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

PubMed

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

2011-01-01

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

Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance

PubMed Central

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

2011-01-01

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities. PMID:21935362

Modeling and Positioning of a PZT Precision Drive System.

PubMed

Liu, Che; Guo, Yanling

2017-11-08

The fact that piezoelectric ceramic transducer (PZT) precision drive systems in 3D printing are faced with nonlinear problems with respect to positioning, such as hysteresis and creep, has had an extremely negative impact on the precision of laser focusing systems. To eliminate the impact of PZT nonlinearity during precision drive movement, mathematical modeling and theoretical analyses of each module comprising the system were carried out in this study, a micro-displacement measurement circuit based on Position Sensitive Detector (PSD) is constructed, followed by the establishment of system closed-loop control and creep control models. An XL-80 laser interferometer (Renishaw, Wotton-under-Edge, UK) was used to measure the performance of the precision drive system, showing that system modeling and control algorithms were correct, with the requirements for precision positioning of the drive system satisfied.

Modeling and Positioning of a PZT Precision Drive System

PubMed Central

Liu, Che; Guo, Yanling

2017-01-01

The fact that piezoelectric ceramic transducer (PZT) precision drive systems in 3D printing are faced with nonlinear problems with respect to positioning, such as hysteresis and creep, has had an extremely negative impact on the precision of laser focusing systems. To eliminate the impact of PZT nonlinearity during precision drive movement, mathematical modeling and theoretical analyses of each module comprising the system were carried out in this study, a micro-displacement measurement circuit based on Position Sensitive Detector (PSD) is constructed, followed by the establishment of system closed-loop control and creep control models. An XL-80 laser interferometer (Renishaw, Wotton-under-Edge, UK) was used to measure the performance of the precision drive system, showing that system modeling and control algorithms were correct, with the requirements for precision positioning of the drive system satisfied. PMID:29117140

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

PubMed Central

Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin

2013-01-01

Previous research has found a relationship between individual differences in children’s precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the present study we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of two years. Additionally, at the last time point, we tested children’s informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3; Ginsburg & Baroody, 2003). We found that children’s numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned, non-symbolic system of quantity representation and the system of mathematical reasoning that children come to master through instruction. PMID:24076381

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

PubMed

Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

2013-12-01

Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Fractal geometry of music.

PubMed Central

Hsü, K J; Hsü, A J

1990-01-01

Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

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

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

PubMed

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

2010-01-01

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

Comparison of Models for Spacer Grid Pressure Loss in Nuclear Fuel Bundles for One and Two-Phase Flows

NASA Astrophysics Data System (ADS)

Maskal, Alan B.

Spacer grids maintain the structural integrity of the fuel rods within fuel bundles of nuclear power plants. They can also improve flow characteristics within the nuclear reactor core. However, spacer grids add reactor coolant pressure losses, which require estimation and engineering into the design. Several mathematical models and computer codes were developed over decades to predict spacer grid pressure loss. Most models use generalized characteristics, measured by older, less precise equipment. The study of OECD/US-NRC BWR Full-Size Fine Mesh Bundle Tests (BFBT) provides updated and detailed experimental single and two-phase results, using technically advanced flow measurements for a wide range of boundary conditions. This thesis compares the predictions from the mathematical models to the BFBT experimental data by utilizing statistical formulae for accuracy and precision. This thesis also analyzes the effects of BFBT flow characteristics on spacer grids. No single model has been identified as valid for all flow conditions. However, some models' predictions perform better than others within a range of flow conditions, based on the accuracy and precision of the models' predictions. This study also demonstrates that pressure and flow quality have a significant effect on two-phase flow spacer grid models' biases.

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

A Model of MTSS: Integrating Precision Teaching of Mathematics and a Multi-Level Assessment System in a Generative Classroom

ERIC Educational Resources Information Center

Weisenburgh-Snyder, Amy B.; Malmquist, Susan K.; Robbins, Joanne K.; Lipshin, Alison M.

2015-01-01

In the generative classroom, teachers provide well-designed learning environments that result in the combination, recombination, and reorganization of repertoires such that new untaught repertoires are likely to occur. One component that can contribute to such generativity is Precision Teaching (PT), a frequency building instructional…

Computational Evaluation of the Traceback Method

ERIC Educational Resources Information Center

Kol, Sheli; Nir, Bracha; Wintner, Shuly

2014-01-01

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

A bio-physical basis of mathematics in synaptic function of the nervous system: a theory.

PubMed

Dempsher, J

1980-01-01

The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the 'mind' and placed where it belongs - in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter ( in a precise structure).

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

PubMed

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

2017-11-01

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

Teacher Code Switching Consistency and Precision in a Multilingual Mathematics Classroom

ERIC Educational Resources Information Center

Chikiwa, Clemence; Schäfer, Marc

2016-01-01

This paper reports on a study that investigated teacher code switching consistency and precision in multilingual secondary school mathematics classrooms in South Africa. Data was obtained through interviewing and observing five lessons of each of three mathematics teachers purposively selected from three township schools in the Eastern Cape…

Attending to Precision with Secret Messages

ERIC Educational Resources Information Center

Starling, Courtney; Whitacre, Ian

2016-01-01

Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

Design and Analysis of Precise Pointing Systems

NASA Technical Reports Server (NTRS)

Kim, Young K.

2000-01-01

The mathematical models of Glovebox Integrated Microgravity Isolation Technology (g- LIMIT) dynamics/control system, which include six degrees of freedom (DOF) equations of motion, mathematical models of position sensors, accelerometers and actuators, and acceleration and position controller, were developed using MATLAB and TREETOPS simulations. Optimal control parameters of G-LIMIT control system were determined through sensitivity studies and its performance were evaluated with the TREETOPS model of G-LIMIT dynamics and control system. The functional operation and performance of the Tektronix DTM920 digital thermometer were studied and the inputs to the crew procedures and training of the DTM920 were documented.

Application of mathematical modeling in sustained release delivery systems.

PubMed

Grassi, Mario; Grassi, Gabriele

2014-08-01

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition.

PubMed

Simeoni, Chiara; Dinicola, Simona; Cucina, Alessandra; Mascia, Corrado; Bizzarri, Mariano

2018-01-01

In this report, we aim at presenting a viable strategy for the study of Epithelial-Mesenchymal Transition (EMT) and its opposite Mesenchymal-Epithelial Transition (MET) by means of a Systems Biology approach combined with a suitable Mathematical Modeling analysis. Precisely, it is shown how the presence of a metastable state, that is identified at a mesoscopic level of description, is crucial for making possible the appearance of a phase transition mechanism in the framework of fast-slow dynamics for Ordinary Differential Equations (ODEs).

Modeling and Implementation of Multi-Position Non-Continuous Rotation Gyroscope North Finder.

PubMed

Luo, Jun; Wang, Zhiqian; Shen, Chengwu; Kuijper, Arjan; Wen, Zhuoman; Liu, Shaojin

2016-09-20

Even when the Global Positioning System (GPS) signal is blocked, a rate gyroscope (gyro) north finder is capable of providing the required azimuth reference information to a certain extent. In order to measure the azimuth between the observer and the north direction very accurately, we propose a multi-position non-continuous rotation gyro north finding scheme. Our new generalized mathematical model analyzes the elements that affect the azimuth measurement precision and can thus provide high precision azimuth reference information. Based on the gyro's principle of detecting a projection of the earth rotation rate on its sensitive axis and the proposed north finding scheme, we are able to deduct an accurate mathematical model of the gyro outputs against azimuth with the gyro and shaft misalignments. Combining the gyro outputs model and the theory of propagation of uncertainty, some approaches to optimize north finding are provided, including reducing the gyro bias error, constraining the gyro random error, increasing the number of rotation points, improving rotation angle measurement precision, decreasing the gyro and the shaft misalignment angles. According them, a north finder setup is built and the azimuth uncertainty of 18" is obtained. This paper provides systematic theory for analyzing the details of the gyro north finder scheme from simulation to implementation. The proposed theory can guide both applied researchers in academia and advanced practitioners in industry for designing high precision robust north finder based on different types of rate gyroscopes.

The VIS-AD data model: Integrating metadata and polymorphic display with a scientific programming language

NASA Technical Reports Server (NTRS)

Hibbard, William L.; Dyer, Charles R.; Paul, Brian E.

1994-01-01

The VIS-AD data model integrates metadata about the precision of values, including missing data indicators and the way that arrays sample continuous functions, with the data objects of a scientific programming language. The data objects of this data model form a lattice, ordered by the precision with which they approximate mathematical objects. We define a similar lattice of displays and study visualization processes as functions from data lattices to display lattices. Such functions can be applied to visualize data objects of all data types and are thus polymorphic.

Intuitive Sense of Number Correlates With Math Scores on College-Entrance Examination

PubMed Central

Libertus, Melissa E.; Odic, Darko; Halberda, Justin

2012-01-01

Many educated adults possess exact mathematical abilities in addition to an approximate, intuitive sense of number, often referred to as the Approximate Number System (ANS). Here we investigate the link between ANS precision and mathematics performance in adults by testing participants on an ANS-precision test and collecting their scores on the Scholastic Aptitude Test (SAT), a standardized college-entrance exam in the USA. In two correlational studies, we found that ANS precision correlated with SAT-Quantitative (i.e., mathematics) scores. This relationship remained robust even when controlling for SAT-Verbal scores, suggesting a small but specific relationship between our primitive sense for number and formal mathematical abilities. PMID:23098904

Uncertainty Analysis of Instrument Calibration and Application

NASA Technical Reports Server (NTRS)

Tripp, John S.; Tcheng, Ping

1999-01-01

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Mathematical and Computational Modeling in Complex Biological Systems

PubMed Central

Li, Wenyang; Zhu, Xiaoliang

2017-01-01

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

Mathematical and Computational Modeling in Complex Biological Systems.

PubMed

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

2017-01-01

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

What If We Took Our Models Seriously? Estimating Latent Scores in Individuals

ERIC Educational Resources Information Center

Schneider, W. Joel

2013-01-01

Researchers often argue that the structural models of the constructs they study are relevant to clinicians. Unfortunately, few clinicians are able to translate the mathematically precise relationships between latent constructs and observed scores into information that can be usefully applied to individuals. Typically this means that when a new…

[Mathematical model of micturition allowing a detailed analysis of free urine flowmetry].

PubMed

Valentini, F; Besson, G; Nelson, P

1999-04-01

A mathematical model of micturition allowing precise analysis of uroflowmetry curves (VBN method) is described together with some of its applications. The physiology of micturition and possible diagnostic hypotheses able to explain the shape of the uroflowmetry curve can be expressed by a series of differential equations. Integration of the system allows the validity of these hypotheses to be tested by simulation. A theoretical uroflowmetry is calculated in less than 1 second and analysis of a dysuric uroflowmetry takes about 5 minutes. The efficacy of the model is due to its rapidity and the precision of the comparisons between measured and predicted values. The method has been applied to almost one thousand curves. The uroflowmetries of normal subjects are restored without adjustment with a quadratic error of less than 1%, while those of dysuric patients require identification of one or two adaptive parameters characteristic of the underlying disease. These parameters remain constant during the same session, but vary with the disease and/or the treatment. This model could become a tool for noninvasive urodynamic studies.

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

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

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

Identifiability of PBPK Models with Applications to ...

EPA Pesticide Factsheets

Any statistical model should be identifiable in order for estimates and tests using it to be meaningful. We consider statistical analysis of physiologically-based pharmacokinetic (PBPK) models in which parameters cannot be estimated precisely from available data, and discuss different types of identifiability that occur in PBPK models and give reasons why they occur. We particularly focus on how the mathematical structure of a PBPK model and lack of appropriate data can lead to statistical models in which it is impossible to estimate at least some parameters precisely. Methods are reviewed which can determine whether a purely linear PBPK model is globally identifiable. We propose a theorem which determines when identifiability at a set of finite and specific values of the mathematical PBPK model (global discrete identifiability) implies identifiability of the statistical model. However, we are unable to establish conditions that imply global discrete identifiability, and conclude that the only safe approach to analysis of PBPK models involves Bayesian analysis with truncated priors. Finally, computational issues regarding posterior simulations of PBPK models are discussed. The methodology is very general and can be applied to numerous PBPK models which can be expressed as linear time-invariant systems. A real data set of a PBPK model for exposure to dimethyl arsinic acid (DMA(V)) is presented to illustrate the proposed methodology. We consider statistical analy

Multiphysics Object-Oriented Simulation Environment (MOOSE)

ScienceCinema

None

2017-12-09

Nuclear reactor operators can expand safety margins with more precise information about how materials behave inside operating reactors. INL's new simulation platform makes such studies easier & more informative by letting researchers "plug-n-play" their mathematical models, skipping years of computer code development.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Invariance, Artifact, and the Psychological Setting of Rasch's Model: Comments on Engelhard

ERIC Educational Resources Information Center

Michell, Joel

2008-01-01

In the following, I confine my comments mainly to the issue of invariance in relation to Rasch's model for dichotomous, ability test items. "It is senseless to seek in the logical process of mathematical elaboration a psychologically significant precision that was not present in the psychological setting of the problem." (Boring, 1920)

Quantitative model of transport-aperture coordination during reach-to-grasp movements.

PubMed

Rand, Miya K; Shimansky, Y P; Hossain, Abul B M I; Stelmach, George E

2008-06-01

It has been found in our previous studies that the initiation of aperture closure during reach-to-grasp movements occurs when the hand distance to target crosses a threshold that is a function of peak aperture amplitude, hand velocity, and hand acceleration. Thus, a stable relationship between those four movement parameters is observed at the moment of aperture closure initiation. Based on the concept of optimal control of movements (Naslin 1969) and its application for reach-to-grasp movement regulation (Hoff and Arbib 1993), it was hypothesized that the mathematical equation expressing that relationship can be generalized to describe coordination between hand transport and finger aperture during the entire reach-to-grasp movement by adding aperture velocity and acceleration to the above four movement parameters. The present study examines whether this hypothesis is supported by the data obtained in experiments in which young adults performed reach-to-grasp movements in eight combinations of two reach-amplitude conditions and four movement-speed conditions. It was found that linear approximation of the mathematical model described the relationship among the six movement parameters for the entire aperture-closure phase with very high precision for each condition, thus supporting the hypothesis for that phase. Testing whether one mathematical model could approximate the data across all the experimental conditions revealed that it was possible to achieve the same high level of data-fitting precision only by including in the model two additional, condition-encoding parameters and using a nonlinear, artificial neural network-based approximator with two hidden layers comprising three and two neurons, respectively. This result indicates that transport-aperture coordination, as a specific relationship between the parameters of hand transport and finger aperture, significantly depends on the condition-encoding variables. The data from the aperture-opening phase also fit a linear model, whose coefficients were substantially different from those identified for the aperture-closure phase. This result supports the above hypothesis for the aperture-opening phase, and consequently, for the entire reach-to-grasp movement. However, the fitting precision was considerably lower than that for the aperture-closure phase, indicating significant trial-to-trial variability of transport-aperture coordination during the aperture-opening phase. Implications for understanding the neural mechanisms employed by the CNS for controlling reach-to-grasp movements and utilization of the mathematical model of transport-aperture coordination for data analysis are discussed.

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.

THE APPLICATION OF CYBERNETICS IN PEDAGOGY.

ERIC Educational Resources Information Center

ATUTOV, P.R.

THE APPLICATION OF CYBERNETICS TO PEDAGOGY CAN CREATE A PRECISE SCIENCE OF INSTRUCTION AND EDUCATION THROUGH THE TIME-CONSUMING BUT INEVITABLE TRANSITION FROM IDENTIFICATION OF QUALITATIVE RELATIONSHIPS AMONG PEDAGOGICAL OBJECTS TO QUANTITATIVE ANALYSIS OF THESE OBJECTS. THE THEORETICAL UTILITY OF MATHEMATICAL MODELS AND FORMULAE FOR EXPLANATORY…

Inferring pathological states in cortical neuron microcircuits.

PubMed

Rydzewski, Jakub; Nowak, Wieslaw; Nicosia, Giuseppe

2015-12-07

The brain activity is to a large extent determined by states of neural cortex microcircuits. Unfortunately, accuracy of results from neural circuits׳ mathematical models is often biased by the presence of uncertainties in underlying experimental data. Moreover, due to problems with uncertainties identification in a multidimensional parameters space, it is almost impossible to classify states of the neural cortex, which correspond to a particular set of the parameters. Here, we develop a complete methodology for determining uncertainties and the novel protocol for classifying all states in any neuroinformatic model. Further, we test this protocol on the mathematical, nonlinear model of such a microcircuit developed by Giugliano et al. (2008) and applied in the experimental data analysis of Huntington׳s disease. Up to now, the link between parameter domains in the mathematical model of Huntington׳s disease and the pathological states in cortical microcircuits has remained unclear. In this paper we precisely identify all the uncertainties, the most crucial input parameters and domains that drive the system into an unhealthy state. The scheme proposed here is general and can be easily applied to other mathematical models of biological phenomena. Copyright © 2015 Elsevier Ltd. All rights reserved.

Age estimation based on pulp chamber volume of first molars from cone-beam computed tomography images.

PubMed

Ge, Zhi-pu; Ma, Ruo-han; Li, Gang; Zhang, Ji-zong; Ma, Xu-chen

2015-08-01

To establish a method that can be used for human age estimation on the basis of pulp chamber volume of first molars and to identify whether the method is good enough for age estimation in real human cases. CBCT images of 373 maxillary first molars and 372 mandibular first molars were collected to establish the mathematical model from 190 female and 213 male patients whose age between 12 and 69 years old. The inclusion criteria of the first molars were: no caries, no excessive tooth wear, no dental restorations, no artifacts due to metal restorative materials present in adjacent teeth, and no pulpal calcification. All the CBCT images were acquired with a CBCT unit NewTom VG (Quantitative Radiology, Verona, Italy) and reconstructed with a voxel-size of 0.15mm. The images were subsequently exported as DICOM data sets and imported into an open source 3D image semi-automatic segmenting and voxel-counting software ITK-SNAP 2.4 for the calculation of pulp chamber volumes. A logarithmic regression analysis was conducted with age as dependent variable and pulp chamber volume as independent variables to establish a mathematical model for the human age estimation. To identify the precision and accuracy of the model for human age estimation, another 104 maxillary first molars and 103 mandibular first molars from 55 female and 57 male patients whose age between 12 and 67 years old were collected, too. Mean absolute error and root mean square error between the actual age and estimated age were used to determine the precision and accuracy of the mathematical model. The study was approved by the Institutional Review Board of Peking University School and Hospital of Stomatology. A mathematical model was suggested for: AGE=117.691-26.442×ln (pulp chamber volume). The regression was statistically significant (p=0.000<0.01). The coefficient of determination (R(2)) was 0.564. There is a mean absolute error of 8.122 and root mean square error of 5.603 between the actual age and estimated age for all the tested teeth. The pulp chamber volume of first molar is a useful index for the estimation of human age with reasonable precision and accuracy. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

High-precision arithmetic in mathematical physics

DOE PAGES

Bailey, David H.; Borwein, Jonathan M.

2015-05-12

For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. Furthermore, this article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

Explorations in Mathematics

ERIC Educational Resources Information Center

Muses, Charles

1977-01-01

Mathematics provides a language by which man can explore, and describe precisely and profoundly, any possible set of characteristics or relationships in nature. Discussed in this article are several mathematical topics including some historical perspectives in mathematics and new pioneering in hypernumbers. Supplementary sections include…

Evaluation of leaf wetness duration models for operational use in strawberry disease-warning systems in four US states.

PubMed

Montone, Verona O; Fraisse, Clyde W; Peres, Natalia A; Sentelhas, Paulo C; Gleason, Mark; Ellis, Michael; Schnabel, Guido

2016-11-01

Leaf wetness duration (LWD) plays a key role in disease development and is often used as an input in disease-warning systems. LWD is often estimated using mathematical models, since measurement by sensors is rarely available and/or reliable. A strawberry disease-warning system called "Strawberry Advisory System" (SAS) is used by growers in Florida, USA, in deciding when to spray their strawberry fields to control anthracnose and Botrytis fruit rot. Currently, SAS is implemented at six locations, where reliable LWD sensors are deployed. A robust LWD model would facilitate SAS expansion from Florida to other regions where reliable LW sensors are not available. The objective of this study was to evaluate the use of mathematical models to estimate LWD and time of spray recommendations in comparison to on site LWD measurements. Specific objectives were to (i) compare model estimated and observed LWD and resulting differences in timing and number of fungicide spray recommendations, (ii) evaluate the effects of weather station sensors precision on LWD models performance, and (iii) compare LWD models performance across four states in the USA. The LWD models evaluated were the classification and regression tree (CART), dew point depression (DPD), number of hours with relative humidity equal or greater than 90 % (NHRH ≥90 %), and Penman-Monteith (P-M). P-M model was expected to have the lowest errors, since it is a physically based and thus portable model. Indeed, the P-M model estimated LWD most accurately (MAE <2 h) at a weather station with high precision sensors but was the least accurate when lower precision sensors of relative humidity and estimated net radiation (based on solar radiation and temperature) were used (MAE = 3.7 h). The CART model was the most robust for estimating LWD and for advising growers on fungicide-spray timing for anthracnose and Botrytis fruit rot control and is therefore the model we recommend for expanding the strawberry disease warning beyond Florida, to other locations where weather stations may be deployed with lower precision sensors, and net radiation observations are not available.

