data System (ADS)

Mekarina, M.; Ningsih, Y. P.

2017-09-01

This classroom action research is based by the facts that the students motivation and achievement mathematics learning is less. One of the factors causing is learning that does not provide flexibility to students to empower the potential of the brain optimally. The aim of this research was to improve the student motivation and achievement in mathematics learning by implementing brain based learning approach. The subject of this research was student of grade XI in senior high school. The research consisted of two cycles. Data of student achievement from test, and the student motivation through questionnaire. Furthermore, the finding of this research showed the result of the analysis was the implementation of brain based learning approach can improve student’s achievement and motivation in mathematics learning.

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

USGS Publications Warehouse

Bolker, Benjamin M.; Gardner, Beth; Maunder, Mark; Berg, Casper W.; Brooks, Mollie; Comita, Liza; Crone, Elizabeth; Cubaynes, Sarah; Davies, Trevor; de Valpine, Perry; Ford, Jessica; Gimenez, Olivier; Kéry, Marc; Kim, Eun Jung; Lennert-Cody, Cleridy; Magunsson, Arni; Martell, Steve; Nash, John; Nielson, Anders; Regentz, Jim; Skaug, Hans; Zipkin, Elise

2013-01-01

1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

On Complex Networks Representation and Computation of Hydrologycal Quantities

NASA Astrophysics Data System (ADS)

Serafin, F.; Bancheri, M.; David, O.; Rigon, R.

2017-12-01

Water is our blue gold. Despite results of discovery-based science keep warning public opinion about the looming worldwide water crisis, water is still treated as a not worth taking resource. Could a different multi-scale perspective affect environmental decision-making more deeply? Can also a further pairing to a new graphical representation of processes interaction sway decision-making more effectively and public opinion consequently?This abstract introduces a complex networks driven way to represent catchments eco-hydrology and related flexible informatics to manage it. The representation is built upon mathematical category. A category is an algebraic structure that comprises "objects" linked by "arrows". It is an evolution of Petri Nets said Time Continuous Petri Nets (TCPN). It aims to display (water) budgets processes and catchment interactions using explicative and self-contained symbolism. The result improves readability of physical processes compared to current descriptions. The IT perspective hinges on the Object Modeling System (OMS) v3. The latter is a non-invasive flexible environmental modeling framework designed to support component-based model development. The implementation of a Directed Acyclic Graph (DAG) data structure, named Net3, has recently enhanced its flexibility. Net3 represents interacting systems as complex networks: vertices match up with any sort of time evolving quantity; edges correspond to their data (fluxes) interchange. It currently hosts JGrass-NewAge components, and those implementing travel time analysis of fluxes. Further bio-physical or management oriented components can be easily added.This talk introduces both graphical representation and related informatics exercising actual applications and examples.

Mathematical correlation of modal-parameter-identification methods via system-realization theory

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan

1987-01-01

A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research toward the unification of the many possible approaches for modal-parameter identification.

Integrated fringe projection 3D scanning system for large-scale metrology based on laser tracker

NASA Astrophysics Data System (ADS)

Du, Hui; Chen, Xiaobo; Zhou, Dan; Guo, Gen; Xi, Juntong

2017-10-01

Large scale components exist widely in advance manufacturing industry,3D profilometry plays a pivotal role for the quality control. This paper proposes a flexible, robust large-scale 3D scanning system by integrating a robot with a binocular structured light scanner and a laser tracker. The measurement principle and system construction of the integrated system are introduced. And a mathematical model is established for the global data fusion. Subsequently, a flexible and robust method and mechanism is introduced for the establishment of the end coordination system. Based on this method, a virtual robot noumenon is constructed for hand-eye calibration. And then the transformation matrix between end coordination system and world coordination system is solved. Validation experiment is implemented for verifying the proposed algorithms. Firstly, hand-eye transformation matrix is solved. Then a car body rear is measured for 16 times for the global data fusion algorithm verification. And the 3D shape of the rear is reconstructed successfully.

Structural Dynamics of Electronic Systems

NASA Astrophysics Data System (ADS)

Suhir, E.

2013-03-01

The published work on analytical ("mathematical") and computer-aided, primarily finite-element-analysis (FEA) based, predictive modeling of the dynamic response of electronic systems to shocks and vibrations is reviewed. While understanding the physics of and the ability to predict the response of an electronic structure to dynamic loading has been always of significant importance in military, avionic, aeronautic, automotive and maritime electronics, during the last decade this problem has become especially important also in commercial, and, particularly, in portable electronics in connection with accelerated testing of various surface mount technology (SMT) systems on the board level. The emphasis of the review is on the nonlinear shock-excited vibrations of flexible printed circuit boards (PCBs) experiencing shock loading applied to their support contours during drop tests. At the end of the review we provide, as a suitable and useful illustration, the exact solution to a highly nonlinear problem of the dynamic response of a "flexible-and-heavy" PCB to an impact load applied to its support contour during drop testing.

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Grey fuzzy optimization model for water quality management of a river system

NASA Astrophysics Data System (ADS)

Karmakar, Subhankar; Mujumdar, P. P.

2006-07-01

A grey fuzzy optimization model is developed for water quality management of river system to address uncertainty involved in fixing the membership functions for different goals of Pollution Control Agency (PCA) and dischargers. The present model, Grey Fuzzy Waste Load Allocation Model (GFWLAM), has the capability to incorporate the conflicting goals of PCA and dischargers in a deterministic framework. The imprecision associated with specifying the water quality criteria and fractional removal levels are modeled in a fuzzy mathematical framework. To address the imprecision in fixing the lower and upper bounds of membership functions, the membership functions themselves are treated as fuzzy in the model and the membership parameters are expressed as interval grey numbers, a closed and bounded interval with known lower and upper bounds but unknown distribution information. The model provides flexibility for PCA and dischargers to specify their aspirations independently, as the membership parameters for different membership functions, specified for different imprecise goals are interval grey numbers in place of a deterministic real number. In the final solution optimal fractional removal levels of the pollutants are obtained in the form of interval grey numbers. This enhances the flexibility and applicability in decision-making, as the decision-maker gets a range of optimal solutions for fixing the final decision scheme considering technical and economic feasibility of the pollutant treatment levels. Application of the GFWLAM is illustrated with case study of the Tunga-Bhadra river system in India.

Computer simulation of the activity of the elderly person living independently in a Health Smart Home.

PubMed

Noury, N; Hadidi, T

2012-12-01

We propose a simulator of human activities collected with presence sensors in our experimental Health Smart Home "Habitat Intelligent pour la Sante (HIS)". We recorded 1492 days of data on several experimental HIS during the French national project "AILISA". On these real data, we built a mathematical model of the behavior of the data series, based on "Hidden Markov Models" (HMM). The model is then played on a computer to produce simulated data series with added flexibility to adjust the parameters in various scenarios. We also tested several methods to measure the similarity between our real and simulated data. Our simulator can produce large data base which can be further used to evaluate the algorithms to raise an alarm in case of loss in autonomy. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

STABCAR: A program for finding characteristic root systems having transcendental stability matrices

NASA Technical Reports Server (NTRS)

Adams, W. M., Jr.; Tiffany, S. H.; Newsom, J. R.; Peele, E. L.

1984-01-01

STABCAR can be used to determine the characteristic roots of flexible, actively controlled aircraft, including the effects of unsteady aerodynamics. A modal formulation and a transfer-matrix representation of the control system are employed. Operable in either a batch or an interactive mode, STABCAR can provide graphical or tabular output of the variation of the roots with velocity, density, altitude, dynamic pressure or feedback gains. Herein the mathematical model, program structure, input requirements, output capabilities, and a series of sample cases are detailed. STABCAR was written for use on CDC CYBER 175 equipment; modification would be required for operation on other machines.

Traction curves for the decohesion of covalent crystals

NASA Astrophysics Data System (ADS)

Enrique, Raúl A.; Van der Ven, Anton

2017-01-01

We study, by first principles, the energy versus separation curves for the cleavage of a family of covalent crystals with the diamond and zincblende structure. We find that there is universality in the curves for different materials which is chemistry independent but specific to the geometry of the particular cleavage plane. Since these curves do not strictly follow the universal binding energy relationship (UBER), we present a derivation of an extension to this relationship that includes non-linear force terms. This extended form of UBER allows for a flexible and practical mathematical description of decohesion curves that can be applied to the quantification of cohesive zone models.

Active Vibration Control of Elastic Beam by Means of Shape Memory Alloy Layers

NASA Technical Reports Server (NTRS)

Chen, Q.; Levy, C.

1996-01-01

The mathematical model of a flexible beam covered with shape memory alloy (SMA) layers is presented. The SMA layers are used as actuators, which are capable of changing their elastic modulus and recovery stress, thus changing the natural frequency of, and adjusting the excitation to, the vibrating beam. The frequency factor variation as a function of SMA Young's modulus, SMA layer thickness and beam thickness is discussed. Also control of the beam employing an optimal linear control law is evaluated. The control results indicate how the system reacts to various levels of excitation input through the non-homogeneous recovery shear term of the governing differential equation.

Spherical roller bearing analysis. SKF computer program SPHERBEAN. Volume 1: Analysis

NASA Technical Reports Server (NTRS)

Kleckner, R. J.; Pirvics, J.

1980-01-01

The models and associated mathematics used within the SPHERBEAN computer program for prediction of the thermomechanical performance characteristics of high speed lubricated double row spherical roller bearings are presented. The analysis allows six degrees of freedom for each roller and three for each half of an optionally split cage. Roller skew, free lubricant, inertial loads, appropriate elastic and friction forces, and flexible outer ring are considered. Roller quasidynamic equilibrium is calculated for a bearing with up to 30 rollers per row, and distinct roller and flange geometries are specifiable. The user is referred to the material contained here for formulation assumptions and algorithm detail.

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.

Idealized models of the joint probability distribution of wind speeds

NASA Astrophysics Data System (ADS)

Monahan, Adam H.

2018-05-01

The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.

Two's company, three (or more) is a simplex : Algebraic-topological tools for understanding higher-order structure in neural data.

PubMed

Giusti, Chad; Ghrist, Robert; Bassett, Danielle S

2016-08-01

The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit of interest in a brain is a dyad - two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model. Here, we describe a generalization of graphs that overcomes these limitations, thereby offering a broad range of new possibilities in terms of modeling and measuring neural phenomena. Specifically, we explore the use of simplicial complexes: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. We review the underlying mathematical formalism as well as the budding literature applying simplicial complexes to neural data, from electrophysiological recordings in animal models to hemodynamic fluctuations in humans. Based on the exceptional flexibility of the tools and recent ground-breaking insights into neural function, we posit that this framework has the potential to eclipse graph theory in unraveling the fundamental mysteries of cognition.

Getting more from accuracy and response time data: methods for fitting the linear ballistic accumulator.

PubMed

Donkin, Chris; Averell, Lee; Brown, Scott; Heathcote, Andrew

2009-11-01

Cognitive models of the decision process provide greater insight into response time and accuracy than do standard ANOVA techniques. However, such models can be mathematically and computationally difficult to apply. We provide instructions and computer code for three methods for estimating the parameters of the linear ballistic accumulator (LBA), a new and computationally tractable model of decisions between two or more choices. These methods-a Microsoft Excel worksheet, scripts for the statistical program R, and code for implementation of the LBA into the Bayesian sampling software WinBUGS-vary in their flexibility and user accessibility. We also provide scripts in R that produce a graphical summary of the data and model predictions. In a simulation study, we explored the effect of sample size on parameter recovery for each method. The materials discussed in this article may be downloaded as a supplement from http://brm.psychonomic-journals.org/content/supplemental.

Petri net-based dependability modeling methodology for reconfigurable field programmable gate arrays

NASA Astrophysics Data System (ADS)

Graczyk, Rafał; Orleański, Piotr; Poźniak, Krzysztof

2015-09-01

Dependability modeling is an important issue for aerospace and space equipment designers. From system level perspective, one has to choose from multitude of possible architectures, redundancy levels, component combinations in a way to meet desired properties and dependability and finally fit within required cost and time budgets. Modeling of such systems is getting harder as its levels of complexity grow together with demand for more functional and flexible, yet more available systems that govern more and more crucial parts of our civilization's infrastructure (aerospace transport systems, telecommunications, exploration probes). In this article promising method of modeling complex systems using Petri networks is introduced in context of qualitative and quantitative dependability analysis. This method, although with some limitation and drawback offer still convenient visual formal method of describing system behavior on different levels (functional, timing, random events) and offers straight correspondence to underlying mathematical engine, perfect for simulations and engineering support.

Rule-based graph theory to enable exploration of the space system architecture design space

NASA Astrophysics Data System (ADS)

Arney, Dale Curtis

The primary goal of this research is to improve upon system architecture modeling in order to enable the exploration of design space options. A system architecture is the description of the functional and physical allocation of elements and the relationships, interactions, and interfaces between those elements necessary to satisfy a set of constraints and requirements. The functional allocation defines the functions that each system (element) performs, and the physical allocation defines the systems required to meet those functions. Trading the functionality between systems leads to the architecture-level design space that is available to the system architect. The research presents a methodology that enables the modeling of complex space system architectures using a mathematical framework. To accomplish the goal of improved architecture modeling, the framework meets five goals: technical credibility, adaptability, flexibility, intuitiveness, and exhaustiveness. The framework is technically credible, in that it produces an accurate and complete representation of the system architecture under consideration. The framework is adaptable, in that it provides the ability to create user-specified locations, steady states, and functions. The framework is flexible, in that it allows the user to model system architectures to multiple destinations without changing the underlying framework. The framework is intuitive for user input while still creating a comprehensive mathematical representation that maintains the necessary information to completely model complex system architectures. Finally, the framework is exhaustive, in that it provides the ability to explore the entire system architecture design space. After an extensive search of the literature, graph theory presents a valuable mechanism for representing the flow of information or vehicles within a simple mathematical framework. Graph theory has been used in developing mathematical models of many transportation and network flow problems in the past, where nodes represent physical locations and edges represent the means by which information or vehicles travel between those locations. In space system architecting, expressing the physical locations (low-Earth orbit, low-lunar orbit, etc.) and steady states (interplanetary trajectory) as nodes and the different means of moving between the nodes (propulsive maneuvers, etc.) as edges formulates a mathematical representation of this design space. The selection of a given system architecture using graph theory entails defining the paths that the systems take through the space system architecture graph. A path through the graph is defined as a list of edges that are traversed, which in turn defines functions performed by the system. A structure to compactly represent this information is a matrix, called the system map, in which the column indices are associated with the systems that exist and row indices are associated with the edges, or functions, to which each system has access. Several contributions have been added to the state of the art in space system architecture analysis. The framework adds the capability to rapidly explore the design space without the need to limit trade options or the need for user interaction during the exploration process. The unique mathematical representation of a system architecture, through the use of the adjacency, incidence, and system map matrices, enables automated design space exploration using stochastic optimization processes. The innovative rule-based graph traversal algorithm ensures functional feasibility of each system architecture that is analyzed, and the automatic generation of the system hierarchy eliminates the need for the user to manually determine the relationships between systems during or before the design space exploration process. Finally, the rapid evaluation of system architectures for various mission types enables analysis of the system architecture design space for multiple destinations within an evolutionary exploration program. (Abstract shortened by UMI.).

Design and optimal control of on-orbit servicing trajectory for target vehicle in non-coplanar elliptical orbit

NASA Astrophysics Data System (ADS)

Zhou, Wenyong; Yuan, Jianping; Luo, Jianjun

2005-11-01

Autonomous on-orbit servicing provides flexibility to space systems and has great value both in civil and in military. When a satellite performs on-orbit servicing tasks, flying around is the basic type of motion. This paper is concerned with the design and control problems of a chaser satellite flying around a target spacecraft in non-coplanar elliptical orbit for a long time. At first, a mathematical model used to design a long-term flying around trajectory is presented, which is applicable to the situation that the target spacecraft flies in an elliptical orbit. The conditions of the target at the centre of the flying around path are deduced. Considering the safety and task requirements, a long-term flying around trajectory is designed. Taking into account perturbations and navigation errors which can cause the trajectory unstable and mission impossible, a two-impulse control method is put forward. Genetic algorithm is used to minimize the cost function which considers fuel consumption and bias simultaneously. Some simulation works are carried out and the results indicate the flying around mathematical model and the trajectory control method can be used in the design and control of a long-term flying around trajectory.

Dynamic characteristics of a variable-mass flexible missile: Dynamics of a two-stage variable-mass flexible rocket

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1969-01-01

The dynamic characteristics of two-stage slender elastic body were investigated. The first stage, containing a solid-fuel rocket, possesses variable mass while the second stage, envisioned as a flexible case, contains packaged instruments of constant mass. The mathematical formulation was in terms of vector equations of motion transformed by a variational principle into sets of scalar differential equations in terms of generalized coordinates. Solutions to the complete equations were obtained numerically by means of finite difference techniques. The problem has been programmed in the FORTRAN 4 language and solved on an IBM 360/50 computer. Results for limited cases are presented showing the nature of the solutions.

Flexible rotor dynamics analysis

NASA Technical Reports Server (NTRS)

Shen, F. A.

1973-01-01

A digital computer program was developed to analyze the general nonaxisymmetric and nonsynchronous transient and steady-state rotor dynamic performance of a bending- and shear-wise flexible rotor-bearing system under various operating conditions. The effects of rotor material mechanical hysteresis, rotor torsion flexibility, transverse effects of rotor axial and torsional loading and the anisotropic, in-phase and out-of-phase bearing stiffness and damping force and moment coefficients were included in the program to broaden its capability. An optimum solution method was found and incorporated in the computer program. Computer simulation of experimental data was made and qualitative agreements observed. The mathematical formulations, computer program verification, test data simulation, and user instruction was presented and discussed.

Relaxed Poisson cure rate models.

PubMed

Rodrigues, Josemar; Cordeiro, Gauss M; Cancho, Vicente G; Balakrishnan, N

2016-03-01

The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Automated data processing and radioassays.

PubMed

Samols, E; Barrows, G H

1978-04-01

Radioassays include (1) radioimmunoassays, (2) competitive protein-binding assays based on competition for limited antibody or specific binding protein, (3) immunoradiometric assay, based on competition for excess labeled antibody, and (4) radioreceptor assays. Most mathematical models describing the relationship between labeled ligand binding and unlabeled ligand concentration have been based on the law of mass action or the isotope dilution principle. These models provide useful data reduction programs, but are theoretically unfactory because competitive radioassay usually is not based on classical dilution principles, labeled and unlabeled ligand do not have to be identical, antibodies (or receptors) are frequently heterogenous, equilibrium usually is not reached, and there is probably steric and cooperative influence on binding. An alternative, more flexible mathematical model based on the probability or binding collisions being restricted by the surface area of reactive divalent sites on antibody and on univalent antigen has been derived. Application of these models to automated data reduction allows standard curves to be fitted by a mathematical expression, and unknown values are calculated from binding data. The vitrues and pitfalls are presented of point-to-point data reduction, linear transformations, and curvilinear fitting approaches. A third-order polynomial using the square root of concentration closely approximates the mathematical model based on probability, and in our experience this method provides the most acceptable results with all varieties of radioassays. With this curvilinear system, linear point connection should be used between the zero standard and the beginning of significant dose response, and also towards saturation. The importance is stressed of limiting the range of reported automated assay results to that portion of the standard curve that delivers optimal sensitivity. Published methods for automated data reduction of Scatchard plots for radioreceptor assay are limited by calculation of a single mean K value. The quality of the input data is generally the limiting factor in achieving good precision with automated as it is with manual data reduction. The major advantages of computerized curve fitting include: (1) handling large amounts of data rapidly and without computational error; (2) providing useful quality-control data; (3) indicating within-batch variance of the test results; (4) providing ongoing quality-control charts and between assay variance.