Evaluation of leaf wetness duration models for operational use in strawberry disease-warning systems in four US states

NASA Astrophysics Data System (ADS)

Montone, Verona O.; Fraisse, Clyde W.; Peres, Natalia A.; Sentelhas, Paulo C.; Gleason, Mark; Ellis, Michael; Schnabel, Guido

2016-11-01

Leaf wetness duration (LWD) plays a key role in disease development and is often used as an input in disease-warning systems. LWD is often estimated using mathematical models, since measurement by sensors is rarely available and/or reliable. A strawberry disease-warning system called "Strawberry Advisory System" (SAS) is used by growers in Florida, USA, in deciding when to spray their strawberry fields to control anthracnose and Botrytis fruit rot. Currently, SAS is implemented at six locations, where reliable LWD sensors are deployed. A robust LWD model would facilitate SAS expansion from Florida to other regions where reliable LW sensors are not available. The objective of this study was to evaluate the use of mathematical models to estimate LWD and time of spray recommendations in comparison to on site LWD measurements. Specific objectives were to (i) compare model estimated and observed LWD and resulting differences in timing and number of fungicide spray recommendations, (ii) evaluate the effects of weather station sensors precision on LWD models performance, and (iii) compare LWD models performance across four states in the USA. The LWD models evaluated were the classification and regression tree (CART), dew point depression (DPD), number of hours with relative humidity equal or greater than 90 % (NHRH ≥90 %), and Penman-Monteith (P-M). P-M model was expected to have the lowest errors, since it is a physically based and thus portable model. Indeed, the P-M model estimated LWD most accurately (MAE <2 h) at a weather station with high precision sensors but was the least accurate when lower precision sensors of relative humidity and estimated net radiation (based on solar radiation and temperature) were used (MAE = 3.7 h). The CART model was the most robust for estimating LWD and for advising growers on fungicide-spray timing for anthracnose and Botrytis fruit rot control and is therefore the model we recommend for expanding the strawberry disease warning beyond Florida, to other locations where weather stations may be deployed with lower precision sensors, and net radiation observations are not available.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

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

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

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

PubMed

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

2018-01-05

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

Mathematical modeling of the heat transfer during pyrolysis process used for end-of-life tires treatment

NASA Astrophysics Data System (ADS)

Zheleva, I.; Georgiev, I.; Filipova, M.; Menseidov, D.

2017-10-01

Mathematical modeling of the heat transfer during the pyrolysis process used for the treatment of the End-of-Lifetires (EOLT) is presented in this paper. The pyrolysis process is 3D and non-stationary and because of this it is very complicated for modeling and studying. To simplify the modeling here a hierarchy of 2D models for the temperature which describe the non-stationary heat transfer in such a pyrolysis station is created. An algorithm for solving the model equations, based on MATLAB software is developed. The results for the temperature for some characteristic periods of operation of pyrolysis station are presented and commented in the paper. The results from this modeling can be used in the real pyrolysis station for more precise displacement of measurement devices and for designing of automated management of the process.

Smallest Nanoelectronics with Adatom Chains

NASA Technical Reports Server (NTRS)

Yamada, Toshishige; Saini, Subhash (Technical Monitor)

1998-01-01

This viewgraph presentation is focused on the general aspect of atomic chain electronics that I have been studying. Results have been published before, but are being rederived here using a new physical/mathematical picture/model, which deepens the physical understanding. Precise adatom structures can be used as a template on a regulated surface with no uncertainty.

Measuring and modeling salience with the theory of visual attention.

PubMed

Krüger, Alexander; Tünnermann, Jan; Scharlau, Ingrid

2017-08-01

For almost three decades, the theory of visual attention (TVA) has been successful in mathematically describing and explaining a wide variety of phenomena in visual selection and recognition with high quantitative precision. Interestingly, the influence of feature contrast on attention has been included in TVA only recently, although it has been extensively studied outside the TVA framework. The present approach further develops this extension of TVA's scope by measuring and modeling salience. An empirical measure of salience is achieved by linking different (orientation and luminance) contrasts to a TVA parameter. In the modeling part, the function relating feature contrasts to salience is described mathematically and tested against alternatives by Bayesian model comparison. This model comparison reveals that the power function is an appropriate model of salience growth in the dimensions of orientation and luminance contrast. Furthermore, if contrasts from the two dimensions are combined, salience adds up additively.

An engineering approach to modelling, decision support and control for sustainable systems.

PubMed

Day, W; Audsley, E; Frost, A R

2008-02-12

Engineering research and development contributes to the advance of sustainable agriculture both through innovative methods to manage and control processes, and through quantitative understanding of the operation of practical agricultural systems using decision models. This paper describes how an engineering approach, drawing on mathematical models of systems and processes, contributes new methods that support decision making at all levels from strategy and planning to tactics and real-time control. The ability to describe the system or process by a simple and robust mathematical model is critical, and the outputs range from guidance to policy makers on strategic decisions relating to land use, through intelligent decision support to farmers and on to real-time engineering control of specific processes. Precision in decision making leads to decreased use of inputs, less environmental emissions and enhanced profitability-all essential to sustainable systems.

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single-Hit Dose-Response Models.

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

Dose-response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi-mechanistic models known as single-hit models, such as the exponential and the exact beta-Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single-hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so-called single-hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single-hit models. Further analysis of the model framework is facilitated by formulating the single-hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single-hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model-consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model-consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model-consistent expression for the mean per-exposure dose that produces the correct total risk from repeated exposures is developed. © 2016 Society for Risk Analysis.

Controlled grafting of vinylic monomers on polyolefins: a robust mathematical modeling approach

PubMed Central

Saeb, Mohammad Reza; Rezaee, Babak; Shadman, Alireza; Formela, Krzysztof; Ahmadi, Zahed; Hemmati, Farkhondeh; Kermaniyan, Tayebeh Sadat; Mohammadi, Yousef

2017-01-01

Abstract Experimental and mathematical modeling analyses were used for controlling melt free-radical grafting of vinylic monomers on polyolefins and, thereby, reducing the disturbance of undesired cross-linking of polyolefins. Response surface, desirability function, and artificial intelligence methodologies were blended to modeling/optimization of grafting reaction in terms of vinylic monomer content, peroxide initiator concentration, and melt-processing time. An in-house code was developed based on artificial neural network that learns and mimics processing torque and grafting of glycidyl methacrylate (GMA) typical vinylic monomer on high-density polyethylene (HDPE). Application of response surface and desirability function enabled concurrent optimization of processing torque and GMA grafting on HDPE, through which we quantified for the first time competition between parallel reactions taking place during melt processing: (i) desirable grafting of GMA on HDPE; (ii) undesirable cross-linking of HDPE. The proposed robust mathematical modeling approach can precisely learn the behavior of grafting reaction of vinylic monomers on polyolefins and be placed into practice in finding exact operating condition needed for efficient grafting of reactive monomers on polyolefins. PMID:29491797

Controlled grafting of vinylic monomers on polyolefins: a robust mathematical modeling approach.

PubMed

Saeb, Mohammad Reza; Rezaee, Babak; Shadman, Alireza; Formela, Krzysztof; Ahmadi, Zahed; Hemmati, Farkhondeh; Kermaniyan, Tayebeh Sadat; Mohammadi, Yousef

2017-01-01

Experimental and mathematical modeling analyses were used for controlling melt free-radical grafting of vinylic monomers on polyolefins and, thereby, reducing the disturbance of undesired cross-linking of polyolefins. Response surface, desirability function, and artificial intelligence methodologies were blended to modeling/optimization of grafting reaction in terms of vinylic monomer content, peroxide initiator concentration, and melt-processing time. An in-house code was developed based on artificial neural network that learns and mimics processing torque and grafting of glycidyl methacrylate (GMA) typical vinylic monomer on high-density polyethylene (HDPE). Application of response surface and desirability function enabled concurrent optimization of processing torque and GMA grafting on HDPE, through which we quantified for the first time competition between parallel reactions taking place during melt processing: (i) desirable grafting of GMA on HDPE; (ii) undesirable cross-linking of HDPE. The proposed robust mathematical modeling approach can precisely learn the behavior of grafting reaction of vinylic monomers on polyolefins and be placed into practice in finding exact operating condition needed for efficient grafting of reactive monomers on polyolefins.

On the development of nugget growth model for resistance spot welding

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

Zhou, Kang, E-mail: zhoukang326@126.com, E-mail: melcai@ust.hk; Cai, Lilong, E-mail: zhoukang326@126.com, E-mail: melcai@ust.hk

2014-04-28

In this paper, we developed a general mathematical model to estimate the nugget growth process based on the heat energy delivered into the welds by the resistance spot welding. According to the principles of thermodynamics and heat transfer, and the effect of electrode force during the welding process, the shape of the nugget can be estimated. Then, a mathematical model between heat energy absorbed and nugget diameter can be obtained theoretically. It is shown in this paper that the nugget diameter can be precisely described by piecewise fractal polynomial functions. Experiments were conducted with different welding operation conditions, such asmore » welding currents, workpiece thickness, and widths, to validate the model and the theoretical analysis. All the experiments confirmed that the proposed model can predict the nugget diameters with high accuracy based on the input heat energy to the welds.« less

Uncertainty quantification and optimal decisions

PubMed Central

2017-01-01

A mathematical model can be analysed to construct policies for action that are close to optimal for the model. If the model is accurate, such policies will be close to optimal when implemented in the real world. In this paper, the different aspects of an ideal workflow are reviewed: modelling, forecasting, evaluating forecasts, data assimilation and constructing control policies for decision-making. The example of the oil industry is used to motivate the discussion, and other examples, such as weather forecasting and precision agriculture, are used to argue that the same mathematical ideas apply in different contexts. Particular emphasis is placed on (i) uncertainty quantification in forecasting and (ii) how decisions are optimized and made robust to uncertainty in models and judgements. This necessitates full use of the relevant data and by balancing costs and benefits into the long term may suggest policies quite different from those relevant to the short term. PMID:28484343

A Review of Calibration Transfer Practices and Instrument Differences in Spectroscopy.

PubMed

Workman, Jerome J

2018-03-01

Calibration transfer for use with spectroscopic instruments, particularly for near-infrared, infrared, and Raman analysis, has been the subject of multiple articles, research papers, book chapters, and technical reviews. There has been a myriad of approaches published and claims made for resolving the problems associated with transferring calibrations; however, the capability of attaining identical results over time from two or more instruments using an identical calibration still eludes technologists. Calibration transfer, in a precise definition, refers to a series of analytical approaches or chemometric techniques used to attempt to apply a single spectral database, and the calibration model developed using that database, for two or more instruments, with statistically retained accuracy and precision. Ideally, one would develop a single calibration for any particular application, and move it indiscriminately across instruments and achieve identical analysis or prediction results. There are many technical aspects involved in such precision calibration transfer, related to the measuring instrument reproducibility and repeatability, the reference chemical values used for the calibration, the multivariate mathematics used for calibration, and sample presentation repeatability and reproducibility. Ideally, a multivariate model developed on a single instrument would provide a statistically identical analysis when used on other instruments following transfer. This paper reviews common calibration transfer techniques, mostly related to instrument differences, and the mathematics of the uncertainty between instruments when making spectroscopic measurements of identical samples. It does not specifically address calibration maintenance or reference laboratory differences.

A refined methodology for modeling volume quantification performance in CT

NASA Astrophysics Data System (ADS)

Chen, Baiyu; Wilson, Joshua; Samei, Ehsan

2014-03-01

The utility of CT lung nodule volume quantification technique depends on the precision of the quantification. To enable the evaluation of quantification precision, we previously developed a mathematical model that related precision to image resolution and noise properties in uniform backgrounds in terms of an estimability index (e'). The e' was shown to predict empirical precision across 54 imaging and reconstruction protocols, but with different correlation qualities for FBP and iterative reconstruction (IR) due to the non-linearity of IR impacted by anatomical structure. To better account for the non-linearity of IR, this study aimed to refine the noise characterization of the model in the presence of textured backgrounds. Repeated scans of an anthropomorphic lung phantom were acquired. Subtracted images were used to measure the image quantum noise, which was then used to adjust the noise component of the e' calculation measured from a uniform region. In addition to the model refinement, the validation of the model was further extended to 2 nodule sizes (5 and 10 mm) and 2 segmentation algorithms. Results showed that the magnitude of IR's quantum noise was significantly higher in structured backgrounds than in uniform backgrounds (ASiR, 30-50%; MBIR, 100-200%). With the refined model, the correlation between e' values and empirical precision no longer depended on reconstruction algorithm. In conclusion, the model with refined noise characterization relfected the nonlinearity of iterative reconstruction in structured background, and further showed successful prediction of quantification precision across a variety of nodule sizes, dose levels, slice thickness, reconstruction algorithms, and segmentation software.

Population dynamics of Aphis gossypii Glover and in sole and intercropping systems of cotton and cowpea.

PubMed

Fernandes, Francisco S; Godoy, Wesley A C; Ramalho, Francisco S; Garcia, Adriano G; Santos, Bárbara D B; Malaquias, José B

2018-01-01

Population dynamics of aphids have been studied in sole and intercropping systems. These studies have required the use of more precise analytical tools in order to better understand patterns in quantitative data. Mathematical models are among the most important tools to explain the dynamics of insect populations. This study investigated the population dynamics of aphids Aphis gossypii and Aphis craccivora over time, using mathematical models composed of a set of differential equations as a helpful analytical tool to understand the population dynamics of aphids in arrangements of cotton and cowpea. The treatments were sole cotton, sole cowpea, and three arrangements of cotton intercropped with cowpea (t1, t2 and t3). The plants were infested with two aphid species and were evaluated at 7, 14, 28, 35, 42, and 49 days after the infestations. Mathematical models were used to fit the population dynamics of two aphid species. There were good fits for aphid dynamics by mathematical model over time. The highest population peak of both species A. gossypii and A. craccivora was found in the sole crops, and the lowest population peak was found in crop system t2. These results are important for integrated management programs of aphids in cotton and cowpea.

Examining the Process of Developing a Research-Based Mathematics Curriculum and Its Policy Implications

ERIC Educational Resources Information Center

Superfine, Alison Castro; Kelso, Catherine Randall; Beal, Susan

2010-01-01

The implementation of "research-based" mathematics curricula is increasingly becoming a central element of mathematics education reform policies. Given the recent focus on grounding mathematics curriculum policies in research, it is important to understand precisely what it means for a curriculum to be research-based. Using the Curriculum Research…

An analysis of the Petri net based model of the human body iron homeostasis process.

PubMed

Sackmann, Andrea; Formanowicz, Dorota; Formanowicz, Piotr; Koch, Ina; Blazewicz, Jacek

2007-02-01

In the paper a Petri net based model of the human body iron homeostasis is presented and analyzed. The body iron homeostasis is an important but not fully understood complex process. The modeling of the process presented in the paper is expressed in the language of Petri net theory. An application of this theory to the description of biological processes allows for very precise analysis of the resulting models. Here, such an analysis of the body iron homeostasis model from a mathematical point of view is given.

The influence of number line estimation precision and numeracy on risky financial decision making.

PubMed

Park, Inkyung; Cho, Soohyun

2018-01-10

This study examined whether different aspects of mathematical proficiency influence one's ability to make adaptive financial decisions. "Numeracy" refers to the ability to process numerical and probabilistic information and is commonly reported as an important factor which contributes to financial decision-making ability. The precision of mental number representation (MNR), measured with the number line estimation (NLE) task has been reported to be another critical factor. This study aimed to examine the contribution of these mathematical proficiencies while controlling for the influence of fluid intelligence, math anxiety and personality factors. In our decision-making task, participants chose between two options offering probabilistic monetary gain or loss. Sensitivity to expected value was measured as an index for the ability to discriminate between optimal versus suboptimal options. Partial correlation and hierarchical regression analyses revealed that NLE precision better explained EV sensitivity compared to numeracy, after controlling for all covariates. These results suggest that individuals with more precise MNR are capable of making more rational financial decisions. We also propose that the measurement of "numeracy," which is commonly used interchangeably with general mathematical proficiency, should include more diverse aspects of mathematical cognition including basic understanding of number magnitude. © 2018 International Union of Psychological Science.

PV cells electrical parameters measurement

NASA Astrophysics Data System (ADS)

Cibira, Gabriel

2017-12-01

When measuring optical parameters of a photovoltaic silicon cell, precise results bring good electrical parameters estimation, applying well-known physical-mathematical models. Nevertheless, considerable re-combination phenomena might occur in both surface and intrinsic thin layers within novel materials. Moreover, rear contact surface parameters may influence close-area re-combination phenomena, too. Therefore, the only precise electrical measurement approach is to prove assumed cell electrical parameters. Based on theoretical approach with respect to experiments, this paper analyses problems within measurement procedures and equipment used for electrical parameters acquisition within a photovoltaic silicon cell, as a case study. Statistical appraisal quality is contributed.

The role of learning-related dopamine signals in addiction vulnerability.

PubMed

Huys, Quentin J M; Tobler, Philippe N; Hasler, Gregor; Flagel, Shelly B

2014-01-01

Dopaminergic signals play a mathematically precise role in reward-related learning, and variations in dopaminergic signaling have been implicated in vulnerability to addiction. Here, we provide a detailed overview of the relationship between theoretical, mathematical, and experimental accounts of phasic dopamine signaling, with implications for the role of learning-related dopamine signaling in addiction and related disorders. We describe the theoretical and behavioral characteristics of model-free learning based on errors in the prediction of reward, including step-by-step explanations of the underlying equations. We then use recent insights from an animal model that highlights individual variation in learning during a Pavlovian conditioning paradigm to describe overlapping aspects of incentive salience attribution and model-free learning. We argue that this provides a computationally coherent account of some features of addiction. © 2014 Elsevier B.V. All rights reserved.

Dendritic trafficking faces physiologically critical speed-precision tradeoffs

DOE PAGES

Williams, Alex H.; O'Donnell, Cian; Sejnowski, Terrence J.; ...

2016-12-30

Nervous system function requires intracellular transport of channels, receptors, mRNAs, and other cargo throughout complex neuronal morphologies. Local signals such as synaptic input can regulate cargo trafficking, motivating the leading conceptual model of neuron-wide transport, sometimes called the ‘sushi-belt model’. Current theories and experiments are based on this model, yet its predictions are not rigorously understood. We formalized the sushi belt model mathematically, and show that it can achieve arbitrarily complex spatial distributions of cargo in reconstructed morphologies. However, the model also predicts an unavoidable, morphology dependent tradeoff between speed, precision and metabolic efficiency of cargo transport. With experimental estimatesmore » of trafficking kinetics, the model predicts delays of many hours or days for modestly accurate and efficient cargo delivery throughout a dendritic tree. In conclusion, these findings challenge current understanding of the efficacy of nucleus-to-synapse trafficking and may explain the prevalence of local biosynthesis in neurons.« less

Dendritic trafficking faces physiologically critical speed-precision tradeoffs

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

Williams, Alex H.; O'Donnell, Cian; Sejnowski, Terrence J.

Nervous system function requires intracellular transport of channels, receptors, mRNAs, and other cargo throughout complex neuronal morphologies. Local signals such as synaptic input can regulate cargo trafficking, motivating the leading conceptual model of neuron-wide transport, sometimes called the ‘sushi-belt model’. Current theories and experiments are based on this model, yet its predictions are not rigorously understood. We formalized the sushi belt model mathematically, and show that it can achieve arbitrarily complex spatial distributions of cargo in reconstructed morphologies. However, the model also predicts an unavoidable, morphology dependent tradeoff between speed, precision and metabolic efficiency of cargo transport. With experimental estimatesmore » of trafficking kinetics, the model predicts delays of many hours or days for modestly accurate and efficient cargo delivery throughout a dendritic tree. In conclusion, these findings challenge current understanding of the efficacy of nucleus-to-synapse trafficking and may explain the prevalence of local biosynthesis in neurons.« less

The Mathematics of Navigating the Solar System

NASA Technical Reports Server (NTRS)

Hintz, Gerald

2000-01-01

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Experimental Mathematics and Mathematical Physics

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

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2009-06-26

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

Underwater terrain-aided navigation system based on combination matching algorithm.

PubMed

Li, Peijuan; Sheng, Guoliang; Zhang, Xiaofei; Wu, Jingqiu; Xu, Baochun; Liu, Xing; Zhang, Yao

2018-07-01

Considering that the terrain-aided navigation (TAN) system based on iterated closest contour point (ICCP) algorithm diverges easily when the indicative track of strapdown inertial navigation system (SINS) is large, Kalman filter is adopted in the traditional ICCP algorithm, difference between matching result and SINS output is used as the measurement of Kalman filter, then the cumulative error of the SINS is corrected in time by filter feedback correction, and the indicative track used in ICCP is improved. The mathematic model of the autonomous underwater vehicle (AUV) integrated into the navigation system and the observation model of TAN is built. Proper matching point number is designated by comparing the simulation results of matching time and matching precision. Simulation experiments are carried out according to the ICCP algorithm and the mathematic model. It can be concluded from the simulation experiments that the navigation accuracy and stability are improved with the proposed combinational algorithm in case that proper matching point number is engaged. It will be shown that the integrated navigation system is effective in prohibiting the divergence of the indicative track and can meet the requirements of underwater, long-term and high precision of the navigation system for autonomous underwater vehicles. Copyright © 2017. Published by Elsevier Ltd.

Accuracy of Cycling Power Meters against a Mathematical Model of Treadmill Cycling.

PubMed

Maier, Thomas; Schmid, Lucas; Müller, Beat; Steiner, Thomas; Wehrlin, Jon Peter

2017-06-01

The aim of this study was to compare the accuracy among a high number of current mobile cycling power meters used by elite and recreational cyclists against a first principle-based mathematical model of treadmill cycling. 54 power meters from 9 manufacturers used by 32 cyclists were calibrated. While the cyclist coasted downhill on a motorised treadmill, a back-pulling system was adjusted to counter the downhill force. The system was then loaded 3 times with 4 different masses while the cyclist pedalled to keep his position. The mean deviation (trueness) to the model and coefficient of variation (precision) were analysed. The mean deviations of the power meters were -0.9±3.2% (mean±SD) with 6 power meters deviating by more than±5%. The coefficients of variation of the power meters were 1.2±0.9% (mean±SD), with Stages varying more than SRM (p<0.001) and PowerTap (p<0.001). In conclusion, current power meters used by elite and recreational cyclists vary considerably in their trueness; precision is generally high but differs between manufacturers. Calibrating and adjusting the trueness of every power meter against a first principle-based reference is advised for accurate measurements. © Georg Thieme Verlag KG Stuttgart · New York.

Mathematical Modeling of RNA-Based Architectures for Closed Loop Control of Gene Expression.

PubMed

Agrawal, Deepak K; Tang, Xun; Westbrook, Alexandra; Marshall, Ryan; Maxwell, Colin S; Lucks, Julius; Noireaux, Vincent; Beisel, Chase L; Dunlop, Mary J; Franco, Elisa

2018-05-08

Feedback allows biological systems to control gene expression precisely and reliably, even in the presence of uncertainty, by sensing and processing environmental changes. Taking inspiration from natural architectures, synthetic biologists have engineered feedback loops to tune the dynamics and improve the robustness and predictability of gene expression. However, experimental implementations of biomolecular control systems are still far from satisfying performance specifications typically achieved by electrical or mechanical control systems. To address this gap, we present mathematical models of biomolecular controllers that enable reference tracking, disturbance rejection, and tuning of the temporal response of gene expression. These controllers employ RNA transcriptional regulators to achieve closed loop control where feedback is introduced via molecular sequestration. Sensitivity analysis of the models allows us to identify which parameters influence the transient and steady state response of a target gene expression process, as well as which biologically plausible parameter values enable perfect reference tracking. We quantify performance using typical control theory metrics to characterize response properties and provide clear selection guidelines for practical applications. Our results indicate that RNA regulators are well-suited for building robust and precise feedback controllers for gene expression. Additionally, our approach illustrates several quantitative methods useful for assessing the performance of biomolecular feedback control systems.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Study of a high-precision SAW-MOEMS strain sensor with laser optics

NASA Astrophysics Data System (ADS)

Liu, Xinwei; Chen, Shufen; Li, Honglang; Zou, Zhengfeng; Fu, Lei; Meng, Yanbin

2015-02-01

A novel structure design of a surface acoustic wave (SAW) micro-optic-electro-mechanical-system (MOEMS) strain sensor with a light readout unit is presented in this paper. By measuring the polarization intensity ratio of the TE/TM mode outputted from the waveguide, the strain produced from an object can be measured precisely. The basic working principle of the SAW MOEMS strain sensor is introduced and the mathematical model of the strain sensor system is established. The SAW characteristics effected by the strain sensor are mathematically deduced. The coupling coefficient between the SAW modes and light modes can be calculated based on the theory of coupling modes. The conversion coefficient of polarized light modes is obtained. Due to the restrictions of the specific parameters of the device, the level of technology and the material characteristics, the sensitivity of the strain sensor system is calculated through simulation as 0.1 μɛ, with a dynamic range of 0 ~ ±50 μɛ.

Precision in the Teaching, Learning, and Communication of Elementary School Mathematics: A Reply to Wilson's "Elementary School Mathematics Priorities"

ERIC Educational Resources Information Center

Maher, Carolyn; Weber, Keith

2009-01-01

In "Elementary School Mathematics Priorities," Wilson (2009 [this issue]) presents a list of five core concepts that students should master in elementary school so that they can succeed in algebra. As researchers in mathematics education, the authors enthusiastically endorse Wilson's recommendations. Learning algebra is key to further study of…

Scale and the evolutionarily based approximate number system: an exploratory study

NASA Astrophysics Data System (ADS)

Delgado, Cesar; Jones, M. Gail; You, Hye Sun; Robertson, Laura; Chesnutt, Katherine; Halberda, Justin

2017-05-01

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.

"Whys" and "Hows" of Using Philosophy in Mathematics Education

ERIC Educational Resources Information Center

Jankvist, Uffe Thomas; Iversen, Steffen Møllegaard

2014-01-01

The article elaborates and exemplifies a potential categorization of the reasons for using philosophy, in particular the philosophy of mathematics, in mathematics education and approaches to doing so-the so-called "whys" and "hows". More precisely, the "whys" are divided into the two categories of "philosophy as…

Using Mental Computation Training to Improve Complex Mathematical Performance

ERIC Educational Resources Information Center

Liu, Allison S.; Kallai, Arava Y.; Schunn, Christian D.; Fiez, Julie A.

2015-01-01

Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have…

Calculation of skiving cutter blade

NASA Astrophysics Data System (ADS)

Xu, Lei; Lao, Qicheng; Shang, Zhiyi

2018-05-01

The gear skiving method is a kind of gear machining technology with high efficiency and high precision. According to the method of gear machining, a method for calculating the blade of skiving cutter in machining an involute gear is proposed. Based on the principle of meshing gear and the kinematic relationship between the machined flank and the gear skiving, the mathematical model of skiving for machining the internal gear is built and the gear tooth surface is obtained by solving the meshing equation. The mathematical model of the gear blade curve of the skiving cutter is obtained by choosing the proper rake face and the cutter tooth surface for intersection. Through the analysis of the simulation of the skiving gear, the feasibility and correctness of the skiving cutter blade design are verified.

Mathematical Model and Calibration Procedure of a PSD Sensor Used in Local Positioning Systems.

PubMed

Rodríguez-Navarro, David; Lázaro-Galilea, José Luis; Bravo-Muñoz, Ignacio; Gardel-Vicente, Alfredo; Domingo-Perez, Francisco; Tsirigotis, Georgios

2016-09-15

Here, we propose a mathematical model and a calibration procedure for a PSD (position sensitive device) sensor equipped with an optical system, to enable accurate measurement of the angle of arrival of one or more beams of light emitted by infrared (IR) transmitters located at distances of between 4 and 6 m. To achieve this objective, it was necessary to characterize the intrinsic parameters that model the system and obtain their values. This first approach was based on a pin-hole model, to which system nonlinearities were added, and this was used to model the points obtained with the nA currents provided by the PSD. In addition, we analyzed the main sources of error, including PSD sensor signal noise, gain factor imbalances and PSD sensor distortion. The results indicated that the proposed model and method provided satisfactory calibration and yielded precise parameter values, enabling accurate measurement of the angle of arrival with a low degree of error, as evidenced by the experimental results.

Theoretical Assessment of the Impact of Climatic Factors in a Vibrio Cholerae Model.

PubMed

Kolaye, G; Damakoa, I; Bowong, S; Houe, R; Békollè, D

2018-05-04

A mathematical model for Vibrio Cholerae (V. Cholerae) in a closed environment is considered, with the aim of investigating the impact of climatic factors which exerts a direct influence on the bacterial metabolism and on the bacterial reservoir capacity. We first propose a V. Cholerae mathematical model in a closed environment. A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. After, we extend this V. cholerae model by taking account climatic factors that influence the bacterial reservoir capacity. We present the theoretical analysis of the model. More precisely, we compute equilibria and study their stabilities. The stability of equilibria was investigated using the theory of periodic cooperative systems with a concave nonlinearity. Theoretical results are supported by numerical simulations which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs.

Shop Math for the Metal Trades. Combination Welder Apprentice, Machinist Helper, Precision Metal Finisher, Sheet Metal Worker Apprentice. A Report on Metal Trades Industry Certified, Single-Concept, Mathematical Learning Projects to Eliminate Student Math Fears.

ERIC Educational Resources Information Center

Newton, Lawrence R.

This project (1) identifies basic and functional mathematics skills (shop mathematics skills), (2) provides pretests on these functional mathematics skills, and (3) provides student learning projects (project sheets) that prepare metal trades students to read, understand, and apply mathematics and measuring skills that meet entry-level job…

Moving beyond Type I and Type II neuron types.

PubMed

Skinner, Frances K

2013-01-01

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

Catastrophe modelling in the biological sciences.

PubMed

Deakin, M A

1990-03-01

Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional "physical" way, it could also be applied in a new "metaphysical" way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology. Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to have been fully realised. This paper will document and classify the work that has been done. It will be argued that, like other applied Mathematics, applied Catastrophe Theory works best where the underlying laws are securely known and precisely quantified, requiring those same guarantees as does any other branch of Mathematics when it confronts a real-life situation.

Study on individual stochastic model of GNSS observations for precise kinematic applications

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik; Szpunar, Ryszard

2015-04-01

The proper definition of mathematical positioning model, which is defined by functional and stochastic models, is a prerequisite to obtain the optimal estimation of unknown parameters. Especially important in this definition is realistic modelling of stochastic properties of observations, which are more receiver-dependent and time-varying than deterministic relationships. This is particularly true with respect to precise kinematic applications which are characterized by weakening model strength. In this case, incorrect or simplified definition of stochastic model causes that the performance of ambiguity resolution and accuracy of position estimation can be limited. In this study we investigate the methods of describing the measurement noise of GNSS observations and its impact to derive precise kinematic positioning model. In particular stochastic modelling of individual components of the variance-covariance matrix of observation noise performed using observations from a very short baseline and laboratory GNSS signal generator, is analyzed. Experimental test results indicate that the utilizing the individual stochastic model of observations including elevation dependency and cross-correlation instead of assumption that raw measurements are independent with the same variance improves the performance of ambiguity resolution as well as rover positioning accuracy. This shows that the proposed stochastic assessment method could be a important part in complex calibration procedure of GNSS equipment.

Mathematical modeling in chronobiology.

PubMed

Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H

2013-01-01

Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.

From particle systems to learning processes. Comment on "Collective learning modeling based on the kinetic theory of active particles" by Diletta Burini, Silvana De Lillo, and Livio Gibelli

NASA Astrophysics Data System (ADS)

Lachowicz, Mirosław

2016-03-01

The very stimulating paper [6] discusses an approach to perception and learning in a large population of living agents. The approach is based on a generalization of kinetic theory methods in which the interactions between agents are described in terms of game theory. Such an approach was already discussed in Ref. [2-4] (see also references therein) in various contexts. The processes of perception and learning are based on the interactions between agents and therefore the general kinetic theory is a suitable tool for modeling them. However the main question that rises is how the perception and learning processes may be treated in the mathematical modeling. How may we precisely deliver suitable mathematical structures that are able to capture various aspects of perception and learning?

Comprehensive mathematical model of oxidative phosphorylation valid for physiological and pathological conditions.

PubMed

Heiske, Margit; Letellier, Thierry; Klipp, Edda

2017-09-01

We developed a mathematical model of oxidative phosphorylation (OXPHOS) that allows for a precise description of mitochondrial function with respect to the respiratory flux and the ATP production. The model reproduced flux-force relationships under various experimental conditions (state 3 and 4, uncoupling, and shortage of respiratory substrate) as well as time courses, exhibiting correct P/O ratios. The model was able to reproduce experimental threshold curves for perturbations of the respiratory chain complexes, the F 1 F 0 -ATP synthase, the ADP/ATP carrier, the phosphate/OH carrier, and the proton leak. Thus, the model is well suited to study complex interactions within the OXPHOS system, especially with respect to physiological adaptations or pathological modifications, influencing substrate and product affinities or maximal catalytic rates. Moreover, it could be a useful tool to study the role of OXPHOS and its capacity to compensate or enhance physiopathologies of the mitochondrial and cellular energy metabolism. © 2017 Federation of European Biochemical Societies.

Simulation of Electrical Characteristics of a Solar Panel

NASA Astrophysics Data System (ADS)

Obukhov, S.; Plotnikov, I.; Kryuchkova, M.

2016-06-01

The fast-growing photovoltaic system market leads to the necessity of the informed choice of major energy components and optimization of operating conditions in order to improve energy efficiency. Development of mathematical models of the main components of photovoltaic systems to ensure their comprehensive study is an urgent problem of improving and practical using of the technology of electrical energy production. The paper presents a mathematical model of the solar module implemented in the popular software MATLAB/Simulink. Equivalent circuit of the solar cell with a diode parallel without derived resistance is used for modelling. The serie8s resistance of the solar module is calculated by Newton's iterative method using the data of its technical specifications. It ensures high precision of simulation. Model validity was evaluated by the well-known technical characteristics of the module Solarex MSX 60. The calculation results of the experiment showed that the obtained current-voltage and current-watt characteristics of the model are compatible with those of the manufacturer.

A High-Level Language for Modeling Algorithms and Their Properties

NASA Astrophysics Data System (ADS)

Akhtar, Sabina; Merz, Stephan; Quinson, Martin

Designers of concurrent and distributed algorithms usually express them using pseudo-code. In contrast, most verification techniques are based on more mathematically-oriented formalisms such as state transition systems. This conceptual gap contributes to hinder the use of formal verification techniques. Leslie Lamport introduced PlusCal, a high-level algorithmic language that has the "look and feel" of pseudo-code, but is equipped with a precise semantics and includes a high-level expression language based on set theory. PlusCal models can be compiled to TLA + and verified using the model checker tlc.

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.

Study on Fuzzy Adaptive Fractional Order PIλDμ Control for Maglev Guiding System

NASA Astrophysics Data System (ADS)

Hu, Qing; Hu, Yuwei

The mathematical model of the linear elevator maglev guiding system is analyzed in this paper. For the linear elevator needs strong stability and robustness to run, the integer order PID was expanded to the fractional order, in order to improve the steady state precision, rapidity and robustness of the system, enhance the accuracy of the parameter in fractional order PIλDμ controller, the fuzzy control is combined with the fractional order PIλDμ control, using the fuzzy logic achieves the parameters online adjustment. The simulations reveal that the system has faster response speed, higher tracking precision, and has stronger robustness to the disturbance.

Definition of the Mathematical Model Coefficients on the Weld Size of Butt Joint Without Edge Preparation

NASA Astrophysics Data System (ADS)

Sidorov, Vladimir P.; Melzitdinova, Anna V.

2017-10-01

This paper represents the definition methods for thermal constants according to the data of the weld width under the normal-circular heat source. The method is based on isoline contouring of “effective power - temperature conductivity coefficient”. The definition of coefficients provides setting requirements to the precision of welding parameters support with the enough accuracy for an engineering practice.

Biology-Inspired Autonomous Control

DTIC Science & Technology

2011-08-31

from load sensing in a turbulent flow field with high levels of plant uncertainty and optical feedback latency. The results of this paper suggest... Mimicry of biological systems, in the form of precise mathematical or physical dynamical modeling, is yielding impressive insight into the underlying...processing and plants , the aerospace industry has been slow to accept adaptive control. In the past decade however, newer methods for design of adaptive

A history of chaos theory.

PubMed

Oestreicher, Christian

2007-01-01

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.

A history of chaos theory

PubMed Central

Oestreicher, Christian

2007-01-01

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865

Feedforward hysteresis compensation in trajectory control of piezoelectrically-driven nanostagers

NASA Astrophysics Data System (ADS)

Bashash, Saeid; Jalili, Nader

2006-03-01

Complex structural nonlinearities of piezoelectric materials drastically degrade their performance in variety of micro- and nano-positioning applications. From the precision positioning and control perspective, the multi-path time-history dependent hysteresis phenomenon is the most concerned nonlinearity in piezoelectric actuators to be analyzed. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligent properties of hysteresis with the effects of non-local memories are discussed. Through performing a set of experiments on a piezoelectrically-driven nanostager with high resolution capacitive position sensor, it is shown that for the precise prediction of hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the system everpresent nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect if memory units are sufficiently chosen for the inverse model.

In Vivo Bioluminescence Tomography for Monitoring Breast Tumor Growth and Metastatic Spreading: Comparative Study and Mathematical Modeling

PubMed Central

Mollard, Séverine; Fanciullino, Raphaelle; Giacometti, Sarah; Serdjebi, Cindy; Benzekry, Sebastien; Ciccolini, Joseph

2016-01-01

This study aimed at evaluating the reliability and precision of Diffuse Luminescent Imaging Tomography (DLIT) for monitoring primary tumor and metastatic spreading in breast cancer mice, and to develop a biomathematical model to describe the collected data. Using orthotopic mammary fat pad model of breast cancer (MDAMB231-Luc) in mice, we monitored tumor and metastatic spreading by three-dimensional (3D) bioluminescence and cross-validated it with standard bioluminescence imaging, caliper measurement and necropsy examination. DLIT imaging proved to be reproducible and reliable throughout time. It was possible to discriminate secondary lesions from the main breast cancer, without removing the primary tumor. Preferential metastatic sites were lungs, peritoneum and lymph nodes. Necropsy examinations confirmed DLIT measurements. Marked differences in growth profiles were observed, with an overestimation of the exponential phase when using a caliper as compared with bioluminescence. Our mathematical model taking into account the balance between living and necrotic cells proved to be able to reproduce the experimental data obtained with a caliper or DLIT imaging, because it could discriminate proliferative living cells from a more composite mass consisting of tumor cells, necrotic cell, or inflammatory tissues. DLIT imaging combined with mathematical modeling could be a powerful and informative tool in experimental oncology. PMID:27812027

MEASUREMENT AND PRECISION, EXPERIMENTAL VERSION.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

THIS DOCUMENT IS AN EXPERIMENTAL VERSION OF A PROGRAMED TEXT ON MEASUREMENT AND PRECISION. PART I CONTAINS 24 FRAMES DEALING WITH PRECISION AND SIGNIFICANT FIGURES ENCOUNTERED IN VARIOUS MATHEMATICAL COMPUTATIONS AND MEASUREMENTS. PART II BEGINS WITH A BRIEF SECTION ON EXPERIMENTAL DATA, COVERING SUCH POINTS AS (1) ESTABLISHING THE ZERO POINT, (2)…

Principles for the dynamic maintenance of cortical polarity

PubMed Central

Marco, Eugenio; Wedlich-Soldner, Roland; Li, Rong; Altschuler, Steven J.; Wu, Lani F.

2007-01-01

Summary Diverse cell types require the ability to dynamically maintain polarized membrane protein distributions through balancing transport and diffusion. However, design principles underlying dynamically maintained cortical polarity are not well understood. Here we constructed a mathematical model for characterizing the morphology of dynamically polarized protein distributions. We developed analytical approaches for measuring all model parameters from single-cell experiments. We applied our methods to a well-characterized system for studying polarized membrane proteins: budding yeast cells expressing activated Cdc42. We found that balanced diffusion and colocalized transport to and from the plasma membrane were sufficient for accurately describing polarization morphologies. Surprisingly, the model predicts that polarized regions are defined with a precision that is nearly optimal for measured transport rates, and that polarity can be dynamically stabilized through positive feedback with directed transport. Our approach provides a step towards understanding how biological systems shape spatially precise, unambiguous cortical polarity domains using dynamic processes. PMID:17448998

Dendritic trafficking faces physiologically critical speed-precision tradeoffs

PubMed Central

Williams, Alex H; O'Donnell, Cian; Sejnowski, Terrence J; O'Leary, Timothy

2016-01-01

Nervous system function requires intracellular transport of channels, receptors, mRNAs, and other cargo throughout complex neuronal morphologies. Local signals such as synaptic input can regulate cargo trafficking, motivating the leading conceptual model of neuron-wide transport, sometimes called the ‘sushi-belt model’ (Doyle and Kiebler, 2011). Current theories and experiments are based on this model, yet its predictions are not rigorously understood. We formalized the sushi belt model mathematically, and show that it can achieve arbitrarily complex spatial distributions of cargo in reconstructed morphologies. However, the model also predicts an unavoidable, morphology dependent tradeoff between speed, precision and metabolic efficiency of cargo transport. With experimental estimates of trafficking kinetics, the model predicts delays of many hours or days for modestly accurate and efficient cargo delivery throughout a dendritic tree. These findings challenge current understanding of the efficacy of nucleus-to-synapse trafficking and may explain the prevalence of local biosynthesis in neurons. DOI: http://dx.doi.org/10.7554/eLife.20556.001 PMID:28034367

Student’s rigorous mathematical thinking based on cognitive style

NASA Astrophysics Data System (ADS)

Fitriyani, H.; Khasanah, U.