Spontaneous knotting of an agitated string.

PubMed

Raymer, Dorian M; Smith, Douglas E

2007-10-16

It is well known that a jostled string tends to become knotted; yet the factors governing the "spontaneous" formation of various knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings. We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose a simple model to describe the knot formation based on random "braid moves" of the string end. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length.

Characterizing the topology of probabilistic biological networks.

PubMed

Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2013-01-01

Biological interactions are often uncertain events, that may or may not take place with some probability. This uncertainty leads to a massive number of alternative interaction topologies for each such network. The existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. In this paper, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. Using our mathematical representation, we develop a method that can accurately describe the degree distribution of such networks. We also take one more step and extend our method to accurately compute the joint-degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. Our method works quickly even for entire protein-protein interaction (PPI) networks. It also helps us find an adequate mathematical model using MLE. We perform a comparative study of node-degree and joint-degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. Our results confirm that power-law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected. We also show that probabilistic networks are more robust for node-degree distribution computation than the deterministic ones. all the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/projects/probNet/.

A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer

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

Liu, Yifang; Lee, Chi-Guhn; Chan, Timothy C. Y., E-mail: tcychan@mie.utoronto.ca

2014-02-15

Purpose: To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy. Methods: The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxelsmore » on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity. Results: The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict. Conclusions: By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer.« less

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.

Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency

NASA Astrophysics Data System (ADS)

Papalexiou, Simon Michael

2018-05-01

Hydroclimatic processes come in all "shapes and sizes". They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific "parent" Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.

A real time Pegasus propulsion system model for VSTOL piloted simulation evaluation

NASA Technical Reports Server (NTRS)

Mihaloew, J. R.; Roth, S. P.; Creekmore, R.

1981-01-01

A real time propulsion system modeling technique suitable for use in man-in-the-loop simulator studies was developd. This technique provides the system accuracy, stability, and transient response required for integrated aircraft and propulsion control system studies. A Pegasus-Harrier propulsion system was selected as a baseline for developing mathematical modeling and simulation techniques for VSTOL. Initially, static and dynamic propulsion system characteristics were modeled in detail to form a nonlinear aerothermodynamic digital computer simulation of a Pegasus engine. From this high fidelity simulation, a real time propulsion model was formulated by applying a piece-wise linear state variable methodology. A hydromechanical and water injection control system was also simulated. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model was programmed for interfacing with a Harrier aircraft simulation. Typical propulsion system simulation results are presented.

Does lake size matter? Combining morphology and process modeling to examine the contribution of lake classes to population-scale processes

USGS Publications Warehouse

Winslow, Luke A.; Read, Jordan S.; Hanson, Paul C.; Stanley, Emily H.

2014-01-01

With lake abundances in the thousands to millions, creating an intuitive understanding of the distribution of morphology and processes in lakes is challenging. To improve researchers’ understanding of large-scale lake processes, we developed a parsimonious mathematical model based on the Pareto distribution to describe the distribution of lake morphology (area, perimeter and volume). While debate continues over which mathematical representation best fits any one distribution of lake morphometric characteristics, we recognize the need for a simple, flexible model to advance understanding of how the interaction between morphometry and function dictates scaling across large populations of lakes. These models make clear the relative contribution of lakes to the total amount of lake surface area, volume, and perimeter. They also highlight the critical thresholds at which total perimeter, area and volume would be evenly distributed across lake size-classes have Pareto slopes of 0.63, 1 and 1.12, respectively. These models of morphology can be used in combination with models of process to create overarching “lake population” level models of process. To illustrate this potential, we combine the model of surface area distribution with a model of carbon mass accumulation rate. We found that even if smaller lakes contribute relatively less to total surface area than larger lakes, the increasing carbon accumulation rate with decreasing lake size is strong enough to bias the distribution of carbon mass accumulation towards smaller lakes. This analytical framework provides a relatively simple approach to upscaling morphology and process that is easily generalizable to other ecosystem processes.

Classification and disease prediction via mathematical programming

NASA Astrophysics Data System (ADS)

Lee, Eva K.; Wu, Tsung-Lin

2007-11-01

In this chapter, we present classification models based on mathematical programming approaches. We first provide an overview on various mathematical programming approaches, including linear programming, mixed integer programming, nonlinear programming and support vector machines. Next, we present our effort of novel optimization-based classification models that are general purpose and suitable for developing predictive rules for large heterogeneous biological and medical data sets. Our predictive model simultaneously incorporates (1) the ability to classify any number of distinct groups; (2) the ability to incorporate heterogeneous types of attributes as input; (3) a high-dimensional data transformation that eliminates noise and errors in biological data; (4) the ability to incorporate constraints to limit the rate of misclassification, and a reserved-judgment region that provides a safeguard against over-training (which tends to lead to high misclassification rates from the resulting predictive rule) and (5) successive multi-stage classification capability to handle data points placed in the reserved judgment region. To illustrate the power and flexibility of the classification model and solution engine, and its multigroup prediction capability, application of the predictive model to a broad class of biological and medical problems is described. Applications include: the differential diagnosis of the type of erythemato-squamous diseases; predicting presence/absence of heart disease; genomic analysis and prediction of aberrant CpG island meythlation in human cancer; discriminant analysis of motility and morphology data in human lung carcinoma; prediction of ultrasonic cell disruption for drug delivery; identification of tumor shape and volume in treatment of sarcoma; multistage discriminant analysis of biomarkers for prediction of early atherosclerois; fingerprinting of native and angiogenic microvascular networks for early diagnosis of diabetes, aging, macular degeneracy and tumor metastasis; prediction of protein localization sites; and pattern recognition of satellite images in classification of soil types. In all these applications, the predictive model yields correct classification rates ranging from 80% to 100%. This provides motivation for pursuing its use as a medical diagnostic, monitoring and decision-making tool.

Magic in the machine: a computational magician's assistant

PubMed Central

Williams, Howard; McOwan, Peter W.

2014-01-01

A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required. The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced. Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact. In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect. We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London. PMID:25452736

Direct imaging of defect formation in strained organic flexible electronics by Scanning Kelvin Probe Microscopy

PubMed Central

Cramer, Tobias; Travaglini, Lorenzo; Lai, Stefano; Patruno, Luca; de Miranda, Stefano; Bonfiglio, Annalisa; Cosseddu, Piero; Fraboni, Beatrice

2016-01-01

The development of new materials and devices for flexible electronics depends crucially on the understanding of how strain affects electronic material properties at the nano-scale. Scanning Kelvin-Probe Microscopy (SKPM) is a unique technique for nanoelectronic investigations as it combines non-invasive measurement of surface topography and surface electrical potential. Here we show that SKPM in non-contact mode is feasible on deformed flexible samples and allows to identify strain induced electronic defects. As an example we apply the technique to investigate the strain response of organic thin film transistors containing TIPS-pentacene patterned on polymer foils. Controlled surface strain is induced in the semiconducting layer by bending the transistor substrate. The amount of local strain is quantified by a mathematical model describing the bending mechanics. We find that the step-wise reduction of device performance at critical bending radii is caused by the formation of nano-cracks in the microcrystal morphology of the TIPS-pentacene film. The cracks are easily identified due to the abrupt variation in SKPM surface potential caused by a local increase in resistance. Importantly, the strong surface adhesion of microcrystals to the elastic dielectric allows to maintain a conductive path also after fracture thus providing the opportunity to attenuate strain effects. PMID:27910889

Cost of Oil and Biomass Supply Shocks under Different Biofuel Supply Chain Configurations

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

Uria Martinez, Rocio; Leiby, Paul Newsome; Brown, Maxwell L.

This analysis estimates the cost of selected oil and biomass supply shocks for producers and consumers in the light-duty vehicle fuel market under various supply chain configurations using a mathematical programing model, BioTrans. The supply chain configurations differ by whether they include selected flexibility levers: multi-feedstock biorefineries; advanced biomass logistics; and the ability to adjust ethanol content of low-ethanol fuel blends, from E10 to E15 or E05. The simulated scenarios explore market responses to supply shocks including substitution between gasoline and ethanol, substitution between different sources of ethanol supply, biorefinery capacity additions or idling, and price adjustments. Welfare effects formore » the various market participants represented in BioTrans are summarized into a net shock cost measure. As oil accounts for a larger fraction of fuel by volume, its supply shocks are costlier than biomass supply shocks. Corn availability and the high cost of adding biorefinery capacity limit increases in ethanol use during gasoline price spikes. During shocks that imply sudden decreases in the price of gasoline, the renewable fuel standard (RFS) biofuel blending mandate limits the extent to which flexibility can be exercised to reduce ethanol use. The selected flexibility levers are most useful in response to cellulosic biomass supply shocks.« less

Mathematical Model and Calibration Experiment of a Large Measurement Range Flexible Joints 6-UPUR Six-Axis Force Sensor

PubMed Central

Zhao, Yanzhi; Zhang, Caifeng; Zhang, Dan; Shi, Zhongpan; Zhao, Tieshi

2016-01-01

Nowadays improving the accuracy and enlarging the measuring range of six-axis force sensors for wider applications in aircraft landing, rocket thrust, and spacecraft docking testing experiments has become an urgent objective. However, it is still difficult to achieve high accuracy and large measuring range with traditional parallel six-axis force sensors due to the influence of the gap and friction of the joints. Therefore, to overcome the mentioned limitations, this paper proposed a 6-Universal-Prismatic-Universal-Revolute (UPUR) joints parallel mechanism with flexible joints to develop a large measurement range six-axis force sensor. The structural characteristics of the sensor are analyzed in comparison with traditional parallel sensor based on the Stewart platform. The force transfer relation of the sensor is deduced, and the force Jacobian matrix is obtained using screw theory in two cases of the ideal state and the state of flexibility of each flexible joint is considered. The prototype and loading calibration system are designed and developed. The K value method and least squares method are used to process experimental data, and in errors of kind Ι and kind II linearity are obtained. The experimental results show that the calibration error of the K value method is more than 13.4%, and the calibration error of the least squares method is 2.67%. The experimental results prove the feasibility of the sensor and the correctness of the theoretical analysis which are expected to be adopted in practical applications. PMID:27529244

A generative spike train model with time-structured higher order correlations.

PubMed

Trousdale, James; Hu, Yu; Shea-Brown, Eric; Josić, Krešimir

2013-01-01

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics.

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.

Corresponding Habits of Mind and Mathematical Ability

NASA Astrophysics Data System (ADS)

Dwirahayu, G.; Kustiawati, D.; Bidari, I.

2017-09-01

Objective of learning process regarding system of Indonesia government should be consist of knowledge, attitudes, and skills, or in general we call cognitive, affective and psychomotor. These objective are apply to mathematics education also. Attitude in mathematics known as habits of mind. The teacher should create a learning objective which including all, cognitive, affective and psychomotor. In general, math teachers in Indonesia pay attention to aspects of knowledge, and they ignore other aspects. Habits of mind is term which means the tendency to behave intellectually or intelligently when faced with problems which is immediately known solution. This article examines the math teacher’s attention to students’ habits of mind. The research done by survey method to 38 students at Islamic School 32 Jakarta academic year 2015/2016 from April to May 2016. Habits of mind are observed in this research restricted to persisting, thinking about thinking, thinking flexible and applying past knowledge to new situation. Based on survey, conclude that teacher, without realizing, they have to improve students’ habits of mind, as long as teaching and learning only persisting and thinking about thinking are already well developed, while flexible thinking and applying past knowledge to new situation has not well developed. We hope, math teacher can pay attention not only cognitive aspect but habits of mind also.

Mathematical correlation of modal parameter identification methods via system realization theory

NASA Technical Reports Server (NTRS)

Juang, J. N.

1986-01-01

A unified approach is introduced using system realization theory to derive and correlate modal parameter identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal parameter identification.

Attitude and vibration control of a satellite containing flexible solar arrays by using reaction wheels, and piezoelectric transducers as sensors and actuators

NASA Astrophysics Data System (ADS)

da Fonseca, Ijar M.; Rade, Domingos A.; Goes, Luiz C. S.; de Paula Sales, Thiago

2017-10-01

The primary purpose of this paper is to provide insight into control-structure interaction for satellites comprising flexible appendages and internal moving components. The physical model considered herein aiming to attend such purpose is a rigid-flexible satellite consisting of a rigid platform containing two rotating flexible solar panels. The solar panels rotation is assumed to be in a sun-synchronous configuration mode. The panels contain surface-bonded piezoelectric patches that can be used either as sensors for the elastic displacements or as actuators to counteract the vibration motion. It is assumed that in the normal mode operation the satellite platform points towards the Earth while the solar arrays rotate so as to follow the Sun. The vehicle moves in a low Earth polar orbit. The technique used to obtain the mathematical model combines the Lagrangian formulation with the Finite Elements Method used to describe the dynamics of the solar panel. The gravity-gradient torque as well as the torque due to the interaction of the Earth magnetic field and the satellite internal residual magnetic moment is included as environmental perturbations. The actuators are three reaction wheels for attitude control and piezoelectric actuators to control the flexible motion of the solar arrays. Computer simulations are performed using the MATLAB® software package. The following on-orbit satellite operating configurations are object of analysis: i) Satellite pointing towards the Earth (Earth acquisition maneuver) by considering the initial conditions in the elastic displacement equal to zero, aiming the assessment of the flexible modes excitation by the referred maneuver; ii) the satellite pointing towards the Earth with the assumption of an initial condition different from zero for the flexible motion such that the attitude alterations are checked against the elastic motion disturbance; and iii) attitude acquisition accomplished by taking into account initial conditions different from zero for both attitude and elastic vibrations. Additionally, the control efforts for the three cases are compared. Results indicate that the attitude control is able to excite the solar panels' vibration modes and vice-versa. The piezoelectric vibration control shows significant performance improvement when compared to contributions of the attitude control to the vibration damping.

Characterizing Representational Learning: A Combined Simulation and Tutorial on Perturbation Theory

ERIC Educational Resources Information Center

Kohnle, Antje; Passante, Gina

2017-01-01

Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them ("representational competence") is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of…

Mapping functional connectivity

Treesearch

Peter Vogt; Joseph R. Ferrari; Todd R. Lookingbill; Robert H. Gardner; Kurt H. Riitters; Katarzyna Ostapowicz

2009-01-01

An objective and reliable assessment of wildlife movement is important in theoretical and applied ecology. The identification and mapping of landscape elements that may enhance functional connectivity is usually a subjective process based on visual interpretations of species movement patterns. New methods based on mathematical morphology provide a generic, flexible,...

The effects of flagellar hook compliance on motility of monotrichous bacteria: A modeling study

NASA Astrophysics Data System (ADS)

Shum, H.; Gaffney, E. A.

2012-06-01

A crucial structure in the motility of flagellated bacteria is the hook, which connects the flagellum filament to the motor in the cell body. Early mathematical models of swimming bacteria assume that the helically shaped flagellum rotates rigidly about its axis, which coincides with the axis of the cell body. Motivated by evidence that the hook is much more flexible than the rest of the flagellum, we develop a new model that allows a naturally straight hook to bend. Hook dynamics are based on the Kirchhoff rod model, which is combined with a boundary element method for solving viscous interactions between the bacterium and the surrounding fluid. For swimming in unbounded fluid, we find good support for using a rigid model since the hook reaches an equilibrium configuration within several revolutions of the motor. However, for effective swimming, there are constraints on the hook stiffness relative to the scale set by the product of the motor torque with the hook length. When the hook is too flexible, its shape cannot be maintained and large deformations and stresses build up. When the hook is too rigid, the flagellum does not align with the cell body axis and the cell "wobbles" with little net forward motion. We also examine the attraction of swimmers to no-slip surfaces and find that the tendency to swim steadily close to a surface can be very sensitive to the combination of the hook rigidity and the precise shape of the cell and flagellum.

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

NASA Astrophysics Data System (ADS)

Leadenham, Stephen; Erturk, Alper

2014-04-01

There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no geometric constraint.

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.

Measurement of Residual Flexibility for Substructures Having Prominent Flexible Interfaces

NASA Technical Reports Server (NTRS)

Tinker, Michael L.; Bookout, Paul S.

1994-01-01

Verification of a dynamic model of a constrained structure requires a modal survey test of the physical structure and subsequent modification of the model to obtain the best agreement possible with test data. Constrained-boundary or fixed-base testing has historically been the most common approach for verifying constrained mathematical models, since the boundary conditions of the test article are designed to match the actual constraints in service. However, there are difficulties involved with fixed-base testing, in some cases making the approach impractical. It is not possible to conduct a truly fixed-base test due to coupling between the test article and the fixture. In addition, it is often difficult to accurately simulate the actual boundary constraints, and the cost of designing and constructing the fixture may be prohibitive. For use when fixed-base testing proves impractical or undesirable, alternate free-boundary test methods have been investigated, including the residual flexibility technique. The residual flexibility approach has been treated analytically in considerable detail and has had limited frequency response measurements for the method. This concern is well-justified for a number of reasons. First, residual flexibilities are very small numbers, typically on the order of 1.0E-6 in/lb for translational diagonal terms, and orders of magnitude smaller for off-diagonal values. This poses difficulty in obtaining accurate and noise-free measurements, especially for points removed from the excitation source. A second difficulty encountered in residual measurements lies in obtaining a clean residual function in the process of subtracting synthesized modal data from a measured response function. Inaccuracies occur since modes are not subtracted exactly, but only to the accuracy of the curve fits for each mode; these errors are compounded with increasing distance from the excitation point. In this paper, the residual flexibility method is applied to a simple structure in both test and analysis. Measured and predicted residual functions are compared, and regions of poor data in the measured curves are described. It is found that for accurate residual measurements, frequency response functions having prominent stiffness lines in the acceleration/force format are needed. The lack of such stiffness lines increases measurement errors. Interface drive point frequency respose functions for shuttle orbiter payloads exhibit dominant stiffness lines, making the residual test approach a good candidate for payload modal tests when constrained tests are inappropriate. Difficulties in extracting a residual flexibility value from noisy test data are discussed. It is shown that use of a weighted second order least-squares curve fit of the measured residual function allows identification of residual flexibility that compares very well with predictions for the simple structure. This approach also provides an estimate of second order residual mass effects.

Flagella bending affects macroscopic properties of bacterial suspensions

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

Potomkin, M.; Tournus, M.; Berlyand, L. V.

To survive in harsh conditions, motile bacteria swim in complex environments and respond to the surrounding flow. Here, we develop a mathematical model describing how flagella bending affects macroscopic properties of bacterial suspensions. First, we show how the flagella bending contributes to the decrease in the effective viscosity observed in dilute suspension. Our results do not impose tumbling (random reorientation) as was previously done to explain the viscosity reduction. Second, we demonstrate how a bacterium escapes from wall entrapment due to the self-induced buckling of flagella. Our results shed light on the role of flexible bacterial flagella in interactions ofmore » bacteria with shear flow and walls or obstacles.« less

A mathematical model for Vertical Attitude Takeoff and Landing (VATOL) aircraft simulation. Volume 3: User's manual for VATOL simulation program

NASA Technical Reports Server (NTRS)

Fortenbaugh, R. L.

1980-01-01

Instructions for using Vertical Attitude Takeoff and Landing Aircraft Simulation (VATLAS), the digital simulation program for application to vertical attitude takeoff and landing (VATOL) aircraft developed for installation on the NASA Ames CDC 7600 computer system are described. The framework for VATLAS is the Off-Line Simulation (OLSIM) routine. The OLSIM routine provides a flexible framework and standardized modules which facilitate the development of off-line aircraft simulations. OLSIM runs under the control of VTOLTH, the main program, which calls the proper modules for executing user specified options. These options include trim, stability derivative calculation, time history generation, and various input-output options.

Optical processing for future computer networks

NASA Technical Reports Server (NTRS)

Husain, A.; Haugen, P. R.; Hutcheson, L. D.; Warrior, J.; Murray, N.; Beatty, M.

1986-01-01

In the development of future data management systems, such as the NASA Space Station, a major problem represents the design and implementation of a high performance communication network which is self-correcting and repairing, flexible, and evolvable. To obtain the goal of designing such a network, it will be essential to incorporate distributed adaptive network control techniques. The present paper provides an outline of the functional and communication network requirements for the Space Station data management system. Attention is given to the mathematical representation of the operations being carried out to provide the required functionality at each layer of communication protocol on the model. The possible implementation of specific communication functions in optics is also considered.

A Novel Approach to Photonic Generation and Modulation of Ultra-Wideband Pulses

NASA Astrophysics Data System (ADS)

Xiang, Peng; Guo, Hao; Chen, Dalei; Zhu, Huatao

2016-01-01

A novel approach to photonic generation of ultra-wideband (UWB) signals is proposed in this paper. The proposed signal generator is capable of generating UWB doublet pulses with flexible reconfigurability, and many different pulse modulation formats, including the commonly used pulse-position modulation (PPM) and bi-phase modulation (BPM) can be realized. Moreover, the photonic UWB pulse generator is capable of generating UWB signals with a tunable spectral notch-band, which is desirable to realize the interference avoidance between UWB and other narrow band systems, such as Wi-Fi. A mathematical model describing the proposed system is developed and the generation of UWB signals with different modulation formats is demonstrated via computer simulations.

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

NASA Technical Reports Server (NTRS)

Glasby, Ryan S.; Erwin, J. Taylor; Stefanski, Douglas L.; Allmaras, Steven R.; Galbraith, Marshall C.; Anderson, W. Kyle; Nichols, Robert H.

2016-01-01

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented.

Fractals in the Classroom

ERIC Educational Resources Information Center

Fraboni, Michael; Moller, Trisha

2008-01-01

Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

Brain Stretchers Book 4--Advanced.

ERIC Educational Resources Information Center

Anderson, Carolyn

This book provides puzzles, games, and mathematical activities for students in elementary grades. Number concepts and arithmetic are common topics. These classic math, logic, and word-problem activities encourage students to become flexible, creative thinkers while teaching them to draw valid conclusions based on logic and evidence. Each activity…

SURF's Up: An Outline of an Innovative Framework for Teaching Mental Computation to Students in the Early Years of Schooling

ERIC Educational Resources Information Center

Russo, James

2015-01-01

In this article James Russo presents the Strategies, Understanding, Reading and Fast Facts Framework (SURF) for mental computation. He explains how this framework can be used to deepen mathematical understanding and build mental flexibility.

Survey of meshless and generalized finite element methods: A unified approach

NASA Astrophysics Data System (ADS)

Babuška, Ivo; Banerjee, Uday; Osborn, John E.

In the past few years meshless methods for numerically solving partial differential equations have come into the focus of interest, especially in the engineering community. This class of methods was essentially stimulated by difficulties related to mesh generation. Mesh generation is delicate in many situations, for instance, when the domain has complicated geometry; when the mesh changes with time, as in crack propagation, and remeshing is required at each time step; when a Lagrangian formulation is employed, especially with nonlinear PDEs. In addition, the need for flexibility in the selection of approximating functions (e.g., the flexibility to use non-polynomial approximating functions), has played a significant role in the development of meshless methods. There are many recent papers, and two books, on meshless methods; most of them are of an engineering character, without any mathematical analysis.In this paper we address meshless methods and the closely related generalized finite element methods for solving linear elliptic equations, using variational principles. We give a unified mathematical theory with proofs, briefly address implementational aspects, present illustrative numerical examples, and provide a list of references to the current literature.The aim of the paper is to provide a survey of a part of this new field, with emphasis on mathematics. We present proofs of essential theorems because we feel these proofs are essential for the understanding of the mathematical aspects of meshless methods, which has approximation theory as a major ingredient. As always, any new field is stimulated by and related to older ideas. This will be visible in our paper.

On continuous and discontinuous approaches for modeling groundwater flow in heterogeneous media using the Numerical Manifold Method: Model development and comparison

NASA Astrophysics Data System (ADS)

Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny

2015-06-01

One major challenge in modeling groundwater flow within heterogeneous geological media is that of modeling arbitrarily oriented or intersected boundaries and inner material interfaces. The Numerical Manifold Method (NMM) has recently emerged as a promising method for such modeling, in its ability to handle boundaries, its flexibility in constructing physical cover functions (continuous or with gradient jump), its meshing efficiency with a fixed mathematical mesh (covers), its convenience for enhancing approximation precision, and its integration precision, achieved by simplex integration. In this paper, we report on developing and comparing two new approaches for boundary constraints using the NMM, namely a continuous approach with jump functions and a discontinuous approach with Lagrange multipliers. In the discontinuous Lagrange multiplier method (LMM), the material interfaces are regarded as discontinuities which divide mathematical covers into different physical covers. We define and derive stringent forms of Lagrange multipliers to link the divided physical covers, thus satisfying the continuity requirement of the refraction law. In the continuous Jump Function Method (JFM), the material interfaces are regarded as inner interfaces contained within physical covers. We briefly define jump terms to represent the discontinuity of the head gradient across an interface to satisfy the refraction law. We then make a theoretical comparison between the two approaches in terms of global degrees of freedom, treatment of multiple material interfaces, treatment of small area, treatment of moving interfaces, the feasibility of coupling with mechanical analysis and applicability to other numerical methods. The newly derived boundary-constraint approaches are coded into a NMM model for groundwater flow analysis, and tested for precision and efficiency on different simulation examples. We first test the LMM for a Dirichlet boundary and then test both LMM and JFM for an idealized heterogeneous model, comparing the numerical results with analytical solutions. Then we test both approaches for a heterogeneous model and compare the results of hydraulic head and specific discharge. We show that both approaches are suitable for modeling material boundaries, considering high accuracy for the boundary constraints, the capability to deal with arbitrarily oriented or complexly intersected boundaries, and their efficiency using a fixed mathematical mesh.

A network biology approach to denitrification in Pseudomonas aeruginosa

DOE PAGES

Arat, Seda; Bullerjahn, George S.; Laubenbacher, Reinhard

2015-02-23

Pseudomonas aeruginosa is a metabolically flexible member of the Gammaproteobacteria. Under anaerobic conditions and the presence of nitrate, P. aeruginosa can perform (complete) denitrification, a respiratory process of dissimilatory nitrate reduction to nitrogen gas via nitrite (NO₂), nitric oxide (NO) and nitrous oxide (N₂O). This study focuses on understanding the influence of environmental conditions on bacterial denitrification performance, using a mathematical model of a metabolic network in P. aeruginosa. To our knowledge, this is the first mathematical model of denitrification for this bacterium. Analysis of the long-term behavior of the network under changing concentration levels of oxygen (O₂), nitrate (NO₃),more » and phosphate (PO₄) suggests that PO₄ concentration strongly affects denitrification performance. The model provides three predictions on denitrification activity of P. aeruginosa under various environmental conditions, and these predictions are either experimentally validated or supported by pertinent biological literature. One motivation for this study is to capture the effect of PO₄ on a denitrification metabolic network of P. aeruginosa in order to shed light on mechanisms for greenhouse gas N₂O accumulation during seasonal oxygen depletion in aquatic environments such as Lake Erie (Laurentian Great Lakes, USA). Simulating the microbial production of greenhouse gases in anaerobic aquatic systems such as Lake Erie allows a deeper understanding of the contributing environmental effects that will inform studies on, and remediation strategies for, other hypoxic sites worldwide.« less

Energy-based culture medium design for biomanufacturing optimization: A case study in monoclonal antibody production by GS-NS0 cells.

PubMed

Quiroga-Campano, Ana L; Panoskaltsis, Nicki; Mantalaris, Athanasios

2018-03-02

Demand for high-value biologics, a rapidly growing pipeline, and pressure from competition, time-to-market and regulators, necessitate novel biomanufacturing approaches, including Quality by Design (QbD) principles and Process Analytical Technologies (PAT), to facilitate accelerated, efficient and effective process development platforms that ensure consistent product quality and reduced lot-to-lot variability. Herein, QbD and PAT principles were incorporated within an innovative in vitro-in silico integrated framework for upstream process development (UPD). The central component of the UPD framework is a mathematical model that predicts dynamic nutrient uptake and average intracellular ATP content, based on biochemical reaction networks, to quantify and characterize energy metabolism and its adaptive response, metabolic shifts, to maintain ATP homeostasis. The accuracy and flexibility of the model depends on critical cell type/product/clone-specific parameters, which are experimentally estimated. The integrated in vitro-in silico platform and the model's predictive capacity reduced burden, time and expense of experimentation resulting in optimal medium design compared to commercially available culture media (80% amino acid reduction) and a fed-batch feeding strategy that increased productivity by 129%. The framework represents a flexible and efficient tool that transforms, improves and accelerates conventional process development in biomanufacturing with wide applications, including stem cell-based therapies. Copyright © 2018. Published by Elsevier Inc.

Capacitive pressure-sensitive composites using nickel-silicone rubber: experiments and modeling

NASA Astrophysics Data System (ADS)

Fan, Yuqin; Liao, Changrong; Liao, Ganliang; Tan, Renbing; Xie, Lei

2017-07-01

Capacitive pressure (i.e., piezo-capacitive) sensors have manifested their superiority as a potential electronic skin. The mechanism of the traditional piezo-capacitive sensors is mainly to change the relative permittivity of the flexible composites by compressing the specially fabricated microstructures in the polymer matrix under pressure. Instead, we study the piezo-capacitive effect for a newly reported isotropic flexible composite consisting of silicone rubber (SR) and uniformly dispersed micron-sized conductive nickel particles experimentally and theoretically. The Young’s modulus of the nickel-SR composites (NSRCs) is designed to meet that of human skin. Experimental results show that the NSRCs exhibit remarkable particle concentration dependent capacitance response under uniaxial pressure, and the NSRCs present a good repeatability. We propose a mathematical model at particle level to provide deep insights into the piezo-capacitive mechanism, by considering the adjacent particles in the axial direction as micro capacitors connected in series and in parallel on the horizontal plane. The piezo-capacitive effect is determined by the relative permittivity induced by the particles rearrangement, longitudinal interparticle gap, and deflection angle of micro particle capacitors under pressure. Specifically, the relative capacitance of NSRC capacitor is deduced to be product of two factors: the degree of particle rearrangement, and the relative capacitance of a micro capacitor with the average longitudinal gap. The proposed model well matches and interprets the experimental results.

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

PubMed

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

2017-12-01

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

Generalizing Prototype Theory: A Formal Quantum Framework

PubMed Central

Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro

2016-01-01

Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436

(Re)evaluating the Implications of the Autoregressive Latent Trajectory Model Through Likelihood Ratio Tests of Its Initial Conditions.

PubMed

Ou, Lu; Chow, Sy-Miin; Ji, Linying; Molenaar, Peter C M

2017-01-01

The autoregressive latent trajectory (ALT) model synthesizes the autoregressive model and the latent growth curve model. The ALT model is flexible enough to produce a variety of discrepant model-implied change trajectories. While some researchers consider this a virtue, others have cautioned that this may confound interpretations of the model's parameters. In this article, we show that some-but not all-of these interpretational difficulties may be clarified mathematically and tested explicitly via likelihood ratio tests (LRTs) imposed on the initial conditions of the model. We show analytically the nested relations among three variants of the ALT model and the constraints needed to establish equivalences. A Monte Carlo simulation study indicated that LRTs, particularly when used in combination with information criterion measures, can allow researchers to test targeted hypotheses about the functional forms of the change process under study. We further demonstrate when and how such tests may justifiably be used to facilitate our understanding of the underlying process of change using a subsample (N = 3,995) of longitudinal family income data from the National Longitudinal Survey of Youth.

Vibration isolation by exploring bio-inspired structural nonlinearity.

PubMed

Wu, Zhijing; Jing, Xingjian; Bian, Jing; Li, Fengming; Allen, Robert

2015-10-08

Inspired by the limb structures of animals/insects in motion vibration control, a bio-inspired limb-like structure (LLS) is systematically studied for understanding and exploring its advantageous nonlinear function in passive vibration isolation. The bio-inspired system consists of asymmetric articulations (of different rod lengths) with inside vertical and horizontal springs (as animal muscle) of different linear stiffness. Mathematical modeling and analysis of the proposed LLS reveal that, (a) the system has very beneficial nonlinear stiffness which can provide flexible quasi-zero, zero and/or negative stiffness, and these nonlinear stiffness properties are adjustable or designable with structure parameters; (b) the asymmetric rod-length ratio and spring-stiffness ratio present very beneficial factors for tuning system equivalent stiffness; (c) the system loading capacity is also adjustable with the structure parameters which presents another flexible benefit in application. Experiments and comparisons with existing quasi-zero-stiffness isolators validate the advantageous features above, and some discussions are also given about how to select structural parameters for practical applications. The results would provide an innovative bio-inspired solution to passive vibration control in various engineering practice.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Students' Perceptions of Learning Mode in Mathematics

ERIC Educational Resources Information Center

Krishnan, Saras

2016-01-01

Blended courses or hybrid courses have gained popularity over the years because of their flexibility and convenience. Technology use in the online component of the blended/hybrid courses is another influence particularly to the younger generation of learners who enjoy learning interactively in a virtual environment. However, depending on the…

The Design and Operation of an Effective Math Laboratory.

ERIC Educational Resources Information Center

Brown, Donald E.

A mathematics laboratory is discussed in terms of (1) administrative support, (2) personnel, (3) curriculum design, (4) flexibility in design and equipment, (5) professional counseling, and (6) motivational devices. The discussion focuses upon the remedial math lab at Alvin Community College, Alvin, Texas. The roles of instructors, lab…

Improving Procedural Knowledge and Transfer by Teaching a Shortcut Strategy First

ERIC Educational Resources Information Center

DeCaro, Marci S.

2015-01-01

Students often memorize and apply procedures to solve mathematics problems without understanding why these procedures work. In turn, students demonstrate limited ability to transfer strategies to new problem types. Math curriculum reform standards underscore the importance of procedural flexibility and transfer, emphasizing that students need to…

DESIGNS FOR SMALL HIGH SCHOOLS.

ERIC Educational Resources Information Center

NIMNICHT, GLENDON P.; PARTRIDGE, ARTHUR R.

BY MULTIPLE-CLASS TEACHING AND FLEXIBLE SCHEDULING, SMALL HIGH SCHOOLS CAN OFFER EDUCATIONAL PROGRAMS COMPARABLE TO THOSE OFFERED BY LARGE HIGH SCHOOLS. WITH ATTENTION TO FACILITY DESIGN, NOT ONLY CAN SCIENCE, MATHEMATICS, FOREIGN LANGUAGE, ART, BUSINESS, INDUSTRIAL ARTS, HOMEMAKING, ENGLISH, AND SOCIAL STUDIES BE OFFERED TO TWO OR MORE GROUPS OF…

Design and Analysis of a Continuous Split Typed Needle-Free Injection System for Animal Vaccination.

PubMed

Chen, Kai; Pan, Min; Liu, Tingting

2017-01-01

Liquid needle-free injection devices (NFIDs) employ a high-velocity liquid jet to deliver drugs and vaccine through transdermal injection. NFIDs for animal vaccination are more complicated than those used for human beings for their much larger and more flexible power sources, as well as rapid, repetitive and continuous injection features. In the paper, spring-powered NFID is designed for animal vaccine injection. For convenience, the device is a split into a power source and handheld injector. A mathematical model is proposed to calculate the injection pressure, taking into the account pressure loss and the strain energy loss in the bendable tube due to elastic deformation. An experimental apparatus was build to verify the calculation results. Under the same system conditions, the calculation results of the dynamic injection pressure match the experimental results. It is found that the bendable tube of the split typed NFID has significant impact on the profile of the injection pressure. The initial peak pressure is less than the initial peak pressure of NFID without bendable tube, and there is occurrence time lag of the peak pressure. The mathematical model is the first attempt to reveal the relationship between the injection pressure and the system variables of split typed NFID.

A Modeling and Experimental Investigation of the Effects of Antigen Density, Binding Affinity, and Antigen Expression Ratio on Bispecific Antibody Binding to Cell Surface Targets*

PubMed Central

Rhoden, John J.; Dyas, Gregory L.