2017-12-01

The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.

Analysis of precision in chemical oscillators: implications for circadian clocks

NASA Astrophysics Data System (ADS)

d'Eysmond, Thomas; De Simone, Alessandro; Naef, Felix

2013-10-01

Biochemical reaction networks often exhibit spontaneous self-sustained oscillations. An example is the circadian oscillator that lies at the heart of daily rhythms in behavior and physiology in most organisms including humans. While the period of these oscillators evolved so that it resonates with the 24 h daily environmental cycles, the precision of the oscillator (quantified via the Q factor) is another relevant property of these cell-autonomous oscillators. Since this quantity can be measured in individual cells, it is of interest to better understand how this property behaves across mathematical models of these oscillators. Current theoretical schemes for computing the Q factors show limitations for both high-dimensional models and in the vicinity of Hopf bifurcations. Here, we derive low-noise approximations that lead to numerically stable schemes also in high-dimensional models. In addition, we generalize normal form reductions that are appropriate near Hopf bifurcations. Applying our approximations to two models of circadian clocks, we show that while the low-noise regime is faithfully recapitulated, increasing the level of noise leads to species-dependent precision. We emphasize that subcomponents of the oscillator gradually decouple from the core oscillator as noise increases, which allows us to identify the subnetworks responsible for robust rhythms.

Number sense across the lifespan as revealed by a massive Internet-based sample

PubMed Central

Halberda, Justin; Ly, Ryan; Wilmer, Jeremy B.; Naiman, Daniel Q.; Germine, Laura

2012-01-01

It has been difficult to determine how cognitive systems change over the grand time scale of an entire life, as few cognitive systems are well enough understood; observable in infants, adolescents, and adults; and simple enough to measure to empower comparisons across vastly different ages. Here we address this challenge with data from more than 10,000 participants ranging from 11 to 85 years of age and investigate the precision of basic numerical intuitions and their relation to students’ performance in school mathematics across the lifespan. We all share a foundational number sense that has been observed in adults, infants, and nonhuman animals, and that, in humans, is generated by neurons in the intraparietal sulcus. Individual differences in the precision of this evolutionarily ancient number sense may impact school mathematics performance in children; however, we know little of its role beyond childhood. Here we find that population trends suggest that the precision of one’s number sense improves throughout the school-age years, peaking quite late at ∼30 y. Despite this gradual developmental improvement, we find very large individual differences in number sense precision among people of the same age, and these differences relate to school mathematical performance throughout adolescence and the adult years. The large individual differences and prolonged development of number sense, paired with its consistent and specific link to mathematics ability across the age span, hold promise for the impact of educational interventions that target the number sense. PMID:22733748

Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia)

PubMed Central

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

2015-01-01

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. We hypothesize that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. Here we show that ninth grade students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low-, typically-, and high-achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relationship persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low- from typically-achieving students, suggesting an ANS deficit that is specific to MLD. PMID:21679173

Receptive Fields and the Reconstruction of Visual Information.

DTIC Science & Technology

1985-09-01

depending on the noise . Thus our model would suggest that the interpolation filters for deblurring are playing a role in Ii hyperacuity. This is novel...of additional precision in the information can be obtained by a process of deblurring , which could be relevant to hyperacuity. It also provides an... impulse of heat diffuses into increasingly larger Gaussian distributions as time proceeds. Mathematically, let f(x) denote the initial temperature

An Archaeoastronomical Adventure.

ERIC Educational Resources Information Center

Russo, Richard

1997-01-01

Describes investigations in archaeoastronomy that combine modern archaeology with the mathematical precision of practical astronomy. Helps students develop an understanding of a society's astronomical systems which can lead to a knowledge of their religion, art, mathematics, writings, calendar, myths, and agricultural practices. (JRH)

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Bi-objective approach for placing ground and air ambulance base and helipad locations in order to optimize EMS response.

PubMed

Shahriari, Milad; Bozorgi-Amiri, Ali; Tavakoli, Shayan; Yousefi-Babadi, Abolghasem

2017-12-01

Shortening the travel time of patient transfer has clinical implications for many conditions such as cardiac arrest, trauma, stroke and STEMI. As resources are often limited precise calculations are needed. In this paper we consider the location problem for both ground and aerial emergency medical services. Given the uncertainty of when patients are in need of prompt medical attention we consider these demand points to be uncertain. We consider various ways in which ground and helicopter ambulances can work together to make the whole process go faster. We develop a mathematical model that minimizes travel time and maximizes service level. We use a compromising programming method to solve this bi-objective mathematical model. For numerical experiments we apply our model to a case study in Lorestan, Iran, using geographical and population data, and the location of the actual hospital based in the capital of the province. Results show that low-accessibility locations are the main focus of the proposed problem and with mathematical modeling access to a hospital is vastly improved. We also found out that once the budget reaches a certain point which suffices for building certain ambulance bases more investments does not necessarily result in less travel time. Copyright © 2017 Elsevier Inc. All rights reserved.

Characteristics of mathematics teaching in Shanghai, China: Through the lens of a Malaysian

NASA Astrophysics Data System (ADS)

Lim, Chap Sam

2007-06-01

The mathematical performance of Chinese students, from mainland China, Hong Kong and Taiwan, is widely acclaimed in international comparisons of mathematics achievement. However, in the eyes of the Western educators, the environments established in Chinese schools are deemed relatively unfavourable for mathematics learning. This paper reports on a study that investigates the characteristics of effective mathematics teaching in five Shanghai schools. Findings reveal that those characteristics include (a) teaching with variation; (b) emphasis of precise and elegant mathematical language; (c) emphasis of logical reasoning, mathematical thinking and proofing during teaching; (d) order and serious classroom discipline; (e) strong and coherence teacher-student rapport, and (f) strong collaborative culture amongst mathematics teachers.

Dose conversion coefficients based on the Chinese mathematical phantom and MCNP code for external photon irradiation.

PubMed

Qiu, Rui; Li, Junli; Zhang, Zhan; Liu, Liye; Bi, Lei; Ren, Li

2009-02-01

A set of conversion coefficients from kerma free-in-air to the organ-absorbed dose are presented for external monoenergetic photon beams from 10 keV to 10 MeV based on the Chinese mathematical phantom, a whole-body mathematical phantom model. The model was developed based on the methods of the Oak Ridge National Laboratory mathematical phantom series and data from the Chinese Reference Man and the Reference Asian Man. This work is carried out to obtain the conversion coefficients based on this model, which represents the characteristics of the Chinese population, as the anatomical parameters of the Chinese are different from those of Caucasians. Monte Carlo simulation with MCNP code is carried out to calculate the organ dose conversion coefficients. Before the calculation, the effects from the physics model and tally type are investigated, considering both the calculation efficiency and precision. In the calculation irradiation conditions include anterior-posterior, posterior-anterior, right lateral, left lateral, rotational and isotropic geometries. Conversion coefficients from this study are compared with those recommended in the Publication 74 of International Commission on Radiological Protection (ICRP74) since both the sets of data are calculated with mathematical phantoms. Overall, consistency between the two sets of data is observed and the difference for more than 60% of the data is below 10%. However, significant deviations are also found, mainly for the superficial organs (up to 65.9%) and bone surface (up to 66%). The big difference of the dose conversion coefficients for the superficial organs at high photon energy could be ascribed to kerma approximation for the data in ICRP74. Both anatomical variations between races and the calculation method contribute to the difference of the data for bone surface.

Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors

NASA Technical Reports Server (NTRS)

Bakhshiyan, B. T.; Nazirov, R. R.; Elyasberg, P. E.

1980-01-01

The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Analysis of the precision parameters of an optoelectronic vector-matrix processor of digital information

NASA Astrophysics Data System (ADS)

Odinokov, S. B.; Petrov, A. V.

1995-10-01

Mathematical models of components of a vector-matrix optoelectronic multiplier are considered. Perturbing factors influencing a real optoelectronic system — noise and errors of radiation sources and detectors, nonlinearity of an analogue—digital converter, nonideal optical systems — are taken into account. Analytic expressions are obtained for relating the precision of such a multiplier to the probability of an error amounting to one bit, to the parameters describing the quality of the multiplier components, and to the quality of the optical system of the processor. Various methods of increasing the dynamic range of a multiplier are considered at the technical systems level.

On a two-particle bound system on the half-line

NASA Astrophysics Data System (ADS)

Kerner, Joachim; Mühlenbruch, Tobias

2017-10-01

In this paper we provide an extension of the model discussed in [10] describing two singularly interacting particles on the half-line ℝ+. In this model, the particles are interacting only whenever at least one particle is situated at the origin. Stimulated by [11] we then provide a generalisation of this model in order to include additional interactions between the particles leading to a molecular-like state. We give a precise mathematical formulation of the Hamiltonian of the system and perform spectral analysis. In particular, we are interested in the effect of the singular two-particle interactions onto the molecule.

Application of mathematical modelling for assessing the biological half-times of chromium and nickel in field studies.

PubMed Central

Tossavainen, A; Nurminen, M; Mutanen, P; Tola, S

1980-01-01

The biological half-times of urinary chromium and nickel excretion and plasma nickel concentration were calculated for four welders and four electroplaters. A linear one-compartment kinetic model gave estimates of the half-times ranging from 15 to 41 hours for chromium in urine, from 17 to 39 hours for nickel in urine, and from 20 to 34 hours for nickel in plasma. The model allows a precise description to be made of a worker's state of exposure as affected by a varying concentration of the metals in the air. PMID:7426481

Students as Toolmakers: Refining the Results in the Accuracy and Precision of a Trigonometric Activity

ERIC Educational Resources Information Center

Igoe, D. P.; Parisi, A. V.; Wagner, S.

2017-01-01

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This…

A Bionic Polarization Navigation Sensor and Its Calibration Method.

PubMed

Zhao, Huijie; Xu, Wujian

2016-08-03

The polarization patterns of skylight which arise due to the scattering of sunlight in the atmosphere can be used by many insects for deriving compass information. Inspired by insects' polarized light compass, scientists have developed a new kind of navigation method. One of the key techniques in this method is the polarimetric sensor which is used to acquire direction information from skylight. In this paper, a polarization navigation sensor is proposed which imitates the working principles of the polarization vision systems of insects. We introduce the optical design and mathematical model of the sensor. In addition, a calibration method based on variable substitution and non-linear curve fitting is proposed. The results obtained from the outdoor experiments provide support for the feasibility and precision of the sensor. The sensor's signal processing can be well described using our mathematical model. A relatively high degree of accuracy in polarization measurement can be obtained without any error compensation.

Phased array feed design technology for Large Aperture Microwave Radiometer (LAMR) Earth observations

NASA Technical Reports Server (NTRS)

Schuman, H. K.

1992-01-01

An assessment of the potential and limitations of phased array antennas in space-based geophysical precision radiometry is described. Mathematical models exhibiting the dependence of system and scene temperatures and system sensitivity on phased array antenna parameters and components such as phase shifters and low noise amplifiers (LNA) are developed. Emphasis is given to minimum noise temperature designs wherein the LNA's are located at the array level, one per element or subarray. Two types of combiners are considered: array lenses (space feeds) and corporate networks. The result of a survey of suitable components and devices is described. The data obtained from that survey are used in conjunction with the mathematical models to yield an assessment of effective array antenna noise temperature for representative geostationary and low Earth orbit systems. Practical methods of calibrating a space-based, phased array radiometer are briefly addressed as well.

A Measuring System for Well Logging Attitude and a Method of Sensor Calibration

PubMed Central

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-01-01

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°. PMID:24859028

A Bionic Polarization Navigation Sensor and Its Calibration Method

PubMed Central

Zhao, Huijie; Xu, Wujian

2016-01-01

The polarization patterns of skylight which arise due to the scattering of sunlight in the atmosphere can be used by many insects for deriving compass information. Inspired by insects’ polarized light compass, scientists have developed a new kind of navigation method. One of the key techniques in this method is the polarimetric sensor which is used to acquire direction information from skylight. In this paper, a polarization navigation sensor is proposed which imitates the working principles of the polarization vision systems of insects. We introduce the optical design and mathematical model of the sensor. In addition, a calibration method based on variable substitution and non-linear curve fitting is proposed. The results obtained from the outdoor experiments provide support for the feasibility and precision of the sensor. The sensor’s signal processing can be well described using our mathematical model. A relatively high degree of accuracy in polarization measurement can be obtained without any error compensation. PMID:27527171

[Application of a mathematical algorithm for the detection of electroneuromyographic results in the pathogenesis study of facial dyskinesia].

PubMed

Gribova, N P; Iudel'son, Ia B; Golubev, V L; Abramenkova, I V

2003-01-01

To carry out a differential diagnosis of two facial dyskinesia (FD) models--facial hemispasm (FH) and facial paraspasm (FP), a combined program of electroneuromyographic (ENMG) examination has been created, using statistical analyses, including that for objects identification based on hybrid neural network with the application of adaptive fuzzy logic method and standard statistics programs (Wilcoxon, Student statistics). In FH, a lesion of peripheral facial neuromotor apparatus with augmentation of functions of inter-neurons in segmental and upper segmental stem levels predominated. In FP, primary afferent strengthening in mimic muscles was accompanied by increased motor neurons activity and reciprocal augmentation of inter-neurons, inhibiting motor portion of V pair. Mathematical algorithm for ENMG results recognition worked out in the study provides a precise differentiation of two FD models and opens possibilities for differential diagnosis of other facial motor disorders.

A measuring system for well logging attitude and a method of sensor calibration.

PubMed

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-05-23

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°.

An innovative method for coordinate measuring machine one-dimensional self-calibration with simplified experimental process.

PubMed

Fang, Cheng; Butler, David Lee

2013-05-01

In this paper, an innovative method for CMM (Coordinate Measuring Machine) self-calibration is proposed. In contrast to conventional CMM calibration that relies heavily on a high precision reference standard such as a laser interferometer, the proposed calibration method is based on a low-cost artefact which is fabricated with commercially available precision ball bearings. By optimizing the mathematical model and rearranging the data sampling positions, the experimental process and data analysis can be simplified. In mathematical expression, the samples can be minimized by eliminating the redundant equations among those configured by the experimental data array. The section lengths of the artefact are measured at arranged positions, with which an equation set can be configured to determine the measurement errors at the corresponding positions. With the proposed method, the equation set is short of one equation, which can be supplemented by either measuring the total length of the artefact with a higher-precision CMM or calibrating the single point error at the extreme position with a laser interferometer. In this paper, the latter is selected. With spline interpolation, the error compensation curve can be determined. To verify the proposed method, a simple calibration system was set up on a commercial CMM. Experimental results showed that with the error compensation curve uncertainty of the measurement can be reduced to 50%.

Towards a formal semantics for Ada 9X

NASA Technical Reports Server (NTRS)

Guaspari, David; Mchugh, John; Wolfgang, Polak; Saaltink, Mark

1995-01-01

The Ada 9X language precision team was formed during the revisions of Ada 83, with the goal of analyzing the proposed design, identifying problems, and suggesting improvements, through the use of mathematical models. This report defines a framework for formally describing Ada 9X, based on Kahn's 'natural semantics', and applies the framework to portions of the language. The proposals for exceptions and optimization freedoms are also analyzed, using a different technique.

Diagnosis of the Computer-Controlled Milling Machine, Definition of the Working Errors and Input Corrections on the Basis of Mathematical Model

NASA Astrophysics Data System (ADS)

Starikov, A. I.; Nekrasov, R. Yu; Teploukhov, O. J.; Soloviev, I. V.; Narikov, K. A.

2016-10-01

Manufactures, machinery and equipment improve of constructively as science advances and technology, and requirements are improving of quality and longevity. That is, the requirements for surface quality and precision manufacturing, oil and gas equipment parts are constantly increasing. Production of oil and gas engineering products on modern machine tools with computer numerical control - is a complex synthesis of technical and electrical equipment parts, as well as the processing procedure. Technical machine part wears during operation and in the electrical part are accumulated mathematical errors. Thus, the above-mentioned disadvantages of any of the following parts of metalworking equipment affect the manufacturing process of products in general, and as a result lead to the flaw.

Statistical mechanics of simple models of protein folding and design.

PubMed Central

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

1997-01-01

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

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

PubMed

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

2018-06-13

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

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

NASA Astrophysics Data System (ADS)

Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

Electrode Models for Electric Current Computed Tomography

PubMed Central

CHENG, KUO-SHENG; ISAACSON, DAVID; NEWELL, J. C.; GISSER, DAVID G.

2016-01-01

This paper develops a mathematical model for the physical properties of electrodes suitable for use in electric current computed tomography (ECCT). The model includes the effects of discretization, shunt, and contact impedance. The complete model was validated by experiment. Bath resistivities of 284.0, 139.7, 62.3, 29.5 Ω · cm were studied. Values of “effective” contact impedance z used in the numerical approximations were 58.0, 35.0, 15.0, and 7.5 Ω · cm2, respectively. Agreement between the calculated and experimentally measured values was excellent throughout the range of bath conductivities studied. It is desirable in electrical impedance imaging systems to model the observed voltages to the same precision as they are measured in order to be able to make the highest resolution reconstructions of the internal conductivity that the measurement precision allows. The complete electrode model, which includes the effects of discretization of the current pattern, the shunt effect due to the highly conductive electrode material, and the effect of an “effective” contact impedance, allows calculation of the voltages due to any current pattern applied to a homogeneous resistivity field. PMID:2777280

Electrode models for electric current computed tomography.

PubMed

Cheng, K S; Isaacson, D; Newell, J C; Gisser, D G

1989-09-01

This paper develops a mathematical model for the physical properties of electrodes suitable for use in electric current computed tomography (ECCT). The model includes the effects of discretization, shunt, and contact impedance. The complete model was validated by experiment. Bath resistivities of 284.0, 139.7, 62.3, 29.5 omega.cm were studied. Values of "effective" contact impedance zeta used in the numerical approximations were 58.0, 35.0, 15.0, and 7.5 omega.cm2, respectively. Agreement between the calculated and experimentally measured values was excellent throughout the range of bath conductivities studied. It is desirable in electrical impedance imaging systems to model the observed voltages to the same precision as they are measured in order to be able to make the highest resolution reconstructions of the internal conductivity that the measurement precision allows. The complete electrode model, which includes the effects of discretization of the current pattern, the shunt effect due to the highly conductive electrode material, and the effect of an "effective" contact impedance, allows calculation of the voltages due to any current pattern applied to a homogeneous resistivity field.

Selection of Wavelengths for Optimum Precision in Simultaneous Spectrophotometric Determinations.

ERIC Educational Resources Information Center

DiTusa, Michael R.; Schilt, Alfred A.

1985-01-01

Although many textbooks include a description of simultaneous determinations employing absorption spectrophotometry and treat the mathematics necessary for analytical quantitations, treatment of analytical wavelength selection has been mostly qualitative. Therefore, a general method for selecting wavelengths for optimum precision in simultaneous…

The evolution of utility functions and psychological altruism.

PubMed

Clavien, Christine; Chapuisat, Michel

2016-04-01

Numerous studies show that humans tend to be more cooperative than expected given the assumption that they are rational maximizers of personal gain. As a result, theoreticians have proposed elaborated formal representations of human decision-making, in which utility functions including "altruistic" or "moral" preferences replace the purely self-oriented "Homo economicus" function. Here we review mathematical approaches that provide insights into the mathematical stability of alternative utility functions. Candidate utility functions may be evaluated with help of game theory, classical modeling of social evolution that focuses on behavioral strategies, and modeling of social evolution that focuses directly on utility functions. We present the advantages of the latter form of investigation and discuss one surprisingly precise result: "Homo economicus" as well as "altruistic" utility functions are less stable than a function containing a preference for the common welfare that is only expressed in social contexts composed of individuals with similar preferences. We discuss the contribution of mathematical models to our understanding of human other-oriented behavior, with a focus on the classical debate over psychological altruism. We conclude that human can be psychologically altruistic, but that psychological altruism evolved because it was generally expressed towards individuals that contributed to the actor's fitness, such as own children, romantic partners and long term reciprocators. Copyright © 2015 Elsevier Ltd. All rights reserved.