2016-01-01

Despite the increasing number of multivalent antibodies, bispecific antibodies, fusion proteins, and targeted nanoparticles that have been generated and studied, the mechanism of multivalent binding to cell surface targets is not well understood. Here, we describe a conceptual and mathematical model of multivalent antibody binding to cell surface antigens. Our model predicts that properties beyond 1:1 antibody:antigen affinity to target antigens have a strong influence on multivalent binding. Predicted crucial properties include the structure and flexibility of the antibody construct, the target antigen(s) and binding epitope(s), and the density of antigens on the cell surface. For bispecific antibodies, the ratio of the expression levels of the two target antigens is predicted to be critical to target binding, particularly for the lower expressed of the antigens. Using bispecific antibodies of different valencies to cell surface antigens including MET and EGF receptor, we have experimentally validated our modeling approach and its predictions and observed several nonintuitive effects of avidity related to antigen density, target ratio, and antibody affinity. In some biological circumstances, the effect we have predicted and measured varied from the monovalent binding interaction by several orders of magnitude. Moreover, our mathematical framework affords us a mechanistic interpretation of our observations and suggests strategies to achieve the desired antibody-antigen binding goals. These mechanistic insights have implications in antibody engineering and structure/activity relationship determination in a variety of biological contexts. PMID:27022022

Semantic modeling of plastic deformation of polycrystalline rock

NASA Astrophysics Data System (ADS)

Babaie, Hassan A.; Davarpanah, Armita

2018-02-01

We have developed the first iteration of the Plastic Rock Deformation (PRD) ontology by modeling the semantics of a selected set of deformational processes and mechanisms that produce, reconfigure, displace, and/or consume the material components of inhomogeneous polycrystalline rocks. The PRD knowledge model also classifies and formalizes the properties (relations) that hold between instances of the dynamic physical and chemical processes and the rock components, the complex physio-chemical, mathematical, and informational concepts of the plastic rock deformation system, the measured or calculated laboratory testing conditions, experimental procedures and protocols, the state and system variables, and the empirical flow laws that define the inter-relationships among the variables. The ontology reuses classes and properties from several existing ontologies that are built for physics, chemistry, biology, and mathematics. With its flexible design, the PRD ontology is well positioned to incrementally develop into a model that more fully represents the knowledge of plastic deformation of polycrystalline rocks in the future. The domain ontology will be used to consistently annotate varied data and information related to the microstructures and the physical and chemical processes that produce them at different spatial and temporal scales in the laboratory and in the solid Earth. The PRDKB knowledge base, when built based on the ontology, will help the community of experimental structural geologists and metamorphic petrologists to coherently and uniformly distribute, discover, access, share, and use their data through automated reasoning and integration and query of heterogeneous experimental deformation data that originate from autonomous rock testing laboratories.

TSAR, a new graph-theoretical approach to computational modeling of protein side-chain flexibility: modeling of ionization properties of proteins.

PubMed

Stroganov, Oleg V; Novikov, Fedor N; Zeifman, Alexey A; Stroylov, Viktor S; Chilov, Ghermes G

2011-09-01

A new graph-theoretical approach called thermodynamic sampling of amino acid residues (TSAR) has been elaborated to explicitly account for the protein side chain flexibility in modeling conformation-dependent protein properties. In TSAR, a protein is viewed as a graph whose nodes correspond to structurally independent groups and whose edges connect the interacting groups. Each node has its set of states describing conformation and ionization of the group, and each edge is assigned an array of pairwise interaction potentials between the adjacent groups. By treating the obtained graph as a belief-network-a well-established mathematical abstraction-the partition function of each node is found. In the current work we used TSAR to calculate partition functions of the ionized forms of protein residues. A simplified version of a semi-empirical molecular mechanical scoring function, borrowed from our Lead Finder docking software, was used for energy calculations. The accuracy of the resulting model was validated on a set of 486 experimentally determined pK(a) values of protein residues. The average correlation coefficient (R) between calculated and experimental pK(a) values was 0.80, ranging from 0.95 (for Tyr) to 0.61 (for Lys). It appeared that the hydrogen bond interactions and the exhaustiveness of side chain sampling made the most significant contribution to the accuracy of pK(a) calculations. Copyright © 2011 Wiley-Liss, Inc.

The AquaDEB project (phase I): Analysing the physiological flexibility of aquatic species and connecting physiological diversity to ecological and evolutionary processes by using Dynamic Energy Budgets

NASA Astrophysics Data System (ADS)

Alunno-Bruscia, Marianne; van der Veer, Henk W.; Kooijman, Sebastiaan A. L. M.

2009-08-01

The European Research Project AquaDEB (2007-2011, http://www.ifremer.fr/aquadeb/) is joining skills and expertise of some French and Dutch research institutes and universities to analyse the physiological flexibility of aquatic organisms and to link it to ecological and evolutionary processes within a common theoretical framework for quantitative bioenergetics [Kooijman, S.A.L.M., 2000. Dynamic energy and mass budgets in biological systems. Cambridge University Press, Cambridge]. The main scientific objectives in AquaDEB are i) to study and compare the sensitivity of aquatic species (mainly molluscs and fish) to environmental variability of natural or human origin, and ii) to evaluate the related consequences at different biological levels (individual, population, ecosystem) and temporal scales (life cycle, population dynamics, evolution). At mid-term life, the AquaDEB collaboration has already yielded interesting results by quantifying bio-energetic processes of various aquatic species (e.g. molluscs, fish, crustaceans, algae) with a single mathematical framework. It has also allowed to federate scientists with different backgrounds, e.g. mathematics, microbiology, ecology, chemistry, and working in different fields, e.g. aquaculture, fisheries, ecology, agronomy, ecotoxicology, climate change. For the two coming years, the focus of the AquaDEB collaboration will be in priority: (i) to compare energetic and physiological strategies among species through the DEB parameter values and to identify the factors responsible for any differences in bioenergetics and physiology; and to compare dynamic (DEB) versus static (SEB) energy models to study the physiological performance of aquatic species; (ii) to consider different scenarios of environmental disruption (excess of nutrients, diffuse or massive pollution, exploitation by man, climate change) to forecast effects on growth, reproduction and survival of key species; (iii) to scale up the models for a few species from the individual level up to the level of evolutionary processes.

A Formal Valuation Framework for Emotions and Their Control.

PubMed

Huys, Quentin J M; Renz, Daniel

2017-09-15

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

Increasing operating room productivity by duration categories and a newsvendor model.

PubMed

Lehtonen, Juha-Matti; Torkki, Paulus; Peltokorpi, Antti; Moilanen, Teemu

2013-01-01

Previous studies approach surgery scheduling mainly from the mathematical modeling perspective which is often hard to apply in a practical environment. The aim of this study is to develop a practical scheduling system that considers the advantages of both surgery categorization and newsvendor model to surgery scheduling. The research was carried out in a Finnish orthopaedic specialist centre that performs only joint replacement surgery. Four surgery categorization scenarios were defined and their productivity analyzed by simulation and newsvendor model. Detailed analyses of surgery durations and the use of more accurate case categories and their combinations in scheduling improved OR productivity 11.3 percent when compared to the base case. Planning to have one OR team to work longer led to remarkable decrease in scheduling inefficiency. In surgical services, productivity and cost-efficiency can be improved by utilizing historical data in case scheduling and by increasing flexibility in personnel management. The study increases the understanding of practical scheduling methods used to improve efficiency in surgical services.

Using discrete multi-physics for detailed exploration of hydrodynamics in an in vitro colon system.

PubMed

Alexiadis, A; Stamatopoulos, K; Wen, W; Batchelor, H K; Bakalis, S; Barigou, M; Simmons, M J H

2017-02-01

We developed a mathematical model that describes the motion of viscous fluids in the partially-filled colon caused by the periodic contractions of flexible walls (peristalsis). In-vitro data are used to validate the model. The model is then used to identify two fundamental mechanisms of mass transport: the surfing mode and the pouring mode. The first mechanism is faster, but only involves the surface of the liquid. The second mechanism causes deeper mixing, and appears to be the main transport mechanism. Based on the gained understanding, we propose a series of measures that can improve the reliability of in-vitro models. The tracer in PET-like experiments, in particular, should not be injected in the first pocket, and its viscosity should be as close as possible to that of the fluid. If these conditions are not met, the dynamics of the tracer and the fluid diverge, compromising the accuracy of the in-vitro data. Copyright © 2017 Elsevier Ltd. All rights reserved.

Hybrid computational phantoms of the 15-year male and female adolescent: Applications to CT organ dosimetry for patients of variable morphometry

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

Lee, Choonsik; Lodwick, Daniel; Williams, Jonathan L.

Currently, two classes of the computational phantoms have been developed for dosimetry calculation: (1) stylized (or mathematical) and (2) voxel (or tomographic) phantoms describing human anatomy through mathematical surface equations and three-dimensional labeled voxel matrices, respectively. Mathematical surface equations in stylized phantoms provide flexibility in phantom design and alteration, but the resulting anatomical description is, in many cases, not very realistic. Voxel phantoms display far better anatomical realism, but they are limited in terms of their ability to alter organ shape, position, and depth, as well as body posture. A new class of computational phantoms - called hybrid phantoms -more » takes advantage of the best features of stylized and voxel phantoms - flexibility and anatomical realism, respectively. In the current study, hybrid computational phantoms representing reference 15-year male and female body anatomy and anthropometry are presented. For the male phantom, organ contours were extracted from the University of Florida (UF) 14-year series B male voxel phantom, while for the female phantom, original computed tomography (CT) data from two 14-year female patients were used. Polygon mesh models for the major organs and tissues were reconstructed for nonuniform rational B-spline (NURBS) surface modeling. The resulting NURBS/polygon mesh models representing body contour and internal anatomy were matched to anthropometric data and reference organ mass data provided by the Centers for Disease Control and Prevention (CDC) and the International Commission on Radiation Protection (ICRP), respectively. Finally, two hybrid 15-year male and female phantoms were completed where a total of eight anthropometric data categories were matched to standard values within 4% and organ masses matched to ICRP data within 1% with the exception of total skin. To highlight the flexibility of the hybrid phantoms, 10th and 90th weight percentile 15-year male and female phantoms were further developed from the 50th percentile phantoms through adjustments in the body contour to match the total body masses given in CDC pediatric growth curves. The resulting six NURBS phantoms, male and female phantoms representing their 10th, 50th, and 90th weight percentiles, were used to investigate the influence of body fat distributions on internal organ doses following CT imaging. The phantoms were exposed to multislice chest and abdomen helical CT scans, and in-field organ absorbed doses were calculated. The results demonstrated that the use of traditional stylized phantoms yielded organ dose estimates that deviate from those given by the UF reference hybrid phantoms by up to a factor of 2. The study also showed that use of reference, or 50th percentile, phantoms to assess organ doses in underweight 15-year-old children would not lead to significant organ dose errors (typically less than 10%). However, more significant errors were noted (up to {approx}30%) when reference phantoms are used to represent overweight children in CT imaging dosimetry. These errors are expected to only further increase as one considers CT organ doses in overweight and obese individuals of the adult patient population, thus emphasizing the advantages of patient-sculptable phantom technology.« less

In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400

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

Oginni, B.M.; Bronson, F.L.; Field, M.B.

2012-07-01

Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extensionmore » to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can now be used for quickly and accurately evaluating efficiencies for wider range of gamma-ray spectroscopy applications. (authors)« less

Using assessment to individualize early mathematics instruction.

PubMed

Connor, Carol McDonald; Mazzocco, Michèle M M; Kurz, Terri; Crowe, Elizabeth C; Tighe, Elizabeth L; Wood, Taffeta S; Morrison, Frederick J

2018-02-01

Accumulating evidence suggests that assessment-informed personalized instruction, tailored to students' individual skills and abilities, is more effective than more one-size-fits-all approaches. In this study, we evaluate the efficacy of Individualizing Student Instruction in Mathematics (ISI-Math) compared to Reading (ISI-Reading) where classrooms were randomly assigned to ISI-Math or ISI-Reading. The literature on child characteristics X instruction or skill X treatment interaction effects point to the complexities of tailoring instruction for individual students who present with constellations of skills. Second graders received mathematics instruction in small flexible learning groups based on their assessed learning needs. Results of the study (n=32 teachers, 370 students) revealed significant treatment effects on standardized mathematics assessments. With effect sizes (d) of 0.41-0.60, we show that we can significantly improve 2nd graders' mathematics achievement, including for children living in poverty, by using assessment data to individualize the mathematics instruction they receive. The instructional regime, ISI-Math, was implemented by regular classroom teachers and it led to about a 4-month achievement advantage on standardized mathematics tests when compared to students in control classrooms. These results were realized within one school year. Moreover, treatment effects were the same regardless of school-level poverty and students' gender, initial mathematics or vocabulary scores. Copyright © 2017 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Predictive models of control strategies involved in containing indoor airborne infections.

PubMed

Chen, S-C; Chang, C-F; Liao, C-M

2006-12-01

Recently developed control measure modeling approaches for containing airborne infections, including engineering controls with respiratory protection and public health interventions, are readily amenable to an integrated-scale analysis. Here we show that such models can be derived from an integrated-scale analysis generated from three different types of functional relationship: Wells-Riley mathematical model, competing-risks model, and Von Foerster equation, both of the key epidemiological determinants involved and of the functional connections between them. We examine mathematically the impact of engineering control measures such as enhanced air exchange and air filtration rates with personal masking combined with public health interventions such as vaccination, isolation, and contact tracing in containing the spread of indoor airborne infections including influenza, chickenpox, measles, and severe acute respiratory syndrome (SARS). If enhanced engineering controls could reduce the basic reproductive number (R0) below 1.60 for chickenpox and 3 for measles, our simulations show that in such a prepared response with public health interventions would have a high probability of containing the indoor airborne infections. Combinations of engineering control measures and public health interventions could moderately contain influenza strains with an R0 as high as 4. Our analysis indicates that effective isolation of symptomatic patients with low-efficacy contact tracing is sufficient to control a SARS outbreak. We suggest that a valuable added dimension to public health inventions could be provided by systematically quantifying transmissibility and proportion of asymptomatic infection of indoor airborne infection. Practical Implications We have developed a flexible mathematical model that can help determine the best intervention strategies for containing indoor airborne infections. The approach presented here is scalable and can be extended to include additional control efficacies. If a newly emergent airborne infection should appear, the model could be quickly calibrated to data and intervention options at the early stage of the outbreak. Data could be provided from the field to estimate value of R0, the serial interval between cases, the distributions of the latent, incubation, and infectious periods, case fatality rates, and secondary spread within important mixing groups. The combination of enhanced engineering control measures and assigned effective public health interventions would have a high probability for containing airborne infection.

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…

NBOD2- PROGRAM TO DERIVE AND SOLVE EQUATIONS OF MOTION FOR COUPLED N-BODY SYSTEMS

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1994-01-01

The analysis of the dynamic characteristics of a complex system, such as a spacecraft or a robot, is usually best accomplished through the study of a simulation model. The simulation model must have the same dynamic characteristics as the complex system, while lending itself to mathematical quantification. The NBOD2 computer program was developed to aid in the analysis of spacecraft attitude dynamics. NBOD2 is a very general program that may be applied to a large class of problems involving coupled N-body systems. NBOD2 provides the dynamics analyst with the capability to automatically derive and numerically solve the equations of motion for any system that can be modeled as a topological tree of coupled rigid bodies, flexible bodies, point masses, and symmetrical momentum wheels. NBOD2 uses a topological tree model of the dynamic system to derive the vector-dyadic equations of motion for the system. The user builds this topological tree model by using rigid and flexible bodies, point masses, and symmetrical momentum wheels with appropriate connections. To insure that the relative motion between contiguous bodies is kinematically constrained, NBOD2 assumes that contiguous rigid and flexible bodies are connected by physically reliable 0, 1, 2, and 3-degrees-of-freedom gimbals. These gimbals prohibit relative translational motion, while permitting up to 3 degrees of relative rotational freedom at hinge points. Point masses may have 0, 1, 2, or 3-degrees of relative translational freedom, and symmetric momentum wheels may have a single degree of rotational freedom relative to the body in which they are imbedded. Flexible bodies may possess several degrees of vibrational freedom in addition to the degrees of freedom associated with the connection gimbals. Data concerning the natural modes and vibrations of the flexible bodies must be supplied by the user. NBOD2 combines the best features of the discrete-body approach and the nested body approach to reduce the topological tree to a complete set of nonlinear equations of motion in vector-dyadic form for the system being analyzed. NBOD2 can then numerically solve the equations of motion. Input to NBOD2 consists of a user-supplied description of the system to be modeled. The NBOD2 system includes an interactive, tutorial, input support program to aid the NBOD2 user in preparing input data. Output from NBOD2 consists of a listing of the complete set of nonlinear equations of motion in vector-dyadic form and any userspecified set of system state variables. The NBOD2 program is written in FORTRAN 77 for batch execution and has been implemented on a DEC VAX-11/780 computer. The NBOD2 program was developed in 1978 and last updated in 1982.

Students’ Creativity: Problem Posing in Structured Situation

NASA Astrophysics Data System (ADS)

Amalina, I. K.; Amirudin, M.; Budiarto, M. T.

2018-01-01

This is a qualitative research concerning on students’ creativity on problem posing task. The study aimed at describing the students’ creative thinking ability to pose the mathematics problem in structured situations with varied condition of given problems. In order to find out the students’ creative thinking ability, an analysis of mathematics problem posing test based on fluency, novelty, and flexibility and interview was applied for categorizing students’ responses on that task. The data analysis used the quality of problem posing and categorized in 4 level of creativity. The results revealed from 29 secondary students grade 8, a student in CTL (Creative Thinking Level) 1 met the fluency. A student in CTL 2 met the novelty, while a student in CTL 3 met both fluency and novelty and no one in CTL 4. These results are affected by students’ mathematical experience. The findings of this study highlight that student’s problem posing creativity are dependent on their experience in mathematics learning and from the point of view of which students start to pose problem.

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…

Study of the Employment Status of Block Program Graduates. Teacher Education Forum; Volume 4, Number 7.

ERIC Educational Resources Information Center

Buffie, Edward G.

The Block Program is one of five major options at Indiana University, Bloomington, for students preparing to become elementary teachers. The project emphasizes team approach to instruction; flexibility of program; carefully articulated work with respect to preparation in language arts, mathematics, science, and social studies; carefully…

Accountability and Virginia Public Schools, 2014-2015 School Year

ERIC Educational Resources Information Center

Virginia Department of Education, 2014

2014-01-01

This report explains that The Elementary and Secondary Education Act (ESEA)--known since 2001 as No Child Left Behind (NCLB)--requires states to set annual objectives for increasing student achievement in reading and mathematics and closing achievement gaps among student subgroups. Under the flexibility waiver granted by the US Department of…

A Joyful Classroom Learning System with Robot Learning Companion for Children to Learn Mathematics Multiplication

ERIC Educational Resources Information Center

Wei, Chun-Wang; Hung, I-Chun; Lee, Ling; Chen, Nian-Shing

2011-01-01

This research demonstrates the design of a Joyful Classroom Learning System (JCLS) with flexible, mobile and joyful features. The theoretical foundations of this research include the experiential learning theory, constructivist learning theory and joyful learning. The developed JCLS consists of the robot learning companion (RLC), sensing input…

Multimedia Open Educational Resources in Mathematics for High School Students with Learning Disabilities

ERIC Educational Resources Information Center

Park, Sanghoon; McLeod, Kenneth

2018-01-01

Open Educational Resources (OER) can offer educators the necessary flexibility for tailoring educational resources to better fit their educational goals. Although the number of OER repositories is growing fast, few studies have been conducted to empirically test the effectiveness of OER integration in the classroom. Furthermore, very little is…

Examining the Flexibility Bind in American Tenure and Promotion Processes: An Institutional Ethnographic Approach

ERIC Educational Resources Information Center

Jones, Kyle; Beddoes, Kacey; Banerjee, Dina; Pawley, Alice L.

2014-01-01

This paper analyses the role that forms of documentation play in faculty members' experiences of tenure and promotion. Taking an institutional ethnography approach, it examines inconsistencies and ambiguities in documents and connects them to the experiences of science, technology, engineering and mathematics (STEM) faculty at one institution in…

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…

A comparison of hydraulic, pneumatic, and electro-mechanical actuators for general aviation flight controls

NASA Technical Reports Server (NTRS)

Roskam, J.; Rice, M.; Eysink, H.

1979-01-01

Mathematical models for electromechanical (EM), pneumatic and hydraulic actuations are discussed. It is shown that EM and hydraulic actuators provide better and faster time responses than pneumatic actuators but EM actuators utilizing the recently developed samarium-cobalt technology have significant advantages in terms of size, weight and power requirements. In terms of ease and flexibility of installation EM actuators apparently have several advantages over hydraulic actuators, and cost is a primary reason for the popularity of EM actuation for secondary control function since no additional systems need to be added to the aircraft. While new rare earth magnets are currently in developmental stage, costs are relatively high; but continued research should bring prices down.

Parameter learning for performance adaptation

NASA Technical Reports Server (NTRS)

Peek, Mark D.; Antsaklis, Panos J.

1990-01-01

A parameter learning method is introduced and used to broaden the region of operability of the adaptive control system of a flexible space antenna. The learning system guides the selection of control parameters in a process leading to optimal system performance. A grid search procedure is used to estimate an initial set of parameter values. The optimization search procedure uses a variation of the Hooke and Jeeves multidimensional search algorithm. The method is applicable to any system where performance depends on a number of adjustable parameters. A mathematical model is not necessary, as the learning system can be used whenever the performance can be measured via simulation or experiment. The results of two experiments, the transient regulation and the command following experiment, are presented.

TLM-Tracker: software for cell segmentation, tracking and lineage analysis in time-lapse microscopy movies.

PubMed

Klein, Johannes; Leupold, Stefan; Biegler, Ilona; Biedendieck, Rebekka; Münch, Richard; Jahn, Dieter

2012-09-01

Time-lapse imaging in combination with fluorescence microscopy techniques enable the investigation of gene regulatory circuits and uncovered phenomena like culture heterogeneity. In this context, computational image processing for the analysis of single cell behaviour plays an increasing role in systems biology and mathematical modelling approaches. Consequently, we developed a software package with graphical user interface for the analysis of single bacterial cell behaviour. A new software called TLM-Tracker allows for the flexible and user-friendly interpretation for the segmentation, tracking and lineage analysis of microbial cells in time-lapse movies. The software package, including manual, tutorial video and examples, is available as Matlab code or executable binaries at http://www.tlmtracker.tu-bs.de.

On a full Bayesian inference for force reconstruction problems

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.

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.

General approach to polymer chains confined by interacting boundaries

NASA Astrophysics Data System (ADS)

Freed, Karl F.; Dudowicz, Jacek; Stukalin, Evgeny B.; Douglas, Jack F.

2010-09-01

Polymer chains, confined to cavities or polymer layers with dimensions less than the chain radius of gyration, appear in many phenomena, such as gel chromatography, rubber elasticity, viscolelasticity of high molar mass polymer melts, the translocation of polymers through nanopores and nanotubes, polymer adsorption, etc. Thus, the description of how the constraints alter polymer thermodynamic properties is a recurrent theoretical problem. A realistic treatment requires the incorporation of impenetrable interacting (attractive or repulsive) boundaries, a process that introduces significant mathematical complications. The standard approach involves developing the generalized diffusion equation description of the interaction of flexible polymers with impenetrable confining surfaces into a discrete eigenfunction expansion, where the solutions are normally truncated at the first mode (the "ground state dominance" approximation). This approximation is mathematically well justified under conditions of strong confinement, i.e., a confinement length scale much smaller than the chain radius of gyration, but becomes unreliable when the polymers are confined to dimensions comparable to their typically nanoscale size. We extend a general approach to describe polymers under conditions of weak to moderate confinement and apply this semianalytic method specifically to determine the thermodynamics and static structure factor for a flexible polymer confined between impenetrable interacting parallel plate boundaries. The method is first illustrated by analyzing chain partitioning between a pore and a large external reservoir, a model system with application to chromatography. Improved agreement is found for the partition coefficients of a polymer chain in the pore geometry. An expression is derived for the structure factor S(k ) in a slit geometry to assist in more accurately estimating chain dimensions from scattering measurements for thin polymer films.

MOOSE: A parallel computational framework for coupled systems of nonlinear equations.

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

Derek Gaston; Chris Newman; Glen Hansen

Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton-Krylov (JFNK) solution methods. Utilizing the mathematical structure present in JFNK, physics expressions are modularized into `Kernels,'' allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics based preconditioning, which provides great flexibility even with large variance in timemore » scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.« less

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…

Fluid Mechanics of Capillary-Elastic Instabilities in Microgravity Environment

NASA Technical Reports Server (NTRS)

Grotberg, James B.

2002-01-01

The aim of this project is to investigate the closure and reopening of lung airways due to surface tension forces, coupled with airway elasticity. Airways are liquid-lined, flexible tubes and closure of airways can occur by a Rayleigh instability of the liquid lining, or an instability of the elastic support for the airway as the surface tension of the air-liquid interface pulls the tube shut, or both. Regardless of the mechanism, the airway is closed because the liquid lining has created a plug that prevents axial gas exchange. In the microgravity environment, surface tension forces dominate lung mechanics and would lead to more prevalent, and more uniformly distributed air-way closure, thereby creating a potential for respiratory problems for astronauts. Once closed the primary option for reopening an airway is by deep inspiration. This maneuver will pull the flexible airways open and force the liquid plug to flow distally by the incoming air stream. Airway reopening depends to a large extent on this plug flow and how it may lead to plug rupture to regain the continuity of gas between the environment and the alveoli. In addition to mathematical modeling of plug flows in liquid-lined, flexible tubes, this work has involved benchtop studies of propagating liquid plugs down tube networks that mimic the human airway tree. We have extended the work to involve animal models of liquid plug propagation in rat lungs. The liquid is radio-opaque and x-ray video imaging is used to ascertain the movement and distribution of the liquid plugs so that comparisons to theory may be made. This research has other uses, such as the delivery of liquids or drugs into the lung that may be used for surfactant replacement therapy or for liquid ventilation.

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…

Remodeling Pearson's Correlation for Functional Brain Network Estimation and Autism Spectrum Disorder Identification.

PubMed

Li, Weikai; Wang, Zhengxia; Zhang, Limei; Qiao, Lishan; Shen, Dinggang

2017-01-01

Functional brain network (FBN) has been becoming an increasingly important way to model the statistical dependence among neural time courses of brain, and provides effective imaging biomarkers for diagnosis of some neurological or psychological disorders. Currently, Pearson's Correlation (PC) is the simplest and most widely-used method in constructing FBNs. Despite its advantages in statistical meaning and calculated performance, the PC tends to result in a FBN with dense connections. Therefore, in practice, the PC-based FBN needs to be sparsified by removing weak (potential noisy) connections. However, such a scheme depends on a hard-threshold without enough flexibility. Different from this traditional strategy, in this paper, we propose a new approach for estimating FBNs by remodeling PC as an optimization problem, which provides a way to incorporate biological/physical priors into the FBNs. In particular, we introduce an L 1 -norm regularizer into the optimization model for obtaining a sparse solution. Compared with the hard-threshold scheme, the proposed framework gives an elegant mathematical formulation for sparsifying PC-based networks. More importantly, it provides a platform to encode other biological/physical priors into the PC-based FBNs. To further illustrate the flexibility of the proposed method, we extend the model to a weighted counterpart for learning both sparse and scale-free networks, and then conduct experiments to identify autism spectrum disorders (ASD) from normal controls (NC) based on the constructed FBNs. Consequently, we achieved an 81.52% classification accuracy which outperforms the baseline and state-of-the-art methods.

A general modeling framework for describing spatially structured population dynamics

USGS Publications Warehouse

Sample, Christine; Fryxell, John; Bieri, Joanna; Federico, Paula; Earl, Julia; Wiederholt, Ruscena; Mattsson, Brady; Flockhart, Tyler; Nicol, Sam; Diffendorfer, James E.; Thogmartin, Wayne E.; Erickson, Richard A.; Norris, D. Ryan

2017-01-01

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network-based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life-history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network-based population is modeled with discrete time steps. Using both theoretical and real-world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network-based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles

Imaging quality evaluation method of pixel coupled electro-optical imaging system

NASA Astrophysics Data System (ADS)

He, Xu; Yuan, Li; Jin, Chunqi; Zhang, Xiaohui

2017-09-01

With advancements in high-resolution imaging optical fiber bundle fabrication technology, traditional photoelectric imaging system have become ;flexible; with greatly reduced volume and weight. However, traditional image quality evaluation models are limited by the coupling discrete sampling effect of fiber-optic image bundles and charge-coupled device (CCD) pixels. This limitation substantially complicates the design, optimization, assembly, and evaluation image quality of the coupled discrete sampling imaging system. Based on the transfer process of grayscale cosine distribution optical signal in the fiber-optic image bundle and CCD, a mathematical model of coupled modulation transfer function (coupled-MTF) is established. This model can be used as a basis for following studies on the convergence and periodically oscillating characteristics of the function. We also propose the concept of the average coupled-MTF, which is consistent with the definition of traditional MTF. Based on this concept, the relationships among core distance, core layer radius, and average coupled-MTF are investigated.

Performance improvement of an active vibration absorber subsystem for an aircraft model using a bees algorithm based on multi-objective intelligent optimization

NASA Astrophysics Data System (ADS)

Zarchi, Milad; Attaran, Behrooz

2017-11-01

This study develops a mathematical model to investigate the behaviour of adaptable shock absorber dynamics for the six-degree-of-freedom aircraft model in the taxiing phase. The purpose of this research is to design a proportional-integral-derivative technique for control of an active vibration absorber system using a hydraulic nonlinear actuator based on the bees algorithm. This optimization algorithm is inspired by the natural intelligent foraging behaviour of honey bees. The neighbourhood search strategy is used to find better solutions around the previous one. The parameters of the controller are adjusted by minimizing the aircraft's acceleration and impact force as the multi-objective function. The major advantages of this algorithm over other optimization algorithms are its simplicity, flexibility and robustness. The results of the numerical simulation indicate that the active suspension increases the comfort of the ride for passengers and the fatigue life of the structure. This is achieved by decreasing the impact force, displacement and acceleration significantly.

Mathematical modeling of a four-stroke resonant engine for micro and mesoscale applications

NASA Astrophysics Data System (ADS)

Preetham, B. S.; Anderson, M.; Richards, C.

2014-12-01

In order to mitigate frictional and leakage losses in small scale engines, a compliant engine design is proposed in which the piston in cylinder arrangement is replaced by a flexible cavity. A physics-based nonlinear lumped-parameter model is derived to predict the performance of a prototype engine. The model showed that the engine performance depends on input parameters, such as heat input, heat loss, and load on the engine. A sample simulation for a reference engine with octane fuel/air ratio of 0.043 resulted in an indicated thermal efficiency of 41.2%. For a fixed fuel/air ratio, higher output power is obtained for smaller loads and vice-versa. The heat loss from the engine and the work done on the engine during the intake stroke are found to decrease the indicated thermal efficiency. The ratio of friction work to indicated work in the prototype engine is about 8%, which is smaller in comparison to the traditional reciprocating engines.

Shear-induced opening of the coronal magnetic field

NASA Technical Reports Server (NTRS)

Wolfson, Richard

1995-01-01

This work describes the evolution of a model solar corona in response to motions of the footpoints of its magnetic field. The mathematics involved is semianalytic, with the only numerical solution being that of an ordinary differential equation. This approach, while lacking the flexibility and physical details of full MHD simulations, allows for very rapid computation along with complete and rigorous exploration of the model's implications. We find that the model coronal field bulges upward, at first slowly and then more dramatically, in response to footpoint displacements. The energy in the field rises monotonically from that of the initial potential state, and the field configuration and energy appraoch asymptotically that of a fully open field. Concurrently, electric currents develop and concentrate into a current sheet as the limiting case of the open field is approached. Examination of the equations shows rigorously that in the asymptotic limit of the fully open field, the current layer becomes a true ideal MHD singularity.

Semantic Interaction for Sensemaking: Inferring Analytical Reasoning for Model Steering.

PubMed

Endert, A; Fiaux, P; North, C

2012-12-01

Visual analytic tools aim to support the cognitively demanding task of sensemaking. Their success often depends on the ability to leverage capabilities of mathematical models, visualization, and human intuition through flexible, usable, and expressive interactions. Spatially clustering data is one effective metaphor for users to explore similarity and relationships between information, adjusting the weighting of dimensions or characteristics of the dataset to observe the change in the spatial layout. Semantic interaction is an approach to user interaction in such spatializations that couples these parametric modifications of the clustering model with users' analytic operations on the data (e.g., direct document movement in the spatialization, highlighting text, search, etc.). In this paper, we present results of a user study exploring the ability of semantic interaction in a visual analytic prototype, ForceSPIRE, to support sensemaking. We found that semantic interaction captures the analytical reasoning of the user through keyword weighting, and aids the user in co-creating a spatialization based on the user's reasoning and intuition.

Dynamics of a split torque helicopter transmission

NASA Technical Reports Server (NTRS)

Rashidi, Majid; Krantz, Timothy

1992-01-01

A high reduction ratio split torque gear train has been proposed as an alternative to a planetary configuration for the final stage of a helicopter transmission. A split torque design allows a high ratio of power-to-weight for the transmission. The design studied in this work includes a pivoting beam that acts to balance thrust loads produced by the helical gear meshes in each of two parallel power paths. When the thrust loads are balanced, the torque is split evenly. A mathematical model was developed to study the dynamics of the system. The effects of time varying gear mesh stiffness, static transmission errors, and flexible bearing supports are included in the model. The model was demonstrated with a test case. Results show that although the gearbox has a symmetric configuration, the simulated dynamic behavior of the first and second compound gears are not the same. Also, results show that shaft location and mesh stiffness tuning are significant design parameters that influence the motions of the system.

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…

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.

N-mix for fish: estimating riverine salmonid habitat selection via N-mixture models

USGS Publications Warehouse

Som, Nicholas A.; Perry, Russell W.; Jones, Edward C.; De Juilio, Kyle; Petros, Paul; Pinnix, William D.; Rupert, Derek L.

2018-01-01

Models that formulate mathematical linkages between fish use and habitat characteristics are applied for many purposes. For riverine fish, these linkages are often cast as resource selection functions with variables including depth and velocity of water and distance to nearest cover. Ecologists are now recognizing the role that detection plays in observing organisms, and failure to account for imperfect detection can lead to spurious inference. Herein, we present a flexible N-mixture model to associate habitat characteristics with the abundance of riverine salmonids that simultaneously estimates detection probability. Our formulation has the added benefits of accounting for demographics variation and can generate probabilistic statements regarding intensity of habitat use. In addition to the conceptual benefits, model application to data from the Trinity River, California, yields interesting results. Detection was estimated to vary among surveyors, but there was little spatial or temporal variation. Additionally, a weaker effect of water depth on resource selection is estimated than that reported by previous studies not accounting for detection probability. N-mixture models show great promise for applications to riverine resource selection.

Vibration attenuation of the NASA Langley evolutionary structure experiment using H(sub infinity) and structured singular value (micron) robust multivariable control techniques

NASA Technical Reports Server (NTRS)

Balas, Gary J.

1992-01-01

The use is studied of active control to attenuate structural vibrations of the NASA Langley Phase Zero Evolutionary Structure due to external disturbance excitations. H sub infinity and structured singular value (mu) based control techniques are used to analyze and synthesize control laws for the NASA Langley Controls Structures Interaction (CSI) Evolutionary Model (CEM). The CEM structure experiment provides an excellent test bed to address control design issues for large space structures. Specifically, control design for structures with numerous lightly damped, coupled flexible modes, collocated and noncollocated sensors and actuators and stringent performance specifications. The performance objectives are to attenuate the vibration of the structure due to external disturbances, and minimize the actuator control force. The control design problem formulation for the CEM Structure uses a mathematical model developed with finite element techniques. A reduced order state space model for the control design is formulated from the finite element model. It is noted that there are significant variations between the design model and the experimentally derived transfer function data.

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…

Elastic Modulus Determination of Normal and Glaucomatous Human Trabecular Meshwork

PubMed Central

Last, Julie A.; Pan, Tingrui; Ding, Yuzhe; Reilly, Christopher M.; Keller, Kate; Acott, Ted S.; Fautsch, Michael P.; Murphy, Christopher J.; Russell, Paul

2011-01-01

Purpose. Elevated intraocular pressure (IOP) is a risk factor for glaucoma. The principal outflow pathway for aqueous humor in the human eye is through the trabecular meshwork (HTM) and Schlemm's canal (SC). The junction between the HTM and SC is thought to have a significant role in the regulation of IOP. A possible mechanism for the increased resistance to flow in glaucomatous eyes is an increase in stiffness (increased elastic modulus) of the HTM. In this study, the stiffness of the HTM in normal and glaucomatous tissue was compared, and a mathematical model was developed to predict the impact of changes in stiffness of the juxtacanalicular layer of HTM on flow dynamics through this region. Methods. Atomic force microscopy (AFM) was used to measure the elastic modulus of normal and glaucomatous HTM. According to these results, a model was developed that simulated the juxtacanalicular layer of the HTM as a flexible membrane with embedded pores. Results. The mean elastic modulus increased substantially in the glaucomatous HTM (mean = 80.8 kPa) compared with that in the normal HTM (mean = 4.0 kPa). Regional variation was identified across the glaucomatous HTM, possibly corresponding to the disease state. Mathematical modeling suggested an increased flow resistance with increasing HTM modulus. Conclusions. The data indicate that the stiffness of glaucomatous HTM is significantly increased compared with that of normal HTM. Modeling exercises support substantial impairment in outflow facility with increased HTM stiffness. Alterations in the biophysical attributes of the HTM may participate directly in the onset and progression of glaucoma. PMID:21220561

A Modeling and Experimental Investigation of the Effects of Antigen Density, Binding Affinity, and Antigen Expression Ratio on Bispecific Antibody Binding to Cell Surface Targets.

PubMed

Rhoden, John J; Dyas, Gregory L; Wroblewski, Victor J

2016-05-20

Despite the increasing number of multivalent antibodies, bispecific antibodies, fusion proteins, and targeted nanoparticles that have been generated and studied, the mechanism of multivalent binding to cell surface targets is not well understood. Here, we describe a conceptual and mathematical model of multivalent antibody binding to cell surface antigens. Our model predicts that properties beyond 1:1 antibody:antigen affinity to target antigens have a strong influence on multivalent binding. Predicted crucial properties include the structure and flexibility of the antibody construct, the target antigen(s) and binding epitope(s), and the density of antigens on the cell surface. For bispecific antibodies, the ratio of the expression levels of the two target antigens is predicted to be critical to target binding, particularly for the lower expressed of the antigens. Using bispecific antibodies of different valencies to cell surface antigens including MET and EGF receptor, we have experimentally validated our modeling approach and its predictions and observed several nonintuitive effects of avidity related to antigen density, target ratio, and antibody affinity. In some biological circumstances, the effect we have predicted and measured varied from the monovalent binding interaction by several orders of magnitude. Moreover, our mathematical framework affords us a mechanistic interpretation of our observations and suggests strategies to achieve the desired antibody-antigen binding goals. These mechanistic insights have implications in antibody engineering and structure/activity relationship determination in a variety of biological contexts. © 2016 by The American Society for Biochemistry and Molecular Biology, Inc.