Research on H2 speed governor for diesel engine of marine power station

NASA Astrophysics Data System (ADS)

Huang, Man-Lei

2007-09-01

The frequency stability of a marine power system is determined by the dynamic characteristic of the diesel engine speed regulation system in a marine power station. In order to reduce the effect of load disturbances and improve the dynamic precision of a diesel engine speed governor, a controller was designed for a diesel engine speed regulation system using H2 control theory. This transforms the specifications of the system into a standard H2 control problem. Firstly, the mathematical model of a diesel engine speed regulation system using an H2 speed governor is presented. To counter external disturbances and model uncertainty, the design of an H2 speed governor rests on the problem of mixed sensitivity. Computer simulation verified that the H2 speed governor improves the dynamic precision of a system and the ability to adapt to load disturbances, thus enhancing the frequency stability of marine power systems.

Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia).

PubMed

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

2011-01-01

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth graders, it is shown that students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low, typically, and high achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relation persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low-achieving from typically achieving students, suggesting an ANS deficit that is specific to MLD. © 2011 The Authors. Child Development © 2011 Society for Research in Child Development, Inc.

Eigenfunction Expansions and Lippmann-Schwinger Formulas

NASA Astrophysics Data System (ADS)

Gadella, M.; Kielanowski, P.

2011-12-01

In this paper we discuss in the mathematically precise way the definition of a resonance, that requires two Hamiltonians (free and perturbed), the notion of Gamow vectors, Lippmann-Schwinger equations and the analytic properties of their solutions in the context of the Gamow vectors. Next we discuss the eigenfunction expansions in the presence of resonances. In the case of the Friedrichs model, the precise form of these generalized eigenfunctions has been given in the literature. Although there are two families of eigenfunction expansions which are related through the time reversal operator, free and perturbed Hamiltonians are time invariant. On the other hand, PT symmetries play no role in this discussion. Our discussion clarifies the results of the paper [1], which contains imprecise or even wrong statements.

Mathematical model governing laser-produced dental cavity

NASA Astrophysics Data System (ADS)

Yilbas, Bekir S.; Karatoy, M.; Yilbas, Z.; Karakas, Eyup S.; Bilge, A.; Ustunbas, Hasan B.; Ceyhan, O.

1990-06-01

Formation of dental cavity may be improved by using a laser beam. This provides nonmechanical contact, precise location of cavity, rapid processing and increased hygienity. Further examination of interaction mechanism is needed to improve the application of lasers in density. Present study examines the tenperature rise and thermal stress development in the enamel during Nd YAG laser irradiation. It is found that the stresses developed in the enamel is not sufficiently high enough to cause crack developed in the enamel.

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

Parameters Identification for Photovoltaic Module Based on an Improved Artificial Fish Swarm Algorithm

PubMed Central

Wang, Hong-Hua

2014-01-01

A precise mathematical model plays a pivotal role in the simulation, evaluation, and optimization of photovoltaic (PV) power systems. Different from the traditional linear model, the model of PV module has the features of nonlinearity and multiparameters. Since conventional methods are incapable of identifying the parameters of PV module, an excellent optimization algorithm is required. Artificial fish swarm algorithm (AFSA), originally inspired by the simulation of collective behavior of real fish swarms, is proposed to fast and accurately extract the parameters of PV module. In addition to the regular operation, a mutation operator (MO) is designed to enhance the searching performance of the algorithm. The feasibility of the proposed method is demonstrated by various parameters of PV module under different environmental conditions, and the testing results are compared with other studied methods in terms of final solutions and computational time. The simulation results show that the proposed method is capable of obtaining higher parameters identification precision. PMID:25243233

Composite adaptive control of belt polishing force for aero-engine blade

NASA Astrophysics Data System (ADS)

Zhsao, Pengbing; Shi, Yaoyao

2013-09-01

The existing methods for blade polishing mainly focus on robot polishing and manual grinding. Due to the difficulty in high-precision control of the polishing force, the blade surface precision is very low in robot polishing, in particular, quality of the inlet and exhaust edges can not satisfy the processing requirements. Manual grinding has low efficiency, high labor intensity and unstable processing quality, moreover, the polished surface is vulnerable to burn, and the surface precision and integrity are difficult to ensure. In order to further improve the profile accuracy and surface quality, a pneumatic flexible polishing force-exerting mechanism is designed and a dual-mode switching composite adaptive control(DSCAC) strategy is proposed, which combines Bang-Bang control and model reference adaptive control based on fuzzy neural network(MRACFNN) together. By the mode decision-making mechanism, Bang-Bang control is used to track the control command signal quickly when the actual polishing force is far away from the target value, and MRACFNN is utilized in smaller error ranges to improve the system robustness and control precision. Based on the mathematical model of the force-exerting mechanism, simulation analysis is implemented on DSCAC. Simulation results show that the output polishing force can better track the given signal. Finally, the blade polishing experiments are carried out on the designed polishing equipment. Experimental results show that DSCAC can effectively mitigate the influence of gas compressibility, valve dead-time effect, valve nonlinear flow, cylinder friction, measurement noise and other interference on the control precision of polishing force, which has high control precision, strong robustness, strong anti-interference ability and other advantages compared with MRACFNN. The proposed research achieves high-precision control of the polishing force, effectively improves the blade machining precision and surface consistency, and significantly reduces the surface roughness.

Mathematical modeling of the process of determining the standards for process losses in the transfer of thermal energy of the coolant

NASA Astrophysics Data System (ADS)

Akhmetova, I. G.; Chichirova, N. D.

2017-11-01

Currently the actual problem is a precise definition of the normative and actual heat loss. Existing methods - experimental, on metering devices, on the basis of mathematical modeling methods are not without drawbacks. Heat losses establishing during the heat carrier transport has an impact on the tariff structure of heat supply organizations. This quantity determination also promotes proper choice of main and auxiliary equipment power, temperature chart of heat supply networks, as well as the heating system structure choice with the decentralization. Calculation of actual heat loss and their comparison with standard values justifies the performance of works on improvement of the heat networks with the replacement of piping or its insulation. To determine the cause of discrepancies between normative and actual heat losses thermal tests on the magnitude of the actual heat losses in the 124 sections of heat networks in Kazan. As were carried out the result mathematical model of the regulatory definition of heat losses is developed and tested. This model differ from differs the existing according the piping insulation type. The application of this factor will bring the value of calculative normative losses heat energy to their actual value. It is of great importance for enterprises operating distribution networks and because of the conditions of their configuration and extensions do not have the technical ability to produce thermal testing.

Produce Intrigue with Crypto!

ERIC Educational Resources Information Center

Avila, Cheryl L.; Ortiz, Enrique

2012-01-01

Learning mathematics is challenging. It requires discipline, logic, precision, perseverance, and accuracy. It can also be fun. When mathematics is set in a context that inspires students to want to solve interesting problems, students will have an intrinsic desire to learn the necessary skills to accomplish a specific goal. The game of Crypto! was…

Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.

PubMed

Zana, F; Klein, J C

2001-01-01

This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.

The effect of mathematics anxiety on the processing of numerical magnitude.

PubMed

Maloney, Erin A; Ansari, Daniel; Fugelsang, Jonathan A

2011-01-01

In an effort to understand the origins of mathematics anxiety, we investigated the processing of symbolic magnitude by high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals by examining their performance on two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. These data support the claim that HMA individuals have less precise representations of numerical magnitude than their LMA peers, suggesting that MA is associated with low-level numerical deficits that compromise the development of higher level mathematical skills.

Study on Heat Transfer Agent Models of Transmission Line and Transformer

NASA Astrophysics Data System (ADS)

Wang, B.; Zhang, P. P.

2018-04-01

When using heat transfer simulation to study the dynamic overload of transmission line and transformer, it needs to establish the mathematical expression of heat transfer. However, the formula is a nonlinear differential equation or equation set and it is not easy to get general solutions. Aiming at this problem, some different temperature change processes caused by different initial conditions are calculated by differential equation and equation set. New agent models are developed according to the characteristics of different temperature change processes. The results show that the agent models have high precision and can solve the problem that the original equation cannot be directly applied in some practical engineers.

The Definition of Mathematics: Philosophical and Pedagogical Aspects

NASA Astrophysics Data System (ADS)

Khait, Alexander

There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. Educational implications of this idea are considered in the light of(1) a strong tendency of most humans to the fuzzy way of thought as described by the dual-process theory developed by researchers of human reasoning;

[The uncertainty evaluation of analytical results of 27 elements in geological samples by X-ray fluorescence spectrometry].

PubMed

Wang, Yi-Ya; Zhan, Xiu-Chun

2014-04-01

Evaluating uncertainty of analytical results with 165 geological samples by polarized dispersive X-ray fluorescence spectrometry (P-EDXRF) has been reported according to the internationally accepted guidelines. One hundred sixty five pressed pellets of similar matrix geological samples with reliable values were analyzed by P-EDXRF. These samples were divided into several different concentration sections in the concentration ranges of every component. The relative uncertainties caused by precision and accuracy of 27 components were evaluated respectively. For one element in one concentration, the relative uncertainty caused by precision can be calculated according to the average value of relative standard deviation with different concentration level in one concentration section, n = 6 stands for the 6 results of one concentration level. The relative uncertainty caused by accuracy in one concentration section can be evaluated by the relative standard deviation of relative deviation with different concentration level in one concentration section. According to the error propagation theory, combining the precision uncertainty and the accuracy uncertainty into a global uncertainty, this global uncertainty acted as method uncertainty. This model of evaluating uncertainty can solve a series of difficult questions in the process of evaluating uncertainty, such as uncertainties caused by complex matrix of geological samples, calibration procedure, standard samples, unknown samples, matrix correction, overlap correction, sample preparation, instrument condition and mathematics model. The uncertainty of analytical results in this method can act as the uncertainty of the results of the similar matrix unknown sample in one concentration section. This evaluation model is a basic statistical method owning the practical application value, which can provide a strong base for the building of model of the following uncertainty evaluation function. However, this model used a lot of samples which cannot simply be applied to other types of samples with different matrix samples. The number of samples is too large to adapt to other type's samples. We will strive for using this study as a basis to establish a reasonable basis of mathematical statistics function mode to be applied to different types of samples.

Novel mathematical model to estimate ball impact force in soccer.

PubMed

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

2017-11-22

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

Installation Restoration Program. Phase II. Confirmation/Quantification. Stage 1 for Tinker AFB, Oklahoma. Volume 2. Appendices,

DTIC Science & Technology

1985-09-01

Special Olt 9-; ~ ~ ~ ~ ~ J -..-- w--- ’- V - V --y a - . . . . . . RADIAN APPENDIX A Definitions, Nomenclatures and Units A- i . -- 5. . -, - - STAGED...contaminatg ed 11 a thei±r~ iMei S-t.r-roundlin. Review the u f -r Ai Force investigationa. These *r-esu I.ts shall~ I & prvie une eatcvr B-5 -9 V q M I ...results or highly complicated nonlinear mathematical modeling , should * be precise, clear and technically defendable. This section should clearly

Mathematical-Programming Approaches to Test Item Pool Design. Research Report.

ERIC Educational Resources Information Center

Veldkamp, Bernard P.; van der Linden, Wim J.; Ariel, Adelaide

This paper presents an approach to item pool design that has the potential to improve on the quality of current item pools in educational and psychological testing and thus to increase both measurement precision and validity. The approach consists of the application of mathematical programming techniques to calculate optimal blueprints for item…

Attending to Precision: Vocabulary Support in Middle School Mathematics Classrooms

ERIC Educational Resources Information Center

Livers, Stefanie D.; Elmore, Patricia

2018-01-01

Mastery of language is critical to the mastery of content in middle school content area classrooms. In order to comprehend the disciplinary-specific texts that they encounter in their social studies, language arts, science, and mathematics classrooms, students must be literate in the content area vocabulary that is specific to those disciplines.…

Perceived Utility of Typesetting Homework in Post-Calculus Mathematics Courses

ERIC Educational Resources Information Center

Quinlan, James; Tennenhouse, Craig

2016-01-01

Too often our students submit incomplete homework that is disorganized, unclear, and nonlinear. Typesetting with LATEX, although time consuming for those new to the software, strengthens communication by forcing organization and proper notation required by the precise, formal language of mathematics. In this manuscript we report on a study of 42…

Design, analysis and control of a novel tendon-driven magnetic resonance-guided robotic system for minimally invasive breast surgery.

PubMed

Jiang, Shan; Lou, Jinlong; Yang, Zhiyong; Dai, Jiansheng; Yu, Yan

2015-09-01

Biopsy and brachytherapy for small core breast cancer are always difficult medical problems in the field of cancer treatment. This research mainly develops a magnetic resonance imaging-guided high-precision robotic system for breast puncture treatment. First, a 5-degree-of-freedom tendon-based surgical robotic system is introduced in detail. What follows are the kinematic analysis and dynamical modeling of the robotic system, where a mathematic dynamic model is established using the Lagrange method and a lumped parameter tendon model is used to identify the nonlinear gain of the tendon-sheath transmission system. Based on the dynamical models, an adaptive proportional-integral-derivative controller with friction compensation is proposed for accurate position control. Through simulations using different sinusoidal input signals, we observe that the sinusoidal tracking error at 1/2π Hz is 0.41 mm. Finally, the experiments on tendon-sheath transmission and needle insertion performance are conducted, which show that the insertion precision is 0.68 mm in laboratory environment. © IMechE 2015.

A new mathematical model for nitrogen gas production with special emphasis on the role of attached growth media in anammox hybrid reactor.

PubMed

Tomar, Swati; Gupta, Sunil Kumar

2015-11-01

The present study emphasised on the development of new mathematical models based on mass balance and stoichiometry of nitrogen removal in anammox hybrid reactor (AHR). The performance of AHR at varying hydraulic retention times (HRTs) and nitrogen loading rates (NLRs) revealed that nitrogen removal efficiency (NRE) increases with increase in HRT and was found optimal (89 %) at HRT of 2 days. Mass balance of nitrogen revealed that major fraction (74.1 %) of input nitrogen is converted into N2 gas followed by 11.2 % utilised in biomass synthesis. Attached growth media (AGM) in AHR contributed to an additional 15.4 % ammonium removal and reduced the sludge washout rate by 29 %. This also enhanced the sludge retention capacity of AHR and thus minimised the formation of nitrate in the treated effluent, which is one of the bottlenecks of anammox process. Process kinetics was also studied using various mathematical models. The mass balance model derived from total nitrogen was found most precise and predicted N2 gas with least error (1.68 ± 4.44 %). Model validation for substrate removal kinetics dictated comparatively higher correlation for Grau second-order model (0.952) than modified Stover-Kincannon model (0.920). The study concluded that owing to features of high biomass retention, less nitrate formation and consistently higher nitrogen removal efficiency, this reactor configuration is techno-economically most efficient and viable. The study opens the door for researchers and scientists for pilot-scale testing of AHR leading to its wide industrial application.

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

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

How Fuzzy-Trace Theory Predicts True and False Memories for Words, Sentences, and Narratives

PubMed Central

Reyna, Valerie F.; Corbin, Jonathan C.; Weldon, Rebecca B.; Brainerd, Charles J.

2016-01-01

Fuzzy-trace theory posits independent verbatim and gist memory processes, a distinction that has implications for such applied topics as eyewitness testimony. This distinction between precise, literal verbatim memory and meaning-based, intuitive gist accounts for memory paradoxes including dissociations between true and false memory, false memories outlasting true memories, and developmental increases in false memory. We provide an overview of fuzzy-trace theory, and, using mathematical modeling, also present results demonstrating verbatim and gist memory in true and false recognition of narrative sentences and inferences. Results supported fuzzy-trace theory's dual-process view of memory: verbatim memory was relied on to reject meaning-consistent, but unpresented, sentences (via recollection rejection). However, verbatim memory was often not retrieved, and gist memory supported acceptance of these sentences (via similarity judgment and phantom recollection). Thus, mathematical models of words can be extended to explain memory for complex stimuli, such as narratives, the kind of memory interrogated in law. PMID:27042402

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

PubMed Central

Lourenco, Stella F.; Bonny, Justin W.; Fernandez, Edmund P.; Rao, Sonia

2012-01-01

Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude. PMID:23091023

Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

PubMed

Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

2013-07-01

Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

Conditionally prepared photon and quantum imaging

NASA Astrophysics Data System (ADS)

Lvovsky, Alexander I.; Aichele, Thomas

2004-10-01

We discuss a classical model allowing one to visualize and characterize the optical mode of the single photon generated by means of a conditional measurement on a biphoton produced in parametric down-conversion. The model is based on Klyshko's advanced wave interpretation, but extends beyond it, providing a precise mathematical description of the advanced wave. The optical mode of the conditional photon is shown to be identical to the mode of the classical difference-frequency field generated due to nonlinear interaction of the partially coherent advanced wave with the pump pulse. With this "nonlinear advanced wave model" most coherence properties of the conditional photon become manifest, which permits one to intuitively understand many recent results, in particular, in quantum imaging.

How Archimedes Helped Students to Unravel the Mystery of the Magical Number Pi

ERIC Educational Resources Information Center

Papadopoulos, Ioannis

2014-01-01

This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes's method of exhaustion in order to compute the number p. Working in a computer environment, students inscribe and…

Similarities and Dissimilarities in Coauthorship Networks: Gestalt Theory as Explanation for Well-Ordered Collaboration Structures and Production of Scientific Literature.

ERIC Educational Resources Information Center

Kretschmer, Hildrun

2002-01-01

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. Develops a mathematical function to describe these gestalts in scientific literature and discusses structural characteristics of…

A mathematical definition of the financial bubbles and crashes

NASA Astrophysics Data System (ADS)

Watanabe, Kota; Takayasu, Hideki; Takayasu, Misako

2007-09-01

We check the validity of the mathematical method of detecting financial bubbles or crashes, which is based on a data fitting with an exponential function. We show that the period of a bubble can be determined nearly uniquely independent of the precision of data. The method is widely applicable for stock market data such as the Internet bubble.

Adiabatic invariants in stellar dynamics. 1: Basic concepts

NASA Technical Reports Server (NTRS)

Weinberg, Martin D.

1994-01-01

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

A Mathematical Model and Algorithm for Routing Air Traffic Under Weather Uncertainty

NASA Technical Reports Server (NTRS)

Sadovsky, Alexander V.

2016-01-01

A central challenge in managing today's commercial en route air traffic is the task of routing the aircraft in the presence of adverse weather. Such weather can make regions of the airspace unusable, so all affected flights must be re-routed. Today this task is carried out by conference and negotiation between human air traffic controllers (ATC) responsible for the involved sectors of the airspace. One can argue that, in so doing, ATC try to solve an optimization problem without giving it a precise quantitative formulation. Such a formulation gives the mathematical machinery for constructing and verifying algorithms that are aimed at solving the problem. This paper contributes one such formulation and a corresponding algorithm. The algorithm addresses weather uncertainty and has closed form, which allows transparent analysis of correctness, realism, and computational costs.

Quality assessment and artificial neural networks modeling for characterization of chemical and physical parameters of potable water.

PubMed

Salari, Marjan; Salami Shahid, Esmaeel; Afzali, Seied Hosein; Ehteshami, Majid; Conti, Gea Oliveri; Derakhshan, Zahra; Sheibani, Solmaz Nikbakht

2018-04-22

Today, due to the increase in the population, the growth of industry and the variety of chemical compounds, the quality of drinking water has decreased. Five important river water quality properties such as: dissolved oxygen (DO), total dissolved solids (TDS), total hardness (TH), alkalinity (ALK) and turbidity (TU) were estimated by parameters such as: electric conductivity (EC), temperature (T), and pH that could be measured easily with almost no costs. Simulate water quality parameters were examined with two methods of modeling include mathematical and Artificial Neural Networks (ANN). Mathematical methods are based on polynomial fitting with least square method and ANN modeling algorithms are feed-forward networks. All conditions/circumstances covered by neural network modeling were tested for all parameters in this study, except for Alkalinity. All optimum ANN models developed to simulate water quality parameters had precision value as R-value close to 0.99. The ANN model extended to simulate alkalinity with R-value equals to 0.82. Moreover, Surface fitting techniques were used to refine data sets. Presented models and equations are reliable/useable tools for studying water quality parameters at similar rivers, as a proper replacement for traditional water quality measuring equipment's. Copyright © 2018 Elsevier Ltd. All rights reserved.

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

It's difficult to build precise mathematical models for complex engineering systems because of the complexity of the structure and dynamics characteristics. Intelligent fault diagnosis introduces artificial intelligence and works in a different way without building the analytical mathematical model of a diagnostic object, so it's a practical approach to solve diagnostic problems of complex systems. This paper presents an intelligent fault diagnosis method, an integrated fault-pattern classifier based on Hidden Markov Model (HMM). This classifier consists of dynamic time warping (DTW) algorithm, self-organizing feature mapping (SOFM) network and Hidden Markov Model. First, after dynamic observation vector in measuring space is processed by DTW, the error vector including the fault feature of being tested system is obtained. Then a SOFM network is used as a feature extractor and vector quantization processor. Finally, fault diagnosis is realized by fault patterns classifying with the Hidden Markov Model classifier. The importing of dynamic time warping solves the problem of feature extracting from dynamic process vectors of complex system such as aeroengine, and makes it come true to diagnose complex system by utilizing dynamic process information. Simulating experiments show that the diagnosis model is easy to extend, and the fault pattern classifier is efficient and is convenient to the detecting and diagnosing of new faults.