Modafinil Reverses Phencyclidine-Induced Deficits in Cognitive Flexibility, Cerebral Metabolism, and Functional Brain Connectivity

PubMed Central

Dawson, Neil; Thompson, Rhiannon J.; McVie, Allan; Thomson, David M.; Morris, Brian J.; Pratt, Judith A.

2012-01-01

Objective: In the present study, we employ mathematical modeling (partial least squares regression, PLSR) to elucidate the functional connectivity signatures of discrete brain regions in order to identify the functional networks subserving PCP-induced disruption of distinct cognitive functions and their restoration by the procognitive drug modafinil. Methods: We examine the functional connectivity signatures of discrete brain regions that show overt alterations in metabolism, as measured by semiquantitative 2-deoxyglucose autoradiography, in an animal model (subchronic phencyclidine [PCP] treatment), which shows cognitive inflexibility with relevance to the cognitive deficits seen in schizophrenia. Results: We identify the specific components of functional connectivity that contribute to the rescue of this cognitive inflexibility and to the restoration of overt cerebral metabolism by modafinil. We demonstrate that modafinil reversed both the PCP-induced deficit in the ability to switch attentional set and the PCP-induced hypometabolism in the prefrontal (anterior prelimbic) and retrosplenial cortices. Furthermore, modafinil selectively enhanced metabolism in the medial prelimbic cortex. The functional connectivity signatures of these regions identified a unifying functional subsystem underlying the influence of modafinil on cerebral metabolism and cognitive flexibility that included the nucleus accumbens core and locus coeruleus. In addition, these functional connectivity signatures identified coupling events specific to each brain region, which relate to known anatomical connectivity. Conclusions: These data support clinical evidence that modafinil may alleviate cognitive deficits in schizophrenia and also demonstrate the benefit of applying PLSR modeling to characterize functional brain networks in translational models relevant to central nervous system dysfunction. PMID:20810469

Reporting Florida's Annual Measurable Objectives (AMOs) in Compliance with ESEA Flexibility Requirements: Guide to Calculations for 2013-14

ERIC Educational Resources Information Center

Florida Department of Education, 2014

2014-01-01

This Annual Measurable Objective (AMO) is designed to keep Florida moving forward toward national and international competitiveness. Florida will compare its National Assessment of Educational Progress (NAEP) scores to those of the top five states and its Trends in International Mathematics and Science Study (TIMSS), Progress in International…

Personalised Learning with Mobile Technologies in Mathematics: An Exploration of Classroom Practice

ERIC Educational Resources Information Center

Willacy, Helen; West, Amie; Murphy, Carol; Calder, Nigel

2017-01-01

Personalised learning is generally understood to be of benefit to students' learning. In addition, the flexible nature of mobile technologies (MTs) and the variety of available apps are seen to respond to the needs of individual students, and hence have the potential to support personalised learning. This paper reports on an aspect of a larger…

An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison

ERIC Educational Resources Information Center

Weng, Pei-Lin; Bouck, Emily C.

2016-01-01

Number comparison is a fundamental skill required for academic and functional mathematics (e.g., time, money, purchasing) for students with disabilities. The most commonly used method to teach number comparison is number lines. Although historically paper number lines are used, app-based number lines may offer greater flexibility. This study…

Adapting Reading and Math Materials for the Inclusive Classroom. Volume 2: Kindergarten through Grade Five. ERIC/OSEP Mini-Library.

ERIC Educational Resources Information Center

Shumm, Jeanne Shay

This book offers guidelines for elementary school teachers for making adaptations in reading and mathematics instruction for students with mild disabilities in the general education classroom. Following an introductory chapter, Chapter 1 presents eight principles for materials adaption organized according to the acronym FLEXIBLE: F-feasible…

Substitution and Sameness: Two Components of a Relational Conception of the Equals Sign

ERIC Educational Resources Information Center

Jones, Ian; Inglis, Matthew; Gilmore, Camilla; Dowens, Margaret

2012-01-01

A sophisticated and flexible understanding of the equals sign (=) is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator and the equals sign as signaling the same value on both sides of the equation. We argue…

LDC and MDC Strategies Help Schools Prepare Students for Careers, Advanced Training and Further Study. Best Practices Newsletter

ERIC Educational Resources Information Center

Southern Regional Education Board (SREB), 2014

2014-01-01

The Literacy Design Collaborative (LDC) and the Mathematics Design Collaborative (MDC) are strategies designed to improve how teachers teach and students learn. The designs encourage teacher collaboration and creativity and offer flexible frameworks for building lessons in all disciplines. Their purpose is to engage students to read challenging…

Teacher Experiences on the Integration of Modern Educational Games in the Middle School Mathematics Classroom

ERIC Educational Resources Information Center

Ritzhaupt, Albert; Higgins, Heidi; Allred, Beth

2010-01-01

What do experienced teachers have to say about integrating modern educational games into their classroom? This paper addresses this question by exploring the discourse of teachers who were provided professional development, technical support, access to a modern educational game, and flexibility in deciding how to integrate the game in their…

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…

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

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

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

Equation-oriented specification of neural models for simulations

PubMed Central

Stimberg, Marcel; Goodman, Dan F. M.; Benichoux, Victor; Brette, Romain

2013-01-01

Simulating biological neuronal networks is a core method of research in computational neuroscience. A full specification of such a network model includes a description of the dynamics and state changes of neurons and synapses, as well as the synaptic connectivity patterns and the initial values of all parameters. A standard approach in neuronal modeling software is to build network models based on a library of pre-defined components and mechanisms; if a model component does not yet exist, it has to be defined in a special-purpose or general low-level language and potentially be compiled and linked with the simulator. Here we propose an alternative approach that allows flexible definition of models by writing textual descriptions based on mathematical notation. We demonstrate that this approach allows the definition of a wide range of models with minimal syntax. Furthermore, such explicit model descriptions allow the generation of executable code for various target languages and devices, since the description is not tied to an implementation. Finally, this approach also has advantages for readability and reproducibility, because the model description is fully explicit, and because it can be automatically parsed and transformed into formatted descriptions. The presented approach has been implemented in the Brian2 simulator. PMID:24550820

Investigation of control system of traction electric drive with feedbacks on load

NASA Astrophysics Data System (ADS)

Kuznetsov, N. K.; Iov, I. A.; Iov, A. A.

2018-03-01

In the article, by the example of a walking excavator, the results of a study of a control system of traction electric drive with a rigid and flexible feedback on the load are mentioned. Based on the analysis of known works, the calculation scheme has been chosen; the equations of motion of the electromechanical system have been obtained, taking into account the elasticity of the rope and feedbacks on the load in the elastic element. A simulation model of this system has been developed and mathematical modeling of the transient processes to evaluate the influence of feedback on the dynamic characteristics of the mechanism and its efficiency of work was carried out. It is shown that the use of rigid and flexible feedbacks makes it possible to reduce dynamic loads in the traction mechanism and to limit the elastic oscillation of the executive mechanism in transient operating modes in comparison with the standard control system; however, there is some decrease in productivity. It has been also established that the sign-variable of the loading of the electric drive, connected with the opening of the backlashes in the gearbox due to the action of feedbacks on the load in the elastic element, under certain conditions, can lead to undesirable phenomena in the operation of the drive and a decrease in the reliability of its operation.

Improved design of support for large aperture space lightweight mirror

NASA Astrophysics Data System (ADS)

Wang, Chao; Ruan, Ping; Liu, Qimin

2013-08-01

In order to design a kind of rational large aperture space mirror which can adapt to the space gravity and thermal environment, by taking the choice of material, the lightweight of the mirror and the design of support into account in detail, a double-deck structure with traditional flexible hinge was designed, then the analytical mathematical model of the mirror system was established. The design adopts six supports on back. in order to avoid the constraints, mirror is connected to three middle transition pieces through six flexible hinges, and then the three transition pieces are connected to support plate through another three flexible hinges. However, the initial structure is unable to reach the expected design target and needs to be made further adjustments. By improving and optimizing the original structure, a new type of flexible hinge in the shape of the letter A is designed finally. Compared with the traditional flexible hinge structure, the new structure is simpler and has less influence on the surface figure accuracy of mirror. By using the finite element analysis method, the static and dynamic characteristics as well as the thermal characteristics of the mirror system are analyzed. Analysis results show that the maximum PV value is 37 nm and the maximum RMS value is 10.4 nm when gravity load is applied. Furthermore, the maximum PV value is 46 nm and the maximum RMS value is 10.5 nm under the load case of gravity coupled with 4℃ uniform temperature rise. The results satisfy the index of optical design. The first order natural frequency of the mirror component is 130 Hz according to the conclusion obtained by modal analytical solution, so the mirror structure has high enough fundamental frequency. And, the structural strength can meet the demand under the overload and the random vibration environment respectively. It indicates that the mirror component structure has enough dynamic, static stiffness and thermal stability, meeting the design requirements.

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…

Constructive biology and approaches to temporal grounding in postreactive robotics

NASA Astrophysics Data System (ADS)

Nehaniv, Chrystopher L.; Dautenhahn, Kerstin; Loomes, Martin J.

1999-08-01

Constructive Biology means understanding biological mechanisms through building systems that exhibit life-like properties. Applications include learning engineering tricks from biological system, as well as the validation in biological modeling. In particular, biological system in the course of development and experience become temporally grounded. Researchers attempting to transcend mere reactivity have been inspired by the drives, motivations, homeostasis, hormonal control, and emotions of animals. In order to contextualize and modulate behavior, these ideas have been introduced into robotics and synthetic agents, while further flexibility is achieved by introducing learning. Broadening scope of the temporal horizon further requires post-reactive techniques that address not only the action in the now, although such action may perhaps be modulated by drives and affect. Support is needed for expressing and benefitting from pats experiences, predictions of the future, and form interaction histories of the self with the world and with other agents. Mathematical methods provide a new way to support such grounding in the construction of post-reactive systems. Moreover, the communication of such mathematical encoded histories of experience between situated agents opens a route to narrative intelligence, analogous to communication or story telling in societies.

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…

Design of optimal groundwater remediation systems under flexible environmental-standard constraints.

PubMed

Fan, Xing; He, Li; Lu, Hong-Wei; Li, Jing

2015-01-01

In developing optimal groundwater remediation strategies, limited effort has been exerted to solve the uncertainty in environmental quality standards. When such uncertainty is not considered, either over optimistic or over pessimistic optimization strategies may be developed, probably leading to the formulation of rigid remediation strategies. This study advances a mathematical programming modeling approach for optimizing groundwater remediation design. This approach not only prevents the formulation of over optimistic and over pessimistic optimization strategies but also provides a satisfaction level that indicates the degree to which the environmental quality standard is satisfied. Therefore the approach may be expected to be significantly more acknowledged by the decision maker than those who do not consider standard uncertainty. The proposed approach is applied to a petroleum-contaminated site in western Canada. Results from the case study show that (1) the peak benzene concentrations can always satisfy the environmental standard under the optimal strategy, (2) the pumping rates of all wells decrease under a relaxed standard or long-term remediation approach, (3) the pumping rates are less affected by environmental quality constraints under short-term remediation, and (4) increased flexible environmental standards have a reduced effect on the optimal remediation strategy.

TRANSURANUS: a fuel rod analysis code ready for use

NASA Astrophysics Data System (ADS)

Lassmann, K.

1992-06-01

TRANSURANUS is a computer program for the thermal and mechanical analysis of fuel rods in nuclear reactors and was developed at the European Institute for Transuranium Elements (TUI). The TRANSURANUS code consists of a clearly defined mechanical-mathematical framework into which physical models can easily be incorporated. Besides its flexibility for different fuel rod designs the TRANSURANUS code can deal with very different situations, as given for instance in an experiment, under normal, off-normal and accident conditions. The time scale of the problems to be treated may range from milliseconds to years. The code has a comprehensive material data bank for oxide, mixed oxide, carbide and nitride fuels, Zircaloy and steel claddings and different coolants. During its development great effort was spent on obtaining an extremely flexible tool which is easy to handle, exhibiting very fast running times. The total development effort is approximately 40 man-years. In recent years the interest to use this code grew and the code is in use in several organisations, both research and private industry. The code is now available to all interested parties. The paper outlines the main features and capabilities of the TRANSURANUS code, its validation and treats also some practical aspects.

The development of a fully-integrated immune response model (FIRM) simulator of the immune response through integration of multiple subset models

PubMed Central

2013-01-01

Background The complexity and multiscale nature of the mammalian immune response provides an excellent test bed for the potential of mathematical modeling and simulation to facilitate mechanistic understanding. Historically, mathematical models of the immune response focused on subsets of the immune system and/or specific aspects of the response. Mathematical models have been developed for the humoral side of the immune response, or for the cellular side, or for cytokine kinetics, but rarely have they been proposed to encompass the overall system complexity. We propose here a framework for integration of subset models, based on a system biology approach. Results A dynamic simulator, the Fully-integrated Immune Response Model (FIRM), was built in a stepwise fashion by integrating published subset models and adding novel features. The approach used to build the model includes the formulation of the network of interacting species and the subsequent introduction of rate laws to describe each biological process. The resulting model represents a multi-organ structure, comprised of the target organ where the immune response takes place, circulating blood, lymphoid T, and lymphoid B tissue. The cell types accounted for include macrophages, a few T-cell lineages (cytotoxic, regulatory, helper 1, and helper 2), and B-cell activation to plasma cells. Four different cytokines were accounted for: IFN-γ, IL-4, IL-10 and IL-12. In addition, generic inflammatory signals are used to represent the kinetics of IL-1, IL-2, and TGF-β. Cell recruitment, differentiation, replication, apoptosis and migration are described as appropriate for the different cell types. The model is a hybrid structure containing information from several mammalian species. The structure of the network was built to be physiologically and biochemically consistent. Rate laws for all the cellular fate processes, growth factor production rates and half-lives, together with antibody production rates and half-lives, are provided. The results demonstrate how this framework can be used to integrate mathematical models of the immune response from several published sources and describe qualitative predictions of global immune system response arising from the integrated, hybrid model. In addition, we show how the model can be expanded to include novel biological findings. Case studies were carried out to simulate TB infection, tumor rejection, response to a blood borne pathogen and the consequences of accounting for regulatory T-cells. Conclusions The final result of this work is a postulated and increasingly comprehensive representation of the mammalian immune system, based on physiological knowledge and susceptible to further experimental testing and validation. We believe that the integrated nature of FIRM has the potential to simulate a range of responses under a variety of conditions, from modeling of immune responses after tuberculosis (TB) infection to tumor formation in tissues. FIRM also has the flexibility to be expanded to include both complex and novel immunological response features as our knowledge of the immune system advances. PMID:24074340

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…

Chaotic dynamics of flexible Euler-Bernoulli beams

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

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl; Krysko, A. V., E-mail: anton.krysko@gmail.com; Kutepov, I. E., E-mail: iekutepov@gmail.com

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions ismore » carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.« less

Application of a simplified mathematical model to estimate the effect of forced aeration on composting in a closed system.

PubMed

Bari, Quazi H; Koenig, Albert

2012-11-01

The aeration rate is a key process control parameter in the forced aeration composting process because it greatly affects different physico-chemical parameters such as temperature and moisture content, and indirectly influences the biological degradation rate. In this study, the effect of a constant airflow rate on vertical temperature distribution and organic waste degradation in the composting mass is analyzed using a previously developed mathematical model of the composting process. The model was applied to analyze the effect of two different ambient conditions, namely, hot and cold ambient condition, and four different airflow rates such as 1.5, 3.0, 4.5, and 6.0 m(3) m(-2) h(-1), respectively, on the temperature distribution and organic waste degradation in a given waste mixture. The typical waste mixture had 59% moisture content and 96% volatile solids, however, the proportion could be varied as required. The results suggested that the model could be efficiently used to analyze composting under variable ambient and operating conditions. A lower airflow rate around 1.5-3.0 m(3) m(-2) h(-1) was found to be suitable for cold ambient condition while a higher airflow rate around 4.5-6.0 m(3) m(-2) h(-1) was preferable for hot ambient condition. The engineered way of application of this model is flexible which allows the changes in any input parameters within the realistic range. It can be widely used for conceptual process design, studies on the effect of ambient conditions, optimization studies in existing composting plants, and process control. Copyright © 2012 Elsevier Ltd. All rights reserved.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

PubMed

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

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)…

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

The sympathy of two pendulum clocks: beyond Huygens' observations.

PubMed

Peña Ramirez, Jonatan; Olvera, Luis Alberto; Nijmeijer, Henk; Alvarez, Joaquin

2016-03-29

This paper introduces a modern version of the classical Huygens' experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks--ad hoc designed and fabricated--which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit 'sympathetic' motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

The predictive protective control of the heat exchanger

NASA Astrophysics Data System (ADS)

Nevriva, Pavel; Filipova, Blanka; Vilimec, Ladislav

2016-06-01

The paper deals with the predictive control applied to flexible cogeneration energy system FES. FES was designed and developed by the VITKOVICE POWER ENGINEERING joint-stock company and represents a new solution of decentralized cogeneration energy sources. In FES, the heating medium is flue gas generated by combustion of a solid fuel. The heated medium is power gas, which is a gas mixture of air and water steam. Power gas is superheated in the main heat exchanger and led to gas turbines. To protect the main heat exchanger against damage by overheating, the novel predictive protective control based on the mathematical model of exchanger was developed. The paper describes the principle, the design and the simulation of the predictive protective method applied to main heat exchanger of FES.

Evolutionary Technologies: Fundamentals and Applications to Information/Communication Systems and Manufacturing/Logistics Systems

NASA Astrophysics Data System (ADS)

Gen, Mitsuo; Kawakami, Hiroshi; Tsujimura, Yasuhiro; Handa, Hisashi; Lin, Lin; Okamoto, Azuma

As efficient utilization of computational resources is increasing, evolutionary technology based on the Genetic Algorithm (GA), Genetic Programming (GP), Evolution Strategy (ES) and other Evolutionary Computations (ECs) is making rapid progress, and its social recognition and the need as applied technology are increasing. This is explained by the facts that EC offers higher robustness for knowledge information processing systems, intelligent production and logistics systems, most advanced production scheduling and other various real-world problems compared to the approaches based on conventional theories, and EC ensures flexible applicability and usefulness for any unknown system environment even in a case where accurate mathematical modeling fails in the formulation. In this paper, we provide a comprehensive survey of the current state-of-the-art in the fundamentals and applications of evolutionary technologies.

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.

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.…

Understanding and responding the students in learning mathematics through the differentiated instruction

NASA Astrophysics Data System (ADS)

Hapsari, T.; Darhim; Dahlan, J. A.