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib

PubMed Central

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J.; Wolf, Stephanie; Mueller, Nikola S.; D'Alessandro, Lorenza A.; Mueller-Bohl, Stephanie; Boehm, Martin E.; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D.; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J.; Ehlting, Christian; Bode, Johannes G.; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines. PMID:29062282

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib.

PubMed

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J; Wolf, Stephanie; Mueller, Nikola S; D'Alessandro, Lorenza A; Mueller-Bohl, Stephanie; Boehm, Martin E; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J; Ehlting, Christian; Bode, Johannes G; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines.

A Density Perturbation Method to Study the Eigenstructure of Two-Phase Flow Equation Systems

NASA Astrophysics Data System (ADS)

Cortes, J.; Debussche, A.; Toumi, I.

1998-12-01

Many interesting and challenging physical mechanisms are concerned with the mathematical notion of eigenstructure. In two-fluid models, complex phasic interactions yield a complex eigenstructure which may raise numerous problems in numerical simulations. In this paper, we develop a perturbation method to examine the eigenvalues and eigenvectors of two-fluid models. This original method, based on the stiffness of the density ratio, provides a convenient tool to study the relevance of pressure momentum interactions and allows us to get precise approximations of the whole flow eigendecomposition for minor requirements. Roe scheme is successfully implemented and some numerical tests are presented.

Adding-point strategy for reduced-order hypersonic aerothermodynamics modeling based on fuzzy clustering

NASA Astrophysics Data System (ADS)

Chen, Xin; Liu, Li; Zhou, Sida; Yue, Zhenjiang

2016-09-01

Reduced order models(ROMs) based on the snapshots on the CFD high-fidelity simulations have been paid great attention recently due to their capability of capturing the features of the complex geometries and flow configurations. To improve the efficiency and precision of the ROMs, it is indispensable to add extra sampling points to the initial snapshots, since the number of sampling points to achieve an adequately accurate ROM is generally unknown in prior, but a large number of initial sampling points reduces the parsimony of the ROMs. A fuzzy-clustering-based adding-point strategy is proposed and the fuzzy clustering acts an indicator of the region in which the precision of ROMs is relatively low. The proposed method is applied to construct the ROMs for the benchmark mathematical examples and a numerical example of hypersonic aerothermodynamics prediction for a typical control surface. The proposed method can achieve a 34.5% improvement on the efficiency than the estimated mean squared error prediction algorithm and shows same-level prediction accuracy.

Benford's law gives better scaling exponents in phase transitions of quantum XY models.

PubMed

Rane, Ameya Deepak; Mishra, Utkarsh; Biswas, Anindya; Sen De, Aditi; Sen, Ujjwal

2014-08-01

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.

Intelligence rules of hysteresis in the feedforward trajectory control of piezoelectrically-driven nanostagers

NASA Astrophysics Data System (ADS)

Bashash, Saeid; Jalili, Nader

2007-02-01

Piezoelectrically-driven nanostagers have limited performance in a variety of feedforward and feedback positioning applications because of their nonlinear hysteretic response to input voltage. The hysteresis phenomenon is well known for its complex and multi-path behavior. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligence properties of hysteresis with the effects of non-local memories are discussed here. Through performing a set of experiments on a piezoelectrically-driven nanostager with a high resolution capacitive position sensor, it is shown that for the precise prediction of the hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of the hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the ever-present nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect, if memory units are sufficiently chosen for the inverse model.

Study on seepage characteristics of inclined wall dam after heavy drought

NASA Astrophysics Data System (ADS)

Wei, YE; Fuheng, MA

2018-05-01

For seepage of the dam slope with cracks after drought, there are two methods to study including the physical model test and numerical calculation. However, the physical model test can not visualize the seepage field in the dam body intuitively, and the mathematical model is not accurate because of the precision of the parameter. So in this paper, combined physical model with mathematical model, the surface crack development on the dam slope and the changes of pore water pressure were studied through the physical model test, and then numerical calculation was carried out to analyze the internal seepage of the dam body. The results showed that cracks were more likely to develop at middle of the upstream dam slope and dam heel, and cracks for different degrees appeared at different parts of the dam slope after drought. The development of cracks provided a preferential permeable channel which caused that the area near the crack was easily to become saturated. The saturated zone kept expanding leading the infiltration line to be close to the transition layer and the infiltration line was no longer a smooth curve. There were seepage damages and landslide hazards existing with such seepage characteristics, which would threaten the safety of the dam.

Hemojuvelin-hepcidin axis modeled and analyzed using Petri nets.

PubMed

Formanowicz, Dorota; Kozak, Adam; Głowacki, Tomasz; Radom, Marcin; Formanowicz, Piotr

2013-12-01

Systems biology approach to investigate biological phenomena seems to be very promising because it is capable to capture one of the fundamental properties of living organisms, i.e. their inherent complexity. It allows for analysis biological entities as complex systems of interacting objects. The first and necessary step of such an analysis is building a precise model of the studied biological system. This model is expressed in the language of some branch of mathematics, as for example, differential equations. During the last two decades the theory of Petri nets has appeared to be very well suited for building models of biological systems. The structure of these nets reflects the structure of interacting biological molecules and processes. Moreover, on one hand, Petri nets have intuitive graphical representation being very helpful in understanding the structure of the system and on the other hand, there is a lot of mathematical methods and software tools supporting an analysis of the properties of the nets. In this paper a Petri net based model of the hemojuvelin-hepcidin axis involved in the maintenance of the human body iron homeostasis is presented. The analysis based mainly on T-invariants of the model properties has been made and some biological conclusions have been drawn. Copyright © 2013 Elsevier Inc. All rights reserved.

Causality

NASA Astrophysics Data System (ADS)

Pearl, Judea

2000-03-01

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

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

PubMed

Wong, Terry Tin-Yau

2017-12-01

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

Digital PCR Modeling for Maximal Sensitivity, Dynamic Range and Measurement Precision

PubMed Central

Majumdar, Nivedita; Wessel, Thomas; Marks, Jeffrey

2015-01-01

The great promise of digital PCR is the potential for unparalleled precision enabling accurate measurements for genetic quantification. A challenge associated with digital PCR experiments, when testing unknown samples, is to perform experiments at dilutions allowing the detection of one or more targets of interest at a desired level of precision. While theory states that optimal precision (Po) is achieved by targeting ~1.59 mean copies per partition (λ), and that dynamic range (R) includes the space spanning one positive (λL) to one negative (λU) result from the total number of partitions (n), these results are tempered for the practitioner seeking to construct digital PCR experiments in the laboratory. A mathematical framework is presented elucidating the relationships between precision, dynamic range, number of partitions, interrogated volume, and sensitivity in digital PCR. The impact that false reaction calls and volumetric variation have on sensitivity and precision is next considered. The resultant effects on sensitivity and precision are established via Monte Carlo simulations reflecting the real-world likelihood of encountering such scenarios in the laboratory. The simulations provide insight to the practitioner on how to adapt experimental loading concentrations to counteract any one of these conditions. The framework is augmented with a method of extending the dynamic range of digital PCR, with and without increasing n, via the use of dilutions. An example experiment demonstrating the capabilities of the framework is presented enabling detection across 3.33 logs of starting copy concentration. PMID:25806524

Network-based machine learning and graph theory algorithms for precision oncology.

PubMed

Zhang, Wei; Chien, Jeremy; Yong, Jeongsik; Kuang, Rui

2017-01-01

Network-based analytics plays an increasingly important role in precision oncology. Growing evidence in recent studies suggests that cancer can be better understood through mutated or dysregulated pathways or networks rather than individual mutations and that the efficacy of repositioned drugs can be inferred from disease modules in molecular networks. This article reviews network-based machine learning and graph theory algorithms for integrative analysis of personal genomic data and biomedical knowledge bases to identify tumor-specific molecular mechanisms, candidate targets and repositioned drugs for personalized treatment. The review focuses on the algorithmic design and mathematical formulation of these methods to facilitate applications and implementations of network-based analysis in the practice of precision oncology. We review the methods applied in three scenarios to integrate genomic data and network models in different analysis pipelines, and we examine three categories of network-based approaches for repositioning drugs in drug-disease-gene networks. In addition, we perform a comprehensive subnetwork/pathway analysis of mutations in 31 cancer genome projects in the Cancer Genome Atlas and present a detailed case study on ovarian cancer. Finally, we discuss interesting observations, potential pitfalls and future directions in network-based precision oncology.

Computing Generalized Matrix Inverse on Spiking Neural Substrate.

PubMed

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines.

Fuzzy PID control algorithm based on PSO and application in BLDC motor

NASA Astrophysics Data System (ADS)

Lin, Sen; Wang, Guanglong

2017-06-01

A fuzzy PID control algorithm is studied based on improved particle swarm optimization (PSO) to perform Brushless DC (BLDC) motor control which has high accuracy, good anti-jamming capability and steady state accuracy compared with traditional PID control. The mathematical and simulation model is established for BLDC motor by simulink software, and the speed loop of the fuzzy PID controller is designed. The simulation results show that the fuzzy PID control algorithm based on PSO has higher stability, high control precision and faster dynamic response speed.

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1996-01-01

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

The association between higher education and approximate number system acuity

PubMed Central

Lindskog, Marcus; Winman, Anders; Juslin, Peter

2014-01-01

Humans are equipped with an approximate number system (ANS) supporting non-symbolic numerosity representation. Studies indicate a relationship between ANS-precision (acuity) and math achievement. Whether the ANS is a prerequisite for learning mathematics or if mathematics education enhances the ANS remains an open question. We investigated the association between higher education and ANS acuity with university students majoring in subjects with varying amounts of mathematics (mathematics, business, and humanities), measured either early (First year) or late (Third year) in their studies. The results suggested a non-significant trend where students taking more mathematics had better ANS acuity and a significant improvement in ANS acuity as a function of study length that was mainly confined to the business students. The results provide partial support for the hypothesis that education in mathematics can enhance the ANS acuity. PMID:24904478

The association between higher education and approximate number system acuity.

PubMed

Lindskog, Marcus; Winman, Anders; Juslin, Peter

2014-01-01

Humans are equipped with an approximate number system (ANS) supporting non-symbolic numerosity representation. Studies indicate a relationship between ANS-precision (acuity) and math achievement. Whether the ANS is a prerequisite for learning mathematics or if mathematics education enhances the ANS remains an open question. We investigated the association between higher education and ANS acuity with university students majoring in subjects with varying amounts of mathematics (mathematics, business, and humanities), measured either early (First year) or late (Third year) in their studies. The results suggested a non-significant trend where students taking more mathematics had better ANS acuity and a significant improvement in ANS acuity as a function of study length that was mainly confined to the business students. The results provide partial support for the hypothesis that education in mathematics can enhance the ANS acuity.

Computational modeling in melanoma for novel drug discovery.

PubMed

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

2016-06-01

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

Basic mathematical function libraries for scientific computation

NASA Technical Reports Server (NTRS)

Galant, David C.

1989-01-01

Ada packages implementing selected mathematical functions for the support of scientific and engineering applications were written. The packages provide the Ada programmer with the mathematical function support found in the languages Pascal and FORTRAN as well as an extended precision arithmetic and a complete complex arithmetic. The algorithms used are fully described and analyzed. Implementation assumes that the Ada type FLOAT objects fully conform to the IEEE 754-1985 standard for single binary floating-point arithmetic, and that INTEGER objects are 32-bit entities. Codes for the Ada packages are included as appendixes.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children.

PubMed

Lourenco, Stella F; Bonny, Justin W

2017-07-01

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude. © 2016 John Wiley & Sons Ltd.

Melanoma Cell Colony Expansion Parameters Revealed by Approximate Bayesian Computation

PubMed Central

Vo, Brenda N.; Drovandi, Christopher C.; Pettitt, Anthony N.; Pettet, Graeme J.

2015-01-01

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ. PMID:26642072

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Design of horizontal-axis wind turbine using blade element momentum method

NASA Astrophysics Data System (ADS)

Bobonea, Andreea; Pricop, Mihai Victor

2013-10-01

The study of mathematical models applied to wind turbine design in recent years, principally in electrical energy generation, has become significant due to the increasing use of renewable energy sources with low environmental impact. Thus, this paper shows an alternative mathematical scheme for the wind turbine design, based on the Blade Element Momentum (BEM) Theory. The results from the BEM method are greatly dependent on the precision of the lift and drag coefficients. The basic of BEM method assumes the blade can be analyzed as a number of independent element in spanwise direction. The induced velocity at each element is determined by performing the momentum balance for a control volume containing the blade element. The aerodynamic forces on the element are calculated using the lift and drag coefficient from the empirical two-dimensional wind tunnel test data at the geometric angle of attack (AOA) of the blade element relative to the local flow velocity.

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

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

2017-01-01

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

Quantitative properties of clustering within modern microscopic nuclear models

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

Volya, A.; Tchuvil’sky, Yu. M., E-mail: tchuvl@nucl-th.sinp.msu.ru

2016-09-15

A method for studying cluster spectroscopic properties of nuclear fragmentation, such as spectroscopic amplitudes, cluster form factors, and spectroscopic factors, is developed on the basis of modern precision nuclear models that take into account the mixing of large-scale shell-model configurations. Alpha-cluster channels are considered as an example. A mathematical proof of the need for taking into account the channel-wave-function renormalization generated by exchange terms of the antisymmetrization operator (Fliessbach effect) is given. Examples where this effect is confirmed by a high quality of the description of experimental data are presented. By and large, the method in question extends substantially themore » possibilities for studying clustering phenomena in nuclei and for improving the quality of their description.« less

Learning to Attend to Precision: The Impact of Micro-Teaching Guided by Expert Secondary Mathematics Teachers on Pre-Service Teachers' Teaching Practice

ERIC Educational Resources Information Center

Cheng, Jing

2017-01-01

Micro-teaching at universities and student teaching in secondary schools are standard forms of practice training for pre-service mathematics teachers in Chinese university teacher education programs. The former is guided by university professors, and the latter is guided by school teachers. In recent years, a special kind of micro-teaching…

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion

NASA Astrophysics Data System (ADS)

Choquet, C.; Diédhiou, M. M.; Rosier, C.

2015-10-01

We consider a new model mixing sharp and diffuse interface approaches for seawater intrusion phenomena in free aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic type describing the evolution of the depths of the two free surfaces, that is the interface between salt- and freshwater and the water table. We prove the existence of a weak solution for the model completed with initial and boundary conditions. We also prove that the depths of the two interfaces satisfy a coupled maximum principle.

Standard model of knowledge representation

NASA Astrophysics Data System (ADS)

Yin, Wensheng

2016-09-01

Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.

Using Productive Disposition to Differentiate between Students' Level of Precision When Critiquing a Peer's Work

ERIC Educational Resources Information Center

Gilbert, Melissa C.

2014-01-01

This study examined the productive disposition of pre-algebra students who demonstrated similar knowledge of the focal content but varied in other academic behaviors expected in the Common Core State Standards for Mathematics (CCSSM). Specifically, the study considered students' attention to precision when critiquing a peer's work. The…

[Mathematical model of oblique three-dimensional intertrochanteric detorsion varus-forming osteotomy of the femur by the Bernbeck method in surgical treatment of congenital hip dysplasia in children].

PubMed

Bohatyrewicz, A

1992-01-01

Whenever the conservative procedure fails to bring about congruence of the dysplastic hip joint, an operative procedure becomes indispensable. In Orthopaedic Clinic of the Pomeranian Medical Academy in Szczecin we implement the oblique three-dimensional intertrochanteric detorsion and varus forming osteotomy after Bernbeck in order to correct the proximal end of the femoral bone. Precise determination of the plane to be cut, prior to the operative procedure, simplifies and shortens the operation itself and facilitates the achieving of the planned angular values in all three planes. Mathematical model of osteotomy according to Bernbeck considering required angles of correction as well as angles determining the plane of osteotomy was worked out. In collaboration of the Szczecin Technical University, a simple computer program was elaborated which allowed the presentation of the results in the form of tables. With the help of tables the optimal cutting plane was chosen and created correct biomechanical and anatomical conditions as well as optimal conditions for stable osteosynthesis of dissected fragments of the femoral bone. That type of osteotomy is useful in most operative correcrions of the dysplastic hip joint (not great varus formation connected with relatively extensive detorsion). The achieved congruence in the 22 dysplastic hip joints operated on was the most important condition for their later physiological development. Short post-operative observations confirm the value of described mathematic model.

Advanced mathematics communication beyond modality of\\xA0sight

NASA Astrophysics Data System (ADS)

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access to visual fields in an advanced mathematics course does not obstruct a blind student's ability to visualize, but transforms it. The goal of this study is not to compare the visually impaired student with non-visually impaired students to address the 'differences' in understanding; instead, I discuss the challenges that a blind student, named Anthony, has encountered and the ways that we tackled those problems. I also demonstrate how the proper and precisely crafted tactile materials empowered Anthony to learn mathematical functions.

Cognitive diagnosis modelling incorporating item response times.

PubMed

Zhan, Peida; Jiao, Hong; Liao, Dandan

2018-05-01

To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy 'and' gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow-up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RTs into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters. © 2017 The British Psychological Society.

Diffusion heterogeneity tensor MRI (?-Dti): mathematics and initial applications in spinal cord regeneration after trauma - biomed 2009.

PubMed

Ellington, Benjamin M; Schmit, Brian D; Gourab, Krishnaj; Sieber-Blum, Maya; Hu, Yao F; Schmainda, Kathleen M

2009-01-01

Diffusion weighted magnetic resonance imaging (DWI) is a powerful tool for evaluation of microstructural anomalies in numerous central nervous system pathologies. Diffusion tensor imaging (DTI) allows for the magnitude and direction of water self diffusion to be estimated by sampling the apparent diffusion coefficient (ADC) in various directions. Clinical DWI and DTI performed at a single level of diffusion weighting, however, does not allow for multiple diffusion compartments to be elicited. Furthermore, assumptions made regarding the precise number of diffusion compartments intrinsic to the tissue of interest have resulted in a lack of consensus between investigations. To overcome these challenges, a stretched-exponential model of diffusion was applied to examine the diffusion coefficient and "heterogeneity index" within highly compartmentalized brain tumors. The purpose of the current study is to expand on the stretched-exponential model of diffusion to include directionality of both diffusion heterogeneity and apparent diffusion coefficient. This study develops the mathematics of this new technique along with an initial application in quantifying spinal cord regeneration following acute injection of epidermal neural crest stem cell (EPI-NCSC) grafts.

Active learning in camera calibration through vision measurement application

NASA Astrophysics Data System (ADS)

Li, Xiaoqin; Guo, Jierong; Wang, Xianchun; Liu, Changqing; Cao, Binfang

2017-08-01

Since cameras are increasingly more used in scientific application as well as in the applications requiring precise visual information, effective calibration of such cameras is getting more important. There are many reasons why the measurements of objects are not accurate. The largest reason is that the lens has a distortion. Another detrimental influence on the evaluation accuracy is caused by the perspective distortions in the image. They happen whenever we cannot mount the camera perpendicularly to the objects we want to measure. In overall, it is very important for students to understand how to correct lens distortions, that is camera calibration. If the camera is calibrated, the images are rectificated, and then it is possible to obtain undistorted measurements in world coordinates. This paper presents how the students should develop a sense of active learning for mathematical camera model besides the theoretical scientific basics. The authors will present the theoretical and practical lectures which have the goal of deepening the students understanding of the mathematical models of area scan cameras and building some practical vision measurement process by themselves.

Modeling a Mathematical to Quantify the Degree of Emergency Department Crowding

NASA Astrophysics Data System (ADS)

Chang, Y.; Pan, C.; Wen, J.

2012-12-01

The purpose of this study is to deduce a function from the admissions/discharge rate of patient flow to estimate a "Critical Point" that provides a reference for warning systems in regards to crowding in the emergency department (ED) of a hospital or medical clinic. In this study, a model of "Input-Throughput-Output" was used in our established mathematical function to evaluate the critical point. The function was defined as ∂ρ/∂t=-K×∂ρ/∂x , where ρ= number of patients per unit distance (also called density), t= time, x= distance, K= distance of patients movement per unit time. Using the average K of ED crowding, we could initiate the warning system at appropriate time and plan necessary emergency response to facilitate the patient process more smoothly. It was concluded that ED crowding can be quantified using the average value of K, and the value can be used as a reference for medical staff to give optimal emergency medical treatment to patients. Therefore, additional practical work should be launched to collect more precise quantitative data.

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.

Five critical elements to ensure the precision medicine.