2018-05-01

This research discusses the differentiated instruction, a mathematic learning which is as expected by the students in connection with the differentiated instruction itself, its implementation, and the students’ responses. This research employs a survey method which involves 62 students as the research respondents. The mathematics learning types required by the students and their responses to the differentiated instruction are examined through questionnaire and interview. The mathematics learning types in orderly required by the students, from the highest frequency cover the easily understood instructions, slowly/not rushing teaching, fun, not complicated, interspersed with humour, various question practices, not too serious, and conducive class atmosphere for the instructions. Implementing the differentiated instruction is not easy. The teacher should be able to constantly assess the students, s/he should have good knowledge of relevant materials and instructions, and properly prepare the instructions, although it is time-consuming. The differentiated instruction is implemented on the instructions of numerical pattern materials. The strategies implemented are flexible grouping, tiered assignment, and compacting. The students positively respond the differentiated learning instruction that they become more motivated and involved in the instruction.

AST: Activity-Security-Trust driven modeling of time varying networks.

PubMed

Wang, Jian; Xu, Jiake; Liu, Yanheng; Deng, Weiwen

2016-02-18

Network modeling is a flexible mathematical structure that enables to identify statistical regularities and structural principles hidden in complex systems. The majority of recent driving forces in modeling complex networks are originated from activity, in which an activity potential of a time invariant function is introduced to identify agents' interactions and to construct an activity-driven model. However, the new-emerging network evolutions are already deeply coupled with not only the explicit factors (e.g. activity) but also the implicit considerations (e.g. security and trust), so more intrinsic driving forces behind should be integrated into the modeling of time varying networks. The agents undoubtedly seek to build a time-dependent trade-off among activity, security, and trust in generating a new connection to another. Thus, we reasonably propose the Activity-Security-Trust (AST) driven model through synthetically considering the explicit and implicit driving forces (e.g. activity, security, and trust) underlying the decision process. AST-driven model facilitates to more accurately capture highly dynamical network behaviors and figure out the complex evolution process, allowing a profound understanding of the effects of security and trust in driving network evolution, and improving the biases induced by only involving activity representations in analyzing the dynamical processes.

Integrated performance and reliability specification for digital avionics systems

NASA Technical Reports Server (NTRS)

Brehm, Eric W.; Goettge, Robert T.

1995-01-01

This paper describes an automated tool for performance and reliability assessment of digital avionics systems, called the Automated Design Tool Set (ADTS). ADTS is based on an integrated approach to design assessment that unifies traditional performance and reliability views of system designs, and that addresses interdependencies between performance and reliability behavior via exchange of parameters and result between mathematical models of each type. A multi-layer tool set architecture has been developed for ADTS that separates the concerns of system specification, model generation, and model solution. Performance and reliability models are generated automatically as a function of candidate system designs, and model results are expressed within the system specification. The layered approach helps deal with the inherent complexity of the design assessment process, and preserves long-term flexibility to accommodate a wide range of models and solution techniques within the tool set structure. ADTS research and development to date has focused on development of a language for specification of system designs as a basis for performance and reliability evaluation. A model generation and solution framework has also been developed for ADTS, that will ultimately encompass an integrated set of analytic and simulated based techniques for performance, reliability, and combined design assessment.

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.

Top-level modeling of an als system utilizing object-oriented techniques

NASA Astrophysics Data System (ADS)

Rodriguez, L. F.; Kang, S.; Ting, K. C.

The possible configuration of an Advanced Life Support (ALS) System capable of supporting human life for long-term space missions continues to evolve as researchers investigate potential technologies and configurations. To facilitate the decision process the development of acceptable, flexible, and dynamic mathematical computer modeling tools capable of system level analysis is desirable. Object-oriented techniques have been adopted to develop a dynamic top-level model of an ALS system.This approach has several advantages; among these, object-oriented abstractions of systems are inherently modular in architecture. Thus, models can initially be somewhat simplistic, while allowing for adjustments and improvements. In addition, by coding the model in Java, the model can be implemented via the World Wide Web, greatly encouraging the utilization of the model. Systems analysis is further enabled with the utilization of a readily available backend database containing information supporting the model. The subsystem models of the ALS system model include Crew, Biomass Production, Waste Processing and Resource Recovery, Food Processing and Nutrition, and the Interconnecting Space. Each subsystem model and an overall model have been developed. Presented here is the procedure utilized to develop the modeling tool, the vision of the modeling tool, and the current focus for each of the subsystem models.

Computational logic: its origins and applications.

PubMed

Paulson, Lawrence C

2018-02-01

Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the 'logic for computable functions (LCF) approach' pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users' code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.

Rational-Spline Subroutines

NASA Technical Reports Server (NTRS)

Schiess, James R.; Kerr, Patricia A.; Smith, Olivia C.

1988-01-01

Smooth curves drawn among plotted data easily. Rational-Spline Approximation with Automatic Tension Adjustment algorithm leads to flexible, smooth representation of experimental data. "Tension" denotes mathematical analog of mechanical tension in spline or other mechanical curve-fitting tool, and "spline" as denotes mathematical generalization of tool. Program differs from usual spline under tension, allows user to specify different values of tension between adjacent pairs of knots rather than constant tension over entire range of data. Subroutines use automatic adjustment scheme that varies tension parameter for each interval until maximum deviation of spline from line joining knots less than or equal to amount specified by user. Procedure frees user from drudgery of adjusting individual tension parameters while still giving control over local behavior of spline.

Depicting 3D shape using lines

NASA Astrophysics Data System (ADS)

DeCarlo, Doug

2012-03-01

Over the last few years, researchers in computer graphics have developed sophisticated mathematical descriptions of lines on 3D shapes that can be rendered convincingly as strokes in drawings. These innovations highlight fundamental questions about how human perception takes strokes in drawings as evidence of 3D structure. Answering these questions will lead to a greater scientific understanding of the flexibility and richness of human perception, as well as to practical techniques for synthesizing clearer and more compelling drawings. This paper reviews what is known about the mathematics and perception of computer-generated line drawings of shape and motivates an ongoing program of research to better characterize the shapes people see when they look at such drawings.

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

ERIC Educational Resources Information Center

Andrews, Paul; Sayers, Judy

2015-01-01

It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire…

Secondary STEM Education: "Designed by Apple in California, Assembled in China". The Progress of Education Reform. Volume 9, Number 4

ERIC Educational Resources Information Center

Zinth, Kyle

2008-01-01

America's advantage has historically been its people's creativity, flexibility and entrepreneurship. But just as painters need to be proficient in technique and theory to produce great masterpieces, the next generation of Americans will likely require a solid grounding in mathematics and science for their creativity to be maximized in a world…

Prospective Elementary Teachers Learning to Reason Flexibly with Sums and Differences: Number Sense Development Viewed through the Lens of Collective Activity

ERIC Educational Resources Information Center

Whitacre, Ian

2018-01-01

I present a viable learning trajectory for prospective elementary teachers' number sense development with a focus on whole-number place value, addition, and subtraction. I document a chronology of classroom mathematical practices in a Number and Operations course. The findings provide insights into prospective elementary teachers' number sense…

Compared with What? The Effects of Different Comparisons on Conceptual Knowledge and Procedural Flexibility for Equation Solving

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Star, Jon R.

2009-01-01

Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh- and eighth-grade students learned to solve equations (a)…

Wisconsin Title I Migrant Education. Section 143 Project: Development of an Item Bank. Summary Report.

ERIC Educational Resources Information Center

Brown, Frank N.; And Others

The successful Wisconsin Title 1 project item bank offers a valid, flexible, and efficient means of providing migrant student tests in reading and mathematics tailored to instructor curricula. The item bank system consists of nine PASCAL computer programs which maintain, search, and select from approximately 1,000 test items stored on floppy disks…

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.

Nonlinear Aeroelastic Equations of Motion of Twisted, Nonuniform, Flexible Horizontal-Axis Wind Turbine Blades

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1980-01-01

The second-degree nonlinear equations of motion for a flexible, twisted, nonuniform, horizontal axis wind turbine blade were developed using Hamilton's principle. A mathematical ordering scheme which was consistent with the assumption of a slender beam was used to discard some higher-order elastic and inertial terms in the second-degree nonlinear equations. The blade aerodynamic loading which was employed accounted for both wind shear and tower shadow and was obtained from strip theory based on a quasi-steady approximation of two-dimensional, incompressible, unsteady, airfoil theory. The resulting equations had periodic coefficients and were suitable for determining the aeroelastic stability and response of large horizontal-axis wind turbine blades.

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;…

Dynamics and stability of spinning flexible space tether systems

NASA Astrophysics Data System (ADS)

Tyc, George

This dissertation focuses on a detailed dynamical investigation of a previously unexplored tether configuration that involves a spinning two-body tethered system with flexible appendages on each end-body where the spin axis is nominally aligned along the tether. The original motivation for this work came after the flight of the first Canadian sub-orbital tether mission OEDIPUS-A in 1989 which employed this spinning tethered configuration. To everyone's surprise, one of the end-bodies was observed to exhibit a rapid divergence of its nutation angle. It was clear after this flight that there were some fundamental mechanisms associated with the interaction between the tether and the end-body that were not fully understood at that time. Hence, a Tether Dynamics Experiment (TDE) was formed and became a formal part of the scientific agenda for the follow-on mission OEDIPUS-C which flew in 1995. This dissertation describes the work that was conducted as part of the TDE and involves: theoretical investigations into the dynamics of this spinning tethered flexible body system; ground testing to validate the models and establish the tether properties; application of the models to develop a stabilization approach for OEDIPUS-C, and comparisons between theory and flight data from both OEDIPUS-A and OEDIPUS-C. Nonlinear equations of motion are developed for a spinning tethered system where the tether could be either spinning with the end-bodies or attached to small de-spun platforms on the end-bodies. Since the tether used for the OEDIPUS missions is not a string, as is often assumed, but rather a wire that has some bending stiffness, albeit small, the tether bending was also taken into account in the formulation. Two sets of ground tests are described that were used to validate the stability conditions and gain confidence in the mathematical models. One set involved hanging a body by a tether and spinning at different speeds to investigate the end-body stability. The other set used a tethered spinning end-body suspended on a set of gimbals and had a means to measure the end-body attitude in real-time. The mathematical models were then applied to investigate suitable stabilization approaches for OEDIPUS-C. In general, very good agreement was found between the theory and both the ground experiments and flight data. One of the surprising results from this work is the significance of the tether root bending effects. It is shown that it is this subtle effect that caused the rapid divergence in one of the end-bodies in the OEDIPUS-A mission which was unstable. For OEDIPUS-C, the situation was rectified by adding the booms to ensure "short term" stability and also by not spinning as rapidly. The OEDIPUS-C was very successful as all systems worked as planned and hence a superb set of flight dynamics data was collected. (Abstract shortened by UMI.)

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…

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)

Hybrid computational phantoms of the male and female newborn patient: NURBS-based whole-body models

NASA Astrophysics Data System (ADS)

Lee, Choonsik; Lodwick, Daniel; Hasenauer, Deanna; Williams, Jonathan L.; Lee, Choonik; Bolch, Wesley E.

2007-07-01

Anthropomorphic computational phantoms are computer models of the human body for use in the evaluation of dose distributions resulting from either internal or external radiation sources. Currently, two classes of computational phantoms have been developed and widely utilized for organ dose assessment: (1) stylized phantoms and (2) voxel phantoms which describe the human anatomy via mathematical surface equations or 3D voxel matrices, respectively. Although stylized phantoms based on mathematical equations can be very flexible in regard to making changes in organ position and geometrical shape, they are limited in their ability to fully capture the anatomic complexities of human internal anatomy. In turn, voxel phantoms have been developed through image-based segmentation and correspondingly provide much better anatomical realism in comparison to simpler stylized phantoms. However, they themselves are limited in defining organs presented in low contrast within either magnetic resonance or computed tomography images—the two major sources in voxel phantom construction. By definition, voxel phantoms are typically constructed via segmentation of transaxial images, and thus while fine anatomic features are seen in this viewing plane, slice-to-slice discontinuities become apparent in viewing the anatomy of voxel phantoms in the sagittal or coronal planes. This study introduces the concept of a hybrid computational newborn phantom that takes full advantage of the best features of both its stylized and voxel counterparts: flexibility in phantom alterations and anatomic realism. Non-uniform rational B-spline (NURBS) surfaces, a mathematical modeling tool traditionally applied to graphical animation studies, was adopted to replace the limited mathematical surface equations of stylized phantoms. A previously developed whole-body voxel phantom of the newborn female was utilized as a realistic anatomical framework for hybrid phantom construction. The construction of a hybrid phantom is performed in three steps: polygonization of the voxel phantom, organ modeling via NURBS surfaces and phantom voxelization. Two 3D graphic tools, 3D-DOCTOR™ and Rhinoceros™, were utilized to polygonize the newborn voxel phantom and generate NURBS surfaces, while an in-house MATLAB™ code was used to voxelize the resulting NURBS model into a final computational phantom ready for use in Monte Carlo radiation transport calculations. A total of 126 anatomical organ and tissue models, including 38 skeletal sites and 31 cartilage sites, were described within the hybrid phantom using either NURBS or polygon surfaces. A male hybrid newborn phantom was constructed following the development of the female phantom through the replacement of female-specific organs with male-specific organs. The outer body contour and internal anatomy of the NURBS-based phantoms were adjusted to match anthropometric and reference newborn data reported by the International Commission on Radiological Protection in their Publication 89. The voxelization process was designed to accurately convert NURBS models to a voxel phantom with minimum volumetric change. A sensitivity study was additionally performed to better understand how the meshing tolerance and voxel resolution would affect volumetric changes between the hybrid-NURBS and hybrid-voxel phantoms. The male and female hybrid-NURBS phantoms were constructed in a manner so that all internal organs approached their ICRP reference masses to within 1%, with the exception of the skin (-6.5% relative error) and brain (-15.4% relative error). Both hybrid-voxel phantoms were constructed with an isotropic voxel resolution of 0.663 mm—equivalent to the ICRP 89 reference thickness of the newborn skin (dermis and epidermis). Hybrid-NURBS phantoms used to create their voxel counterpart retain the non-uniform scalability of stylized phantoms, while maintaining the anatomic realism of segmented voxel phantoms with respect to organ shape, depth and inter-organ positioning. This work was supported by the National Cancer Institute.

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…

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…

A new approach to correct the QT interval for changes in heart rate using a nonparametric regression model in beagle dogs.

PubMed

Watanabe, Hiroyuki; Miyazaki, Hiroyasu

2006-01-01

Over- and/or under-correction of QT intervals for changes in heart rate may lead to misleading conclusions and/or masking the potential of a drug to prolong the QT interval. This study examines a nonparametric regression model (Loess Smoother) to adjust the QT interval for differences in heart rate, with an improved fitness over a wide range of heart rates. 240 sets of (QT, RR) observations collected from each of 8 conscious and non-treated beagle dogs were used as the materials for investigation. The fitness of the nonparametric regression model to the QT-RR relationship was compared with four models (individual linear regression, common linear regression, and Bazett's and Fridericia's correlation models) with reference to Akaike's Information Criterion (AIC). Residuals were visually assessed. The bias-corrected AIC of the nonparametric regression model was the best of the models examined in this study. Although the parametric models did not fit, the nonparametric regression model improved the fitting at both fast and slow heart rates. The nonparametric regression model is the more flexible method compared with the parametric method. The mathematical fit for linear regression models was unsatisfactory at both fast and slow heart rates, while the nonparametric regression model showed significant improvement at all heart rates in beagle dogs.

Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm

NASA Astrophysics Data System (ADS)

Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji

2015-12-01

Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.

Modelling the influence of total suspended solids on E. coli removal in river water.

PubMed

Qian, Jueying; Walters, Evelyn; Rutschmann, Peter; Wagner, Michael; Horn, Harald

2016-01-01

Following sewer overflows, fecal indicator bacteria enter surface waters and may experience different lysis or growth processes. A 1D mathematical model was developed to predict total suspended solids (TSS) and Escherichia coli concentrations based on field measurements in a large-scale flume system simulating a combined sewer overflow. The removal mechanisms of natural inactivation, UV inactivation, and sedimentation were modelled. For the sedimentation process, one, two or three particle size classes were incorporated separately into the model. Moreover, the UV sensitivity coefficient α and natural inactivation coefficient kd were both formulated as functions of TSS concentration. It was observed that the E. coli removal was predicted more accurately by incorporating two particle size classes. However, addition of a third particle size class only improved the model slightly. When α and kd were allowed to vary with the TSS concentration, the model was able to predict E. coli fate and transport at different TSS concentrations accurately and flexibly. A sensitivity analysis revealed that the mechanisms of UV and natural inactivation were more influential at low TSS concentrations, whereas the sedimentation process became more important at elevated TSS concentrations.

Mathematical characterization of the milk progesterone profile as a leg up to individualized monitoring of reproduction status in dairy cows.

PubMed

Adriaens, Ines; Huybrechts, Tjebbe; Geerinckx, Katleen; Daems, Devin; Lammertyn, Jeroen; De Ketelaere, Bart; Saeys, Wouter; Aernouts, Ben

2017-11-01

Reproductive performance is an important factor affecting the profitability of dairy farms. Optimal fertility results are often confined by the time-consuming nature of classical heat detection, the fact that high-producing dairy cows show estrous symptoms shorter and less clearly, and the occurrence of ovarian problems. Today's commercially available solutions for automatic estrus detection include monitoring of activity, temperature and progesterone. The latter has the advantage that, besides estrus, it also allows to detect pregnancy and ovarian problems. Due to the large variation in progesterone profiles, even between cycles within the same cow, the use of general thresholds is suboptimal. To this end, an intelligent and individual interpretation of the progesterone measurements is required. Therefore, an alternative solution is proposed, which takes individual and complete cycle progesterone profiles into account for reproduction monitoring. In this way, profile characteristics can be translated into specific attentions for the farmers, based on individual rather than general guidelines. To enable the use of the profile and cycle characteristics, an appropriate model to describe the milk progesterone profile was developed. The proposed model describes the basal adrenal progesterone production and the growing and regressing cyclic corpus luteum. To identify the most appropriate way to describe the increasing and decreasing part of each cycle, three mathematical candidate functions were evaluated on the increasing and decreasing parts of the progesterone cycle separately: the Hill function, the logistic growth curve and the Gompertz growth curve. These functions differ in the way they describe the sigmoidal shape of each profile. The increasing and decreasing parts of the P4 cycles were described best by the model based on respectively the Hill and Gompertz function. Combining these two functions, a full mathematical model to characterize the progesterone cycle was obtained. It was shown that this approach retains the flexibility to deal with both varying baseline and luteal progesterone values, as well as prolonged or delayed cycles. Copyright © 2017 Elsevier Inc. All rights reserved.

An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect.