PubMed

Chen, Chengshui; He, Mingyan; Zhu, Yichun; Shi, Lin; Wang, Xiangdong

2015-06-01

The precision medicine as a new emerging area and therapeutic strategy has occurred and was practiced in the individual and brought unexpected successes, and gained high attentions from professional and social aspects as a new path to improve the treatment and prognosis of patients. There will be a number of new components to appear or be discovered, of which clinical bioinformatics integrates clinical phenotypes and informatics with bioinformatics, computational science, mathematics, and systems biology. In addition to those tools, precision medicine calls more accurate and repeatable methodologies for the identification and validation of gene discovery. Precision medicine will bring more new therapeutic strategies, drug discovery and development, and gene-oriented treatment. There is an urgent need to identify and validate disease-specific, mechanism-based, or epigenetics-dependent biomarkers to monitor precision medicine, and develop "precision" regulations to guard the application of precision medicine.

A characterization of linearly repetitive cut and project sets

NASA Astrophysics Data System (ADS)

Haynes, Alan; Koivusalo, Henna; Walton, James

2018-02-01

For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

Modelling heterogeneity variances in multiple treatment comparison meta-analysis--are informative priors the better solution?

PubMed

Thorlund, Kristian; Thabane, Lehana; Mills, Edward J

2013-01-11

Multiple treatment comparison (MTC) meta-analyses are commonly modeled in a Bayesian framework, and weakly informative priors are typically preferred to mirror familiar data driven frequentist approaches. Random-effects MTCs have commonly modeled heterogeneity under the assumption that the between-trial variance for all involved treatment comparisons are equal (i.e., the 'common variance' assumption). This approach 'borrows strength' for heterogeneity estimation across treatment comparisons, and thus, ads valuable precision when data is sparse. The homogeneous variance assumption, however, is unrealistic and can severely bias variance estimates. Consequently 95% credible intervals may not retain nominal coverage, and treatment rank probabilities may become distorted. Relaxing the homogeneous variance assumption may be equally problematic due to reduced precision. To regain good precision, moderately informative variance priors or additional mathematical assumptions may be necessary. In this paper we describe four novel approaches to modeling heterogeneity variance - two novel model structures, and two approaches for use of moderately informative variance priors. We examine the relative performance of all approaches in two illustrative MTC data sets. We particularly compare between-study heterogeneity estimates and model fits, treatment effect estimates and 95% credible intervals, and treatment rank probabilities. In both data sets, use of moderately informative variance priors constructed from the pair wise meta-analysis data yielded the best model fit and narrower credible intervals. Imposing consistency equations on variance estimates, assuming variances to be exchangeable, or using empirically informed variance priors also yielded good model fits and narrow credible intervals. The homogeneous variance model yielded high precision at all times, but overall inadequate estimates of between-trial variances. Lastly, treatment rankings were similar among the novel approaches, but considerably different when compared with the homogenous variance approach. MTC models using a homogenous variance structure appear to perform sub-optimally when between-trial variances vary between comparisons. Using informative variance priors, assuming exchangeability or imposing consistency between heterogeneity variances can all ensure sufficiently reliable and realistic heterogeneity estimation, and thus more reliable MTC inferences. All four approaches should be viable candidates for replacing or supplementing the conventional homogeneous variance MTC model, which is currently the most widely used in practice.

Discrete mathematics, formal methods, the Z schema and the software life cycle

NASA Technical Reports Server (NTRS)

Bown, Rodney L.

1991-01-01

The proper role and scope for the use of discrete mathematics and formal methods in support of engineering the security and integrity of components within deployed computer systems are discussed. It is proposed that the Z schema can be used as the specification language to capture the precise definition of system and component interfaces. This can be accomplished with an object oriented development paradigm.

Sensor-Based Inspection of the Formation Accuracy in Ultra-Precision Grinding (UPG) of Aspheric Surface Considering the Chatter Vibration

NASA Astrophysics Data System (ADS)

Lei, Yao; Bai, Yue; Xu, Zhijun

2018-06-01

This paper proposes an experimental approach for monitoring and inspection of the formation accuracy in ultra-precision grinding (UPG) with respect to the chatter vibration. Two factors related to the grinding progress, the grinding speed of grinding wheel and spindle, and the oil pressure of the hydrostatic bearing are taken into account to determining the accuracy. In the meantime, a mathematical model of the radius deviation caused by the micro vibration is also established and applied in the experiments. The results show that the accuracy is sensitive to the vibration and the forming accuracy is much improved with proper processing parameters. It is found that the accuracy of aspheric surface can be less than 4 μm when the grinding speed is 1400 r/min and the wheel speed is 100 r/min with the oil pressure being 1.1 MPa.

[Landscape classification: research progress and development trend].

PubMed

Liang, Fa-Chao; Liu, Li-Ming

2011-06-01

Landscape classification is the basis of the researches on landscape structure, process, and function, and also, the prerequisite for landscape evaluation, planning, protection, and management, directly affecting the precision and practicability of landscape research. This paper reviewed the research progress on the landscape classification system, theory, and methodology, and summarized the key problems and deficiencies of current researches. Some major landscape classification systems, e. g. , LANMAP and MUFIC, were introduced and discussed. It was suggested that a qualitative and quantitative comprehensive classification based on the ideology of functional structure shape and on the integral consideration of landscape classification utility, landscape function, landscape structure, physiogeographical factors, and human disturbance intensity should be the major research directions in the future. The integration of mapping, 3S technology, quantitative mathematics modeling, computer artificial intelligence, and professional knowledge to enhance the precision of landscape classification would be the key issues and the development trend in the researches of landscape classification.

Improving accessibility to mathematical formulas: the Wikipedia Math Accessor

NASA Astrophysics Data System (ADS)

Fuentes Sepúlveda, J.; Ferres, L.

2012-09-01

Mathematics accessibility is an important topic for inclusive education. In this paper, we make Wikipedia's repository of mathematical formulas accessible by providing a natural language description of its more than 420,000 formulas using a well-researched sub-language. We also contribute by targeting Spanish speakers, for whom assistive technologies, particularly domain-specific technologies like the one described here, are scarce. Our focus on the semantics of formulas (rather than their visual appearance) allowed us to generate verbalizations with a precision of approximately 80% of understandable descriptions, as shown in an evaluation with sighted users.

Real-time flood forecasting

USGS Publications Warehouse

Lai, C.; Tsay, T.-K.; Chien, C.-H.; Wu, I.-L.

2009-01-01

Researchers at the Hydroinformatic Research and Development Team (HIRDT) of the National Taiwan University undertook a project to create a real time flood forecasting model, with an aim to predict the current in the Tamsui River Basin. The model was designed based on deterministic approach with mathematic modeling of complex phenomenon, and specific parameter values operated to produce a discrete result. The project also devised a rainfall-stage model that relates the rate of rainfall upland directly to the change of the state of river, and is further related to another typhoon-rainfall model. The geographic information system (GIS) data, based on precise contour model of the terrain, estimate the regions that were perilous to flooding. The HIRDT, in response to the project's progress, also devoted their application of a deterministic model to unsteady flow of thermodynamics to help predict river authorities issue timely warnings and take other emergency measures.

Allosteric regulation of phosphofructokinase controls the emergence of glycolytic oscillations in isolated yeast cells.

PubMed

Gustavsson, Anna-Karin; van Niekerk, David D; Adiels, Caroline B; Kooi, Bob; Goksör, Mattias; Snoep, Jacky L

2014-06-01

Oscillations are widely distributed in nature and synchronization of oscillators has been described at the cellular level (e.g. heart cells) and at the population level (e.g. fireflies). Yeast glycolysis is the best known oscillatory system, although it has been studied almost exclusively at the population level (i.e. limited to observations of average behaviour in synchronized cultures). We studied individual yeast cells that were positioned with optical tweezers in a microfluidic chamber to determine the precise conditions for autonomous glycolytic oscillations. Hopf bifurcation points were determined experimentally in individual cells as a function of glucose and cyanide concentrations. The experiments were analyzed in a detailed mathematical model and could be interpreted in terms of an oscillatory manifold in a three-dimensional state-space; crossing the boundaries of the manifold coincides with the onset of oscillations and positioning along the longitudinal axis of the volume sets the period. The oscillatory manifold could be approximated by allosteric control values of phosphofructokinase for ATP and AMP. The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.mib.ac.uk/webMathematica/UItester.jsp?modelName=gustavsson5. [Database section added 14 May 2014 after original online publication]. © 2014 FEBS.

Investigations into phase effects from diffracted Gaussian beams for high-precision interferometry

NASA Astrophysics Data System (ADS)

Lodhia, Deepali

Gravitational wave detectors are a new class of observatories aiming to detect gravitational waves from cosmic sources. All-reflective interferometer configurations have been proposed for future detectors, replacing transmissive optics with diffractive elements, thereby reducing thermal issues associated with power absorption. However, diffraction gratings introduce additional phase noise, creating more stringent conditions for alignment stability, and further investigations are required into all-reflective interferometers. A suitable mathematical framework using Gaussian modes is required for analysing the alignment stability using diffraction gratings. Such a framework was created, whereby small beam displacements are modelled using a modal technique. It was confirmed that the original modal-based model does not contain the phase changes associated with grating displacements. Experimental tests verified that the phase of a diffracted Gaussian beam is independent of the beam shape. Phase effects were further examined using a rigorous time-domain simulation tool. These findings show that the perceived phase difference is based on an intrinsic change of coordinate system within the modal-based model, and that the extra phase can be added manually to the modal expansion. This thesis provides a well-tested and detailed mathematical framework that can be used to develop simulation codes to model more complex layouts of all-reflective interferometers.

The IDEA model: A single equation approach to the Ebola forecasting challenge.

PubMed

Tuite, Ashleigh R; Fisman, David N

2018-03-01

Mathematical modeling is increasingly accepted as a tool that can inform disease control policy in the face of emerging infectious diseases, such as the 2014-2015 West African Ebola epidemic, but little is known about the relative performance of alternate forecasting approaches. The RAPIDD Ebola Forecasting Challenge (REFC) tested the ability of eight mathematical models to generate useful forecasts in the face of simulated Ebola outbreaks. We used a simple, phenomenological single-equation model (the "IDEA" model), which relies only on case counts, in the REFC. Model fits were performed using a maximum likelihood approach. We found that the model performed reasonably well relative to other more complex approaches, with performance metrics ranked on average 4th or 5th among participating models. IDEA appeared better suited to long- than short-term forecasts, and could be fit using nothing but reported case counts. Several limitations were identified, including difficulty in identifying epidemic peak (even retrospectively), unrealistically precise confidence intervals, and difficulty interpolating daily case counts when using a model scaled to epidemic generation time. More realistic confidence intervals were generated when case counts were assumed to follow a negative binomial, rather than Poisson, distribution. Nonetheless, IDEA represents a simple phenomenological model, easily implemented in widely available software packages that could be used by frontline public health personnel to generate forecasts with accuracy that approximates that which is achieved using more complex methodologies. Copyright © 2016 The Author(s). Published by Elsevier B.V. All rights reserved.

Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

NASA Astrophysics Data System (ADS)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2017-09-01

The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques - project status and first results

NASA Astrophysics Data System (ADS)

Schmidt, M.; Hugentobler, U.; Jakowski, N.; Dettmering, D.; Liang, W.; Limberger, M.; Wilken, V.; Gerzen, T.; Hoque, M.; Berdermann, J.

2012-04-01

Near real-time high resolution and high precision ionosphere models are needed for a large number of applications, e.g. in navigation, positioning, telecommunications or astronautics. Today these ionosphere models are mostly empirical, i.e., based purely on mathematical approaches. In the DFG project 'Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques (MuSIK)' the complex phenomena within the ionosphere are described vertically by combining the Chapman electron density profile with a plasmasphere layer. In order to consider the horizontal and temporal behaviour the fundamental target parameters of this physics-motivated approach are modelled by series expansions in terms of tensor products of localizing B-spline functions depending on longitude, latitude and time. For testing the procedure the model will be applied to an appropriate region in South America, which covers relevant ionospheric processes and phenomena such as the Equatorial Anomaly. The project connects the expertise of the three project partners, namely Deutsches Geodätisches Forschungsinstitut (DGFI) Munich, the Institute of Astronomical and Physical Geodesy (IAPG) of the Technical University Munich (TUM) and the German Aerospace Center (DLR), Neustrelitz. In this presentation we focus on the current status of the project. In the first year of the project we studied the behaviour of the ionosphere in the test region, we setup appropriate test periods covering high and low solar activity as well as winter and summer and started the data collection, analysis, pre-processing and archiving. We developed partly the mathematical-physical modelling approach and performed first computations based on simulated input data. Here we present information on the data coverage for the area and the time periods of our investigations and we outline challenges of the multi-dimensional mathematical-physical modelling approach. We show first results, discuss problems in modelling and possible solution strategies and finally, we address open questions.

Analytical Kinematics and Coupled Vibrations Analysis of Mechanical System Operated by Solar Array Drive Assembly

NASA Astrophysics Data System (ADS)

Sattar, M.; Wei, C.; Jalali, A.; Sattar, R.

2017-07-01

To address the impact of solar array (SA) anomalies and vibrations on performance of precision space-based operations, it is important to complete its accurate jitter analysis. This work provides mathematical modelling scheme to approximate kinematics and coupled micro disturbance dynamics of rigid load supported and operated by solar array drive assembly (SADA). SADA employed in analysis provides a step wave excitation torque to activate the system. Analytical investigations into kinematics is accomplished by using generalized linear and Euler angle coordinates, applying multi-body dynamics concepts and transformations principles. Theoretical model is extended, to develop equations of motion (EoM), through energy method (Lagrange equation). The main emphasis is to research coupled frequency response by determining energies dissipated and observing dynamic behaviour of internal vibratory systems of SADA. The disturbance model captures discrete active harmonics of SADA, natural modes and vibration amplifications caused by interactions between active harmonics and structural modes of mechanical assembly. The proposed methodology can help to predict true micro disturbance nature of SADA operating rigid load. Moreover, performance outputs may be compared against actual mission requirements to assess precise spacecraft controller design to meet next space generation stringent accuracy goals.

Scientific thinking in young children: theoretical advances, empirical research, and policy implications.

PubMed

Gopnik, Alison

2012-09-28

New theoretical ideas and empirical research show that very young children's learning and thinking are strikingly similar to much learning and thinking in science. Preschoolers test hypotheses against data and make causal inferences; they learn from statistics and informal experimentation, and from watching and listening to others. The mathematical framework of probabilistic models and Bayesian inference can describe this learning in precise ways. These discoveries have implications for early childhood education and policy. In particular, they suggest both that early childhood experience is extremely important and that the trend toward more structured and academic early childhood programs is misguided.

Advanced techniques for the storage and use of very large, heterogeneous spatial databases. The representation of geographic knowledge: Toward a universal framework. [relations (mathematics)

NASA Technical Reports Server (NTRS)

Peuquet, Donna J.

1987-01-01

A new approach to building geographic data models that is based on the fundamental characteristics of the data is presented. An overall theoretical framework for representing geographic data is proposed. An example of utilizing this framework in a Geographic Information System (GIS) context by combining artificial intelligence techniques with recent developments in spatial data processing techniques is given. Elements of data representation discussed include hierarchical structure, separation of locational and conceptual views, and the ability to store knowledge at variable levels of completeness and precision.

An experiment-based comparative study of fuzzy logic control

NASA Technical Reports Server (NTRS)

Berenji, Hamid R.; Chen, Yung-Yaw; Lee, Chuen-Chein; Murugesan, S.; Jang, Jyh-Shing

1989-01-01

An approach is presented to the control of a dynamic physical system through the use of approximate reasoning. The approach has been implemented in a program named POLE, and the authors have successfully built a prototype hardware system to solve the cartpole balancing problem in real-time. The approach provides a complementary alternative to the conventional analytical control methodology and is of substantial use when a precise mathematical model of the process being controlled is not available. A set of criteria for comparing controllers based on approximate reasoning and those based on conventional control schemes is furnished.

Mathematical models of cytotoxic effects in endpoint tumor cell line assays: critical assessment of the application of a single parametric value as a standard criterion to quantify the dose-response effects and new unexplored proposal formats.

PubMed

Calhelha, Ricardo C; Martínez, Mireia A; Prieto, M A; Ferreira, Isabel C F R

2017-10-23

The development of convenient tools for describing and quantifying the effects of standard and novel therapeutic agents is essential for the research community, to perform more precise evaluations. Although mathematical models and quantification criteria have been exchanged in the last decade between different fields of study, there are relevant methodologies that lack proper mathematical descriptions and standard criteria to quantify their responses. Therefore, part of the relevant information that can be drawn from the experimental results obtained and the quantification of its statistical reliability are lost. Despite its relevance, there is not a standard form for the in vitro endpoint tumor cell lines' assays (TCLA) that enables the evaluation of the cytotoxic dose-response effects of anti-tumor drugs. The analysis of all the specific problems associated with the diverse nature of the available TCLA used is unfeasible. However, since most TCLA share the main objectives and similar operative requirements, we have chosen the sulforhodamine B (SRB) colorimetric assay for cytotoxicity screening of tumor cell lines as an experimental case study. In this work, the common biological and practical non-linear dose-response mathematical models are tested against experimental data and, following several statistical analyses, the model based on the Weibull distribution was confirmed as the convenient approximation to test the cytotoxic effectiveness of anti-tumor compounds. Then, the advantages and disadvantages of all the different parametric criteria derived from the model, which enable the quantification of the dose-response drug-effects, are extensively discussed. Therefore, model and standard criteria for easily performing the comparisons between different compounds are established. The advantages include a simple application, provision of parametric estimations that characterize the response as standard criteria, economization of experimental effort and enabling rigorous comparisons among the effects of different compounds and experimental approaches. In all experimental data fitted, the calculated parameters were always statistically significant, the equations proved to be consistent and the correlation coefficient of determination was, in most of the cases, higher than 0.98.

Computational model for vocal tract dynamics in a suboscine bird.

PubMed

Assaneo, M F; Trevisan, M A

2010-09-01

In a recent work, active use of the vocal tract has been reported for singing oscines. The reconfiguration of the vocal tract during song serves to match its resonances to the syringeal fundamental frequency, demonstrating a precise coordination of the two main pieces of the avian vocal system for songbirds characterized by tonal songs. In this work we investigated the Great Kiskadee (Pitangus sulfuratus), a suboscine bird whose calls display a rich harmonic content. Using a recently developed mathematical model for the syrinx and a mobile vocal tract, we set up a computational model that provides a plausible reconstruction of the vocal tract movement using a few spectral features taken from the utterances. Moreover, synthetic calls were generated using the articulated vocal tract that accounts for all the acoustical features observed experimentally.

The NURBS curves in modelling the shape of the boundary in the parametric integral equations systems for solving the Laplace equation

NASA Astrophysics Data System (ADS)

Zieniuk, Eugeniusz; Kapturczak, Marta; Sawicki, Dominik

2016-06-01

In solving of boundary value problems the shapes of the boundary can be modelled by the curves widely used in computer graphics. In parametric integral equations system (PIES) such curves are directly included into the mathematical formalism. Its simplify the way of definition and modification of the shape of the boundary. Until now in PIES the B-spline, Bézier and Hermite curves were used. Recent developments in the computer graphics paid our attention, therefore we implemented in PIES possibility of defining the shape of boundary using the NURBS curves. The curves will allow us to modeling different shapes more precisely. In this paper we will compare PIES solutions (with applied NURBS) with the solutions existing in the literature.

Precise determination of anthropometric dimensions by means of image processing methods for estimating human body segment parameter values.

PubMed

Baca, A

1996-04-01

A method has been developed for the precise determination of anthropometric dimensions from the video images of four different body configurations. High precision is achieved by incorporating techniques for finding the location of object boundaries with sub-pixel accuracy, the implementation of calibration algorithms, and by taking into account the varying distances of the body segments from the recording camera. The system allows automatic segment boundary identification from the video image, if the boundaries are marked on the subject by black ribbons. In connection with the mathematical finite-mass-element segment model of Hatze, body segment parameters (volumes, masses, the three principal moments of inertia, the three local coordinates of the segmental mass centers etc.) can be computed by using the anthropometric data determined videometrically as input data. Compared to other, recently published video-based systems for the estimation of the inertial properties of body segments, the present algorithms reduce errors originating from optical distortions, inaccurate edge-detection procedures, and user-specified upper and lower segment boundaries or threshold levels for the edge-detection. The video-based estimation of human body segment parameters is especially useful in situations where ease of application and rapid availability of comparatively precise parameter values are of importance.

Computing Generalized Matrix Inverse on Spiking Neural Substrate

PubMed Central

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines. PMID:29593483

Desired Precision in Multi-Objective Optimization: Epsilon Archiving or Rounding Objectives?

NASA Astrophysics Data System (ADS)

Asadzadeh, M.; Sahraei, S.