PubMed

Royston, Patrick; Parmar, Mahesh K B

2014-08-07

Most randomized controlled trials with a time-to-event outcome are designed and analysed under the proportional hazards assumption, with a target hazard ratio for the treatment effect in mind. However, the hazards may be non-proportional. We address how to design a trial under such conditions, and how to analyse the results. We propose to extend the usual approach, a logrank test, to also include the Grambsch-Therneau test of proportional hazards. We test the resulting composite null hypothesis using a joint test for the hazard ratio and for time-dependent behaviour of the hazard ratio. We compute the power and sample size for the logrank test under proportional hazards, and from that we compute the power of the joint test. For the estimation of relevant quantities from the trial data, various models could be used; we advocate adopting a pre-specified flexible parametric survival model that supports time-dependent behaviour of the hazard ratio. We present the mathematics for calculating the power and sample size for the joint test. We illustrate the methodology in real data from two randomized trials, one in ovarian cancer and the other in treating cellulitis. We show selected estimates and their uncertainty derived from the advocated flexible parametric model. We demonstrate in a small simulation study that when a treatment effect either increases or decreases over time, the joint test can outperform the logrank test in the presence of both patterns of non-proportional hazards. Those designing and analysing trials in the era of non-proportional hazards need to acknowledge that a more complex type of treatment effect is becoming more common. Our method for the design of the trial retains the tools familiar in the standard methodology based on the logrank test, and extends it to incorporate a joint test of the null hypothesis with power against non-proportional hazards. For the analysis of trial data, we propose the use of a pre-specified flexible parametric model that can represent a time-dependent hazard ratio if one is present.

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.

Characterization and experimental validation of a squeeze film damper with MR fluid in a rotor-bearing system

NASA Astrophysics Data System (ADS)

Dominguez-Nuñez, L. A.; Silva-Navarro, G.

2014-04-01

The general study and applications of Magneto-Rhelogical (MR) dampers have been spread in the lasts years but only some studies have been focusing on the vibration control problems on rotor-bearings systems. Squeeze-Film Dampers (SFD) are now commonly used to passively control the vibration response on rotor-bearing systems because they can provide flexibility, damping and extend the so-called stability thresholds in rotating machinery. More recently, SFD are combined with MR or Electro-Rheological (ER) fluids to introduce a semiactive control mechanism to modify the rotordynamic coefficients and deal with the robust performance of the overall system response for higher operating speeds. There are, however, some theoretical and technological problems that complicate their extensive use, like the relationship between the centering spring flexibility and the rheological behavior of the smart fluid to produce the SFD forces. In this work it is considered a SFD with MR fluid and a set of circular section beams in a squirrel cage arrangement in combination with latex seals as centering springs. The mathematical model analysis includes the controllable viscoelastic properties associated to the MR fluid. The characterization of the SFD is made by the determination of some coefficients associated with a modified Choi-Lee-Park polynomial model. During the analysis is considered a rotor-bearing system modeled using finite element methods. The SFD with MR fluid is connected to an experimental platform to validate and experimentally evaluate the overall system. Finally, to improve the open-loop system performance, a methodology for the use of different control schemes is proposed.

Remodeling Pearson's Correlation for Functional Brain Network Estimation and Autism Spectrum Disorder Identification

PubMed Central

Li, Weikai; Wang, Zhengxia; Zhang, Limei; Qiao, Lishan; Shen, Dinggang

2017-01-01

Functional brain network (FBN) has been becoming an increasingly important way to model the statistical dependence among neural time courses of brain, and provides effective imaging biomarkers for diagnosis of some neurological or psychological disorders. Currently, Pearson's Correlation (PC) is the simplest and most widely-used method in constructing FBNs. Despite its advantages in statistical meaning and calculated performance, the PC tends to result in a FBN with dense connections. Therefore, in practice, the PC-based FBN needs to be sparsified by removing weak (potential noisy) connections. However, such a scheme depends on a hard-threshold without enough flexibility. Different from this traditional strategy, in this paper, we propose a new approach for estimating FBNs by remodeling PC as an optimization problem, which provides a way to incorporate biological/physical priors into the FBNs. In particular, we introduce an L1-norm regularizer into the optimization model for obtaining a sparse solution. Compared with the hard-threshold scheme, the proposed framework gives an elegant mathematical formulation for sparsifying PC-based networks. More importantly, it provides a platform to encode other biological/physical priors into the PC-based FBNs. To further illustrate the flexibility of the proposed method, we extend the model to a weighted counterpart for learning both sparse and scale-free networks, and then conduct experiments to identify autism spectrum disorders (ASD) from normal controls (NC) based on the constructed FBNs. Consequently, we achieved an 81.52% classification accuracy which outperforms the baseline and state-of-the-art methods. PMID:28912708

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).

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

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Modelling the Cast Component Weight in Hot Chamber Die Casting using Combined Taguchi and Buckingham's π Approach

NASA Astrophysics Data System (ADS)

Singh, Rupinder

2018-02-01

Hot chamber (HC) die casting process is one of the most widely used commercial processes for the casting of low temperature metals and alloys. This process gives near-net shape product with high dimensional accuracy. However in actual field environment the best settings of input parameters is often conflicting as the shape and size of the casting changes and one have to trade off among various output parameters like hardness, dimensional accuracy, casting defects, microstructure etc. So for online inspection of the cast components properties (without affecting the production line) the weight measurement has been established as one of the cost effective method (as the difference in weight of sound and unsound casting reflects the possible casting defects) in field environment. In the present work at first stage the effect of three input process parameters (namely: pressure at 2nd phase in HC die casting; metal pouring temperature and die opening time) has been studied for optimizing the cast component weight `W' as output parameter in form of macro model based upon Taguchi L9 OA. After this Buckingham's π approach has been applied on Taguchi based macro model for the development of micro model. This study highlights the Taguchi-Buckingham based combined approach as a case study (for conversion of macro model into micro model) by identification of optimum levels of input parameters (based on Taguchi approach) and development of mathematical model (based on Buckingham's π approach). Finally developed mathematical model can be used for predicting W in HC die casting process with more flexibility. The results of study highlights second degree polynomial equation for predicting cast component weight in HC die casting and suggest that pressure at 2nd stage is one of the most contributing factors for controlling the casting defect/weight of casting.

Load transfer in the stiffener-to-skin joints of a pressurized fuselage

NASA Technical Reports Server (NTRS)

Johnson, Eric R.; Rastogi, Naveen

1995-01-01

Structural analyses are developed to determine the linear elastic and the geometrically nonlinear elastic response of an internally pressurized, orthogonally stiffened, composite material cylindrical shell. The configuration is a long circular cylindrical shell stiffened on the inside by a regular arrangement of identical stringers and identical rings. Periodicity permits the analysis of a unit cell model consisting of a portion of the shell wall centered over one stringer-ring joint. The stringer-ring-shell joint is modeled in an idealized manner; the stiffeners are mathematically permitted to pass through one another without contact, but do interact indirectly through their mutual contact with the shell at the joint. Discrete beams models of the stiffeners include a stringer with a symmetrical cross section and a ring with either a symmetrical or an asymmetrical open section. Mathematical formulations presented for the linear response include the effect of transverse shear deformations and the effect of warping of the ring's cross section due to torsion. These effects are important when the ring has an asymmetrical cross section because the loss of symmetry in the problem results in torsion and out-of-plane bending of the ring, and a concomitant rotation of the joint at the stiffener intersection about the circumferential axis. Data from a composite material crown panel typical of a large transport fuselage structure are used for two numerical examples. Although the inclusion of geometric nonlinearity reduces the 'pillowing' of the shell, it is found that bending is localized to a narrow region near the stiffener. Including warping deformation of the ring into the analysis changes the sense of the joint rotation. Transverse shear deformation models result in increased joint flexibility.

Chemometric analysis of Hymenoptera toxins and defensins: A model for predicting the biological activity of novel peptides from venoms and hemolymph.

PubMed

Saidemberg, Daniel M; Baptista-Saidemberg, Nicoli B; Palma, Mario S

2011-09-01

When searching for prospective novel peptides, it is difficult to determine the biological activity of a peptide based only on its sequence. The "trial and error" approach is generally laborious, expensive and time consuming due to the large number of different experimental setups required to cover a reasonable number of biological assays. To simulate a virtual model for Hymenoptera insects, 166 peptides were selected from the venoms and hemolymphs of wasps, bees and ants and applied to a mathematical model of multivariate analysis, with nine different chemometric components: GRAVY, aliphaticity index, number of disulfide bonds, total residues, net charge, pI value, Boman index, percentage of alpha helix, and flexibility prediction. Principal component analysis (PCA) with non-linear iterative projections by alternating least-squares (NIPALS) algorithm was performed, without including any information about the biological activity of the peptides. This analysis permitted the grouping of peptides in a way that strongly correlated to the biological function of the peptides. Six different groupings were observed, which seemed to correspond to the following groups: chemotactic peptides, mastoparans, tachykinins, kinins, antibiotic peptides, and a group of long peptides with one or two disulfide bonds and with biological activities that are not yet clearly defined. The partial overlap between the mastoparans group and the chemotactic peptides, tachykinins, kinins and antibiotic peptides in the PCA score plot may be used to explain the frequent reports in the literature about the multifunctionality of some of these peptides. The mathematical model used in the present investigation can be used to predict the biological activities of novel peptides in this system, and it may also be easily applied to other biological systems. Copyright © 2011 Elsevier Inc. All rights reserved.

The Effects of Insulin Resistance on Individual Tissues: An Application of a Mathematical Model of Metabolism in Humans.

PubMed

Pearson, Taliesin; Wattis, Jonathan A D; King, John R; MacDonald, Ian A; Mazzatti, Dawn J

2016-06-01

Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for both carbohydrates and fats, around all tissues of the body. Insulin-resistant states such as type 2 diabetes and obesity are characterised by reduced efficiency of these mechanisms. Exactly how these insulin-resistant states develop, for example whether there is an order in which tissues become insulin resistant, is an active area of research with the hope of gaining a better overall understanding of insulin resistance. In this paper, we use a previously derived system of 12 first-order coupled differential equations that describe the transport between, and storage in, different tissues of the human body. We briefly revisit the derivation of the model before parametrising the model to account for insulin resistance. We then solve the model numerically, separately simulating each individual tissue as insulin resistant, and discuss and compare these results, drawing three main conclusions. The implications of these results are in accordance with biological intuition. First, insulin resistance in a tissue creates a knock-on effect on the other tissues in the body, whereby they attempt to compensate for the reduced efficiency of the insulin-resistant tissue. Second, insulin resistance causes a fatty liver, and the insulin resistance of tissues other than the liver can cause fat to accumulate in the liver. Finally, although insulin resistance in individual tissues can cause slightly reduced skeletal muscle metabolic flexibility, it is when the whole body is insulin resistant that the biggest effect on skeletal muscle flexibility is seen.

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

Experimental validation of flexible robot arm modeling and control

NASA Technical Reports Server (NTRS)

Ulsoy, A. Galip

1989-01-01

Flexibility is important for high speed, high precision operation of lightweight manipulators. Accurate dynamic modeling of flexible robot arms is needed. Previous work has mostly been based on linear elasticity with prescribed rigid body motions (i.e., no effect of flexible motion on rigid body motion). Little or no experimental validation of dynamic models for flexible arms is available. Experimental results are also limited for flexible arm control. Researchers include the effects of prismatic as well as revolute joints. They investigate the effect of full coupling between the rigid and flexible motions, and of axial shortening, and consider the control of flexible arms using only additional sensors.

Mental health professional experiences of the flexible assertive community treatment model: a grounded theory study.

PubMed

Lexén, Annika; Svensson, Bengt

2016-08-01

Despite the lack of evidence for effectiveness of the Flexible Assertive Community Treatment (Flexible ACT), the model is considered feasible and is well received by mental health professionals. No current studies have adequately examined mental health professional experiences of working with Flexible ACT. The aim of this study was to explore mental health professional experiences of working with the Flexible ACT model compared with standard care. The study was guided by grounded theory and based on the interviews with 19 theoretically chosen mental health professionals in Swedish urban areas primarily working with consumers with psychosis, who had worked with the Flexible ACT model for at least 6 months. The analysis resulted in the core category: "Flexible ACT and the shared caseload create a common action space" and three main categories: (1) "Flexible ACT fills the need for a systematic approach to crisis intervention"; (2) "Flexible ACT has advantages in the psychosocial working environment"; and (3) "Flexible ACT increases the quality of care". Mental health professionals may benefit from working with the Flexible ACT model through decreased job-strain and stress, increased feeling of being in control over their work situation, and experiences of providing higher quality of care.

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

PACE 2: Pricing and Cost Estimating Handbook

NASA Technical Reports Server (NTRS)

Stewart, R. D.; Shepherd, T.

1977-01-01

An automatic data processing system to be used for the preparation of industrial engineering type manhour and material cost estimates has been established. This computer system has evolved into a highly versatile and highly flexible tool which significantly reduces computation time, eliminates computational errors, and reduces typing and reproduction time for estimators and pricers since all mathematical and clerical functions are automatic once basic inputs are derived.

Using a Response to Intervention Framework to Improve Student Learning: A Pocket Guide for State and District Leaders. Implementing ESEA Flexibility Plans

ERIC Educational Resources Information Center

McInerney, Maurice; Elledge, Amy

2013-01-01

The 2002 reauthorization of the Elementary and Secondary Education Act (ESEA) contained provisions that expanded state and district accountability for improving all schools and increasing the learning and achievement of all students, including those who struggle to master basic skills in reading and mathematics. In 2011, the U.S. Department of…

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

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

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

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

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

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

2015-01-01

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

Delay-aware adaptive sleep mechanism for green wireless-optical broadband access networks

NASA Astrophysics Data System (ADS)

Wang, Ruyan; Liang, Alei; Wu, Dapeng; Wu, Dalei

2017-07-01

Wireless-Optical Broadband Access Network (WOBAN) is capacity-high, reliable, flexible, and ubiquitous, as it takes full advantage of the merits from both optical communication and wireless communication technologies. Similar to other access networks, the high energy consumption poses a great challenge for building up WOBANs. To shot this problem, we can make some load-light Optical Network Units (ONUs) sleep to reduce the energy consumption. Such operation, however, causes the increased packet delay. Jointly considering the energy consumption and transmission delay, we propose a delay-aware adaptive sleep mechanism. Specifically, we develop a new analytical method to evaluate the transmission delay and queuing delay over the optical part, instead of adopting M/M/1 queuing model. Meanwhile, we also analyze the access delay and queuing delay of the wireless part. Based on such developed delay models, we mathematically derive ONU's optimal sleep time. In addition, we provide numerous simulation results to show the effectiveness of the proposed mechanism.

Controlling the temperature of bones using pulsed CO2 lasers: observations and mathematical modeling.

PubMed

Lévesque, Luc; Noël, Jean-Marc; Scott, Calum

2015-12-01

Temperature of porcine bone specimens are investigated by aiming a pulsed CO2 laser beam at the bone-air surface. This method of controlling temperature is believed to be flexible in medical applications as it avoids the uses of thermal devices, which are often cumbersome and generate rather larger temperature variations with time. The control of temperature using this method is modeled by the heat-conduction equation. In this investigation, it is assumed that the energy delivered by the CO2 laser is confined within a very thin surface layer of roughly 9 μm. It is shown that temperature can be maintained at a steady temperature using a CO2 laser and we demonstrate that the method can be adapted to be used in tandem with another laser beam. This method to control the temperature is believed to be useful in de-contamination of bone during the implantation treatment, in bone augmentation when using natural or synthetic materials and in low-level laser therapy.

Control systems using modal domain optical fiber sensors for smart structure applications

NASA Technical Reports Server (NTRS)

Lindner, Douglas K.; Reichard, Karl M.

1991-01-01

Recently, a new class of sensors has emerged for structural control which respond to environmental changes over a significant gauge length; these sensors are called distributed-effect sensors. These sensors can be fabricated with spatially varying sensitivity to the distributed measurand, and can be configured to measure a variety of structural parameters which can not be measured directly using point sensors. Examples of distributed-effect sensors include piezoelectric film, holographic sensors, and modal domain optical fiber sensors. Optical fiber sensors are particularly attractive for smart structure applications because they are flexible, have low mass, and can easily be embedded directly into materials. In this paper we describe the implementation of weighted modal domain optical fiber sensors. The mathematical model of the modal domain optical fiber sensor model is described and used to derive an expression for the sensor sensitivity. The effects of parameter variations on the sensor sensitivity are demonstrated to illustrate methods of spatially varying the sensor sensitivity.

Multiresolution multiscale active mask segmentation of fluorescence microscope images

NASA Astrophysics Data System (ADS)

Srinivasa, Gowri; Fickus, Matthew; Kovačević, Jelena

2009-08-01

We propose an active mask segmentation framework that combines the advantages of statistical modeling, smoothing, speed and flexibility offered by the traditional methods of region-growing, multiscale, multiresolution and active contours respectively. At the crux of this framework is a paradigm shift from evolving contours in the continuous domain to evolving multiple masks in the discrete domain. Thus, the active mask framework is particularly suited to segment digital images. We demonstrate the use of the framework in practice through the segmentation of punctate patterns in fluorescence microscope images. Experiments reveal that statistical modeling helps the multiple masks converge from a random initial configuration to a meaningful one. This obviates the need for an involved initialization procedure germane to most of the traditional methods used to segment fluorescence microscope images. While we provide the mathematical details of the functions used to segment fluorescence microscope images, this is only an instantiation of the active mask framework. We suggest some other instantiations of the framework to segment different types of images.

Risk Evaluation for Identification and Intervention in Dual Use Research of Concern (DURC) for International Biological R&D Activity

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

Jones, Katherine A.; DeMenno, Mercy; Hoffman, Matthew John

This report summarizes the work performed as part of a Laboratory Directed Research and Development project focused on evaluating and mitigating risk associated with biological dual use research of concern. The academic and scientific community has identified the funding stage as the appropriate place to intervene and mitigate risk, so the framework developed here uses a portfolio-level approach and balances biosafety and biosecurity risks, anticipated project benefits, and available mitigations to identify the best available investment strategies subject to cost constraints. The modeling toolkit was designed for decision analysis for dual use research of concern, but is flexible enough tomore » support a wide variety of portfolio-level funding decisions where risk/benefit tradeoffs are involved. Two mathematical optimization models with two solution methods are included to accommodate stakeholders with varying levels of certainty about priorities between metrics. An example case study is presented.« less

Parallel Reconstruction Using Null Operations (PRUNO)

PubMed Central

Zhang, Jian; Liu, Chunlei; Moseley, Michael E.

2011-01-01

A novel iterative k-space data-driven technique, namely Parallel Reconstruction Using Null Operations (PRUNO), is presented for parallel imaging reconstruction. In PRUNO, both data calibration and image reconstruction are formulated into linear algebra problems based on a generalized system model. An optimal data calibration strategy is demonstrated by using Singular Value Decomposition (SVD). And an iterative conjugate- gradient approach is proposed to efficiently solve missing k-space samples during reconstruction. With its generalized formulation and precise mathematical model, PRUNO reconstruction yields good accuracy, flexibility, stability. Both computer simulation and in vivo studies have shown that PRUNO produces much better reconstruction quality than autocalibrating partially parallel acquisition (GRAPPA), especially under high accelerating rates. With the aid of PRUO reconstruction, ultra high accelerating parallel imaging can be performed with decent image quality. For example, we have done successful PRUNO reconstruction at a reduction factor of 6 (effective factor of 4.44) with 8 coils and only a few autocalibration signal (ACS) lines. PMID:21604290

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

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

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

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

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