2016-12-01

Multi-objective optimization (MO) aids in supporting the decision making process in water resources engineering and design problems. One of the main goals of solving a MO problem is to archive a set of solutions that is well-distributed across a wide range of all the design objectives. Modern MO algorithms use the epsilon dominance concept to define a mesh with pre-defined grid-cell size (often called epsilon) in the objective space and archive at most one solution at each grid-cell. Epsilon can be set to the desired precision level of each objective function to make sure that the difference between each pair of archived solutions is meaningful. This epsilon archiving process is computationally expensive in problems that have quick-to-evaluate objective functions. This research explores the applicability of a similar but computationally more efficient approach to respect the desired precision level of all objectives in the solution archiving process. In this alternative approach each objective function is rounded to the desired precision level before comparing any new solution to the set of archived solutions that already have rounded objective function values. This alternative solution archiving approach is compared to the epsilon archiving approach in terms of efficiency and quality of archived solutions for solving mathematical test problems and hydrologic model calibration problems.

Quantization of the nonlinear sigma model revisited

NASA Astrophysics Data System (ADS)

Nguyen, Timothy

2016-08-01

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

Approximate number sense correlates with math performance in gifted adolescents.

PubMed

Wang, Jinjing Jenny; Halberda, Justin; Feigenson, Lisa

2017-05-01

Nonhuman animals, human infants, and human adults all share an Approximate Number System (ANS) that allows them to imprecisely represent number without counting. Among humans, people differ in the precision of their ANS representations, and these individual differences have been shown to correlate with symbolic mathematics performance in both children and adults. For example, children with specific math impairment (dyscalculia) have notably poor ANS precision. However, it remains unknown whether ANS precision contributes to individual differences only in populations of people with lower or average mathematical abilities, or whether this link also is present in people who excel in math. Here we tested non-symbolic numerical approximation in 13- to 16-year old gifted children enrolled in a program for talented adolescents (the Center for Talented Youth). We found that in this high achieving population, ANS precision significantly correlated with performance on the symbolic math portion of two common standardized tests (SAT and ACT) that typically are administered to much older students. This relationship was robust even when controlling for age, verbal performance, and reaction times in the approximate number task. These results suggest that the Approximate Number System is linked to symbolic math performance even at the top levels of math performance. Copyright © 2017 Elsevier B.V. All rights reserved.

Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models

USGS Publications Warehouse

Lin, Ting; Harmsen, Stephen C.; Baker, Jack W.; Luco, Nicolas

2013-01-01

The conditional spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground-motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground-motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions, as well as the epistemic uncertainties in ground-motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western United States. The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the United States using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

The Influence of Normalization Weight in Population Pharmacokinetic Covariate Models.

PubMed

Goulooze, Sebastiaan C; Völler, Swantje; Välitalo, Pyry A J; Calvier, Elisa A M; Aarons, Leon; Krekels, Elke H J; Knibbe, Catherijne A J

2018-03-23

In covariate (sub)models of population pharmacokinetic models, most covariates are normalized to the median value; however, for body weight, normalization to 70 kg or 1 kg is often applied. In this article, we illustrate the impact of normalization weight on the precision of population clearance (CL pop ) parameter estimates. The influence of normalization weight (70, 1 kg or median weight) on the precision of the CL pop estimate, expressed as relative standard error (RSE), was illustrated using data from a pharmacokinetic study in neonates with a median weight of 2.7 kg. In addition, a simulation study was performed to show the impact of normalization to 70 kg in pharmacokinetic studies with paediatric or obese patients. The RSE of the CL pop parameter estimate in the neonatal dataset was lowest with normalization to median weight (8.1%), compared with normalization to 1 kg (10.5%) or 70 kg (48.8%). Typical clearance (CL) predictions were independent of the normalization weight used. Simulations showed that the increase in RSE of the CL pop estimate with 70 kg normalization was highest in studies with a narrow weight range and a geometric mean weight away from 70 kg. When, instead of normalizing with median weight, a weight outside the observed range is used, the RSE of the CL pop estimate will be inflated, and should therefore not be used for model selection. Instead, established mathematical principles can be used to calculate the RSE of the typical CL (CL TV ) at a relevant weight to evaluate the precision of CL predictions.

Development Mathematic Assessment to Increase Mathematical Prerequisite Ability on The Student with Learning Disabilities in Inclusive Elementary School

NASA Astrophysics Data System (ADS)

Robiansyah, S. T. U.; Nanang, F.; Hidayat

2018-01-01

The purpose of this study was to introduce about mathematic assessment is a process of obtaining data or information about the mastery of a student's mathematical skills as an ingredient in preparing a learning program. With this mathematics assessment can be known obstacles, difficulties and needs of students especially in the field of mathematic, so that the learning program will be in accordance with the potential students because it is tailored to what is required of students. This research study was conducted at elementary school of inclusive precisely at SDN Sukagalih I Bandung City based learning in setting of inclusive education. This research study is motivated by the existence of a first-grade student who has disabilities learning in mathematics, the ability of the mathematical prerequisite mastery of the classification of objects by color. The results of the research can provide a profile picture of student data information, the data obtained from the results of the development of systematic and formal mathematical assessment. After doing the development of mathematics assessment then the teacher gets important related information: 1. process the analysis of students’ learning needs, especially in the field of mathematics, 2. preparing the learning program planning according to student learning needs, 3. Designing procedural of method remedial program.

Real Time Precise Point Positioning: Preliminary Results for the Brazilian Region

NASA Astrophysics Data System (ADS)

Marques, Haroldo; Monico, João.; Hirokazu Shimabukuro, Milton; Aquino, Marcio

2010-05-01

GNSS positioning can be carried out in relative or absolute approach. In the last years, more attention has been driven to the real time precise point positioning (PPP). To achieve centimeter accuracy with this method in real time it is necessary to have available the satellites precise coordinates as well as satellites clocks corrections. The coordinates can be used from the predicted IGU ephemeris, but the satellites clocks must be estimated in a real time. It can be made from a GNSS network as can be seen from EUREF Permanent Network. The infra-structure to realize the PPP in real time is being available in Brazil through the Brazilian Continuous Monitoring Network (RBMC) together with the Sao Paulo State GNSS network which are transmitting GNSS data using NTRIP (Networked Transport of RTCM via Internet Protocol) caster. Based on this information it was proposed a PhD thesis in the Univ. Estadual Paulista (UNESP) aiming to investigate and develop the methodology to estimate the satellites clocks and realize PPP in real time. Then, software is being developed to process GNSS data in the real time PPP mode. A preliminary version of the software was called PPP_RT and is able to process GNSS code and phase data using precise ephemeris and satellites clocks. The PPP processing can be accomplished considering the absolute satellite antenna Phase Center Variation (PCV), Ocean Tide Loading (OTL), Earth Body Tide, among others. The first order ionospheric effects can be eliminated or minimized by ion-free combination or parameterized in the receiver-satellite direction using a stochastic process, e.g. random walk or white noise. In the case of ionosphere estimation, a pseudo-observable is introduced in the mathematical model for each satellite and the initial value can be computed from Klobuchar model or from Global Ionospheric Map (GIM). The adjustment is realized in the recursive mode and the DIA (Detection Identification and Adaptation) is used for quality control. In this paper our proposition is to present the mathematical models implemented in the PPP_RT software and some proposal to accomplish the PPP in real time as for example using tropospheric model from Brazilian Numerical Weather Forecast Model (BNWFM) and estimating the ionosphere using stochastic process. GPS data sample from the Brazilian region was processed using the PPP_RT software considering periods under low and high ionospheric activities and the results estimating the ionosphere were compared with the ion-free combination. The PPP results also were analyzed considering the strategy of the troposphere estimation, Hopfield model or using the BNWFM. For the troposphere case, the values from BNWFM can reach similar results when estimating the troposphere. For the ionosphere case, the results have shown that ionosphere estimation can improve the time convergence of the PPP processing what is very important for PPP in real time.

Noise in restaurants: levels and mathematical model.

PubMed

To, Wai Ming; Chung, Andy

2014-01-01

Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.

Method for the simulation of blood platelet shape and its evolution during activation

PubMed Central

Muliukov, Artem R.; Litvinenko, Alena L.; Nekrasov, Vyacheslav M.; Chernyshev, Andrei V.; Maltsev, Valeri P.

2018-01-01

We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem. PMID:29518073

Kinetics of killing Listeria monocytogenes by macrophages: correlation of /sup 3/H-DNA release from labeled bacteria and changes in numbers of viable organisms by mathematical model

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

Davies, W.A.

1982-12-01

Conventional methods of assessing antibacterial activities of macrophages by viable counting are limited by the precision of the statistics and are difficult to interpret quantitatively because of unrestrained extracellular growth of bacteria. An alternative technique based on the release of radioactive DNA from labeled bacteria has been offered as overcoming these drawbacks. To assess it for use with macrophages I have made a correlation with the conventional viable counting method using a mathematical model. Opsonized Listeria monocytogenes labeled with /sup 3/H-thymidine were exposed to rat macrophages for periods up to 4 hr. Numbers of viable bacteria determined after sonication increasedmore » exponentially in the absence of live cells and this growth rate was progressively inhibited by increasing numbers of macrophages. After a lag period of 30-60 min soluble /sup 3/H appeared in the supernatant, the amount increasing with time and numbers of macrophages. To correlate these data I developed a mathematical model that considered that changes in numbers of viable organisms were due to the difference between rates of 1) growth of extracellular bacteria and 2) killing within the macrophage. On the basis of this model curves of best fit to the viable counts data were used to predict the release of radioactivity, assuming that death of a bacterium led to the total release of its label. These predictions and the experimental data agreed well, the lag period of 30-60 min between death of the bacterium and release of radioactivity being consistent with intracellular digestion. Release of soluble radioactivity appears to be an accurate reflection of the number of bacteria killed within the macrophage.« less

Prototype Biology-Based Radiation Risk Module Project

NASA Technical Reports Server (NTRS)

Terrier, Douglas; Clayton, Ronald G.; Patel, Zarana; Hu, Shaowen; Huff, Janice

2015-01-01

Biological effects of space radiation and risk mitigation are strategic knowledge gaps for the Evolvable Mars Campaign. The current epidemiology-based NASA Space Cancer Risk (NSCR) model contains large uncertainties (HAT #6.5a) due to lack of information on the radiobiology of galactic cosmic rays (GCR) and lack of human data. The use of experimental models that most accurately replicate the response of human tissues is critical for precision in risk projections. Our proposed study will compare DNA damage, histological, and cell kinetic parameters after irradiation in normal 2D human cells versus 3D tissue models, and it will use a multi-scale computational model (CHASTE) to investigate various biological processes that may contribute to carcinogenesis, including radiation-induced cellular signaling pathways. This cross-disciplinary work, with biological validation of an evolvable mathematical computational model, will help reduce uncertainties within NSCR and aid risk mitigation for radiation-induced carcinogenesis.

Some aspects of the anemia of chronic disorders modeled and analyzed by petri net based approach.

PubMed

Formanowicz, Dorota; Sackmann, Andrea; Kozak, Adam; Błażewicz, Jacek; Formanowicz, Piotr

2011-06-01

Anemia of chronic disorders is a very important phenomenon and iron is a crucial factor of this complex process. To better understand this process and its influence on some other factors we have built a mathematical model of the human body iron homeostasis, which possibly most exactly would reflect the metabolism of iron in the case of anemia and inflammation. The model has been formulated in the language of Petri net theory, which allows for its simulation and precise analysis. The obtained results of the analysis of the model's behavior, concerning the influence of anemia and inflammation on the transferrin receptors, and hepcidin concentration changes are the valuable complements to the knowledge following from clinical research. This analysis is one of the first attempts to investigate properties and behavior of a not fully understood biological system on a basis of its Petri net based model.

Non-Invasive Investigation of Bone Adaptation in Humans to Mechanical Loading

NASA Technical Reports Server (NTRS)

Whalen, R.

1999-01-01

Experimental studies have identified peak cyclic forces, number of loading cycles, and loading rate as contributors to the regulation of bone metabolism. We have proposed a theoretical model that relates bone density to a mechanical stimulus derived from average daily cumulative peak cyclic 'effective' tissue stresses. In order to develop a non-invasive experimental model to test the theoretical model we need to: (1) monitor daily cumulative loading on a bone, (2) compute the internal stress state(s) resulting from the imposed loading, and (3) image volumetric bone density accurately, precisely, and reproducibly within small contiguous volumes throughout the bone. We have chosen the calcaneus (heel) as an experimental model bone site because it is loaded by ligament, tendon and joint contact forces in equilibrium with daily ground reaction forces that we can measure; it is a peripheral bone site and therefore more easily and accurately imaged with computed tomography; it is composed primarily of cancellous bone; and it is a relevant site for monitoring bone loss and adaptation in astronauts and the general population. This paper presents an overview of our recent advances in the areas of monitoring daily ground reaction forces, biomechanical modeling of the forces on the calcaneus during gait, mathematical modeling of calcaneal bone adaptation in response to cumulative daily activity, accurate and precise imaging of the calcaneus with quantitative computed tomography (QCT), and application to long duration space flight.

Atmospheric constituent density profiles from full disk solar occultation experiments

NASA Technical Reports Server (NTRS)

Lumpe, J. D.; Chang, C. S.; Strickland, D. J.

1991-01-01

Mathematical methods are described which permit the derivation of the number of density profiles of atmospheric constituents from solar occultation measurements. The algorithm is first applied to measurements corresponding to an arbitrary solar-intensity distribution to calculate the normalized absorption profile. The application of Fourier transform to the integral equation yields a precise expression for the corresponding number density, and the solution is employed with the data given in the form of Laguerre polynomials. The algorithm is employed to calculate the results for the case of uniform distribution of solar intensity, and the results demonstrate the convergence properties of the method. The algorithm can be used to effectively model representative model-density profiles with constant and altitude-dependent scale heights.

The work of Glenn F. Webb.

PubMed

Fitzgibbon, William E

2015-08-01

It is my distinct pleasure to introduce this volume honoring the 70th birthday of Professor Glenn F. Webb. The existence of this compiled volume is in itself a testimony of Glenn's dedication to, his pursuit of, and his achievement of scientific excellence. As we honor Glenn, we honor what is excellent in our profession. Aristotle clearly articulated his concept of excellence. ``We are what we repeatedly do. Excellence, then, is not an act, but a habit." As we look over the course of his career we observe ample evidence of Glenn Webb's habitual practice of excellence. Beginning with Glenn's first paper [1], one observes a constant stream of productivity and high impact work. Glenn has authored or co-authored over 160 papers, written one research monograph, and co-edited six volumes. He has delivered plenary lectures, colloquia, and seminars across the globe, and he serves on the editorial boards of 11 archival journals. He is a Fellow of the American Mathematical Society. Glenn's scientific career chronicles an evolution of scientific work that began with his interest in nonlinear semigroup theory and leads up to his current activity in biomedical mathematics. At each stage we see seminal contributions in the areas of nonlinear semigroups, functional differential equations, infinite dimensional dynamical systems, mathematical population dynamics, mathematical biology and biomedical mathematics. Glenn's work is distinguished by a clarity and accessibility of exposition, a precise identification and description of the problem or model under consideration, and thorough referencing. He uses elementary methods whenever possible but couples this with an ability to employ power abstract methods when necessitated by the problem.

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

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.

Precise orbit determination based on raw GPS measurements

NASA Astrophysics Data System (ADS)

Zehentner, Norbert; Mayer-Gürr, Torsten

2016-03-01

Precise orbit determination is an essential part of the most scientific satellite missions. Highly accurate knowledge of the satellite position is used to geolocate measurements of the onboard sensors. For applications in the field of gravity field research, the position itself can be used as observation. In this context, kinematic orbits of low earth orbiters (LEO) are widely used, because they do not include a priori information about the gravity field. The limiting factor for the achievable accuracy of the gravity field through LEO positions is the orbit accuracy. We make use of raw global positioning system (GPS) observations to estimate the kinematic satellite positions. The method is based on the principles of precise point positioning. Systematic influences are reduced by modeling and correcting for all known error sources. Remaining effects such as the ionospheric influence on the signal propagation are either unknown or not known to a sufficient level of accuracy. These effects are modeled as unknown parameters in the estimation process. The redundancy in the adjustment is reduced; however, an improvement in orbit accuracy leads to a better gravity field estimation. This paper describes our orbit determination approach and its mathematical background. Some examples of real data applications highlight the feasibility of the orbit determination method based on raw GPS measurements. Its suitability for gravity field estimation is presented in a second step.

Basic research and data analysis for the earth and ocean physics applications program and for the National Geodetic Satellite Program

NASA Technical Reports Server (NTRS)

1976-01-01

Data analysis and supporting research in connection with the following objectives are discussed: (1) provide a precise and accurate geometric description of the earth's surface, (2) provide a precise and accurate mathematical description of the earth's gravitational field, and (3) determine time variations of the geometry of the ocean surface, the solid earth, the gravity field and other geophysical parameters.

Precision microbiome reconstitution restores bile acid mediated resistance to Clostridium difficile

NASA Astrophysics Data System (ADS)

Buffie, Charlie G.; Bucci, Vanni; Stein, Richard R.; McKenney, Peter T.; Ling, Lilan; Gobourne, Asia; No, Daniel; Liu, Hui; Kinnebrew, Melissa; Viale, Agnes; Littmann, Eric; van den Brink, Marcel R. M.; Jenq, Robert R.; Taur, Ying; Sander, Chris; Cross, Justin R.; Toussaint, Nora C.; Xavier, Joao B.; Pamer, Eric G.

2015-01-01

The gastrointestinal tracts of mammals are colonized by hundreds of microbial species that contribute to health, including colonization resistance against intestinal pathogens. Many antibiotics destroy intestinal microbial communities and increase susceptibility to intestinal pathogens. Among these, Clostridium difficile, a major cause of antibiotic-induced diarrhoea, greatly increases morbidity and mortality in hospitalized patients. Which intestinal bacteria provide resistance to C. difficile infection and their in vivo inhibitory mechanisms remain unclear. Here we correlate loss of specific bacterial taxa with development of infection, by treating mice with different antibiotics that result in distinct microbiota changes and lead to varied susceptibility to C. difficile. Mathematical modelling augmented by analyses of the microbiota of hospitalized patients identifies resistance-associated bacteria common to mice and humans. Using these platforms, we determine that Clostridium scindens, a bile acid 7α-dehydroxylating intestinal bacterium, is associated with resistance to C. difficile infection and, upon administration, enhances resistance to infection in a secondary bile acid dependent fashion. Using a workflow involving mouse models, clinical studies, metagenomic analyses, and mathematical modelling, we identify a probiotic candidate that corrects a clinically relevant microbiome deficiency. These findings have implications for the rational design of targeted antimicrobials as well as microbiome-based diagnostics and therapeutics for individuals at risk of C. difficile infection.

Study on mathematical model to predict aerated power consumption in a gas-liquid stirred tank

NASA Astrophysics Data System (ADS)

Luan, Deyu; Zhang, Shengfeng; Wei, Xing; Chen, Yiming

The aerated power consumption characteristics in a transparent tank with diameter of 0.3 m and flat bottom stirred by a Rushton impeller were investigated by means of experimental measurement. The test fluid used was tap water as liquid and air as gas. Based on Weibull model, the complete correlation of aerated power with aerated flow number was established through non-linear fit analysis. The effects of aerated rate and impeller speed on aerated power consumption were made an exploration. Results show that the changeable trend of the aerated power consumption is found to be similar under different impeller speeds and impeller diameters, i.e. the aerated power is close to dropping linear at the beginning of gas input, and then the drop tendency decreases as the aerated rate increases, at the end, the aerated power is a constant on the whole as the aerated rate reaches up the loading state. The non-linear fit curve is done using the software Origin based on the experimental data. The fairly high precision of data fit is obtained, which indicates that the mathematical model established can be used to accurately predict the aerated power consumption, comparatively. The proposed research provides a valuable instruction and reference for the design and enlargement of stirred vessel.

Improved Bayesian Infrasonic Source Localization for regional infrasound

DOE PAGES

Blom, Philip S.; Marcillo, Omar; Arrowsmith, Stephen J.

2015-10-20

The Bayesian Infrasonic Source Localization (BISL) methodology is examined and simplified providing a generalized method of estimating the source location and time for an infrasonic event and the mathematical framework is used therein. The likelihood function describing an infrasonic detection used in BISL has been redefined to include the von Mises distribution developed in directional statistics and propagation-based, physically derived celerity-range and azimuth deviation models. Frameworks for constructing propagation-based celerity-range and azimuth deviation statistics are presented to demonstrate how stochastic propagation modelling methods can be used to improve the precision and accuracy of the posterior probability density function describing themore » source localization. Infrasonic signals recorded at a number of arrays in the western United States produced by rocket motor detonations at the Utah Test and Training Range are used to demonstrate the application of the new mathematical framework and to quantify the improvement obtained by using the stochastic propagation modelling methods. Moreover, using propagation-based priors, the spatial and temporal confidence bounds of the source decreased by more than 40 per cent in all cases and by as much as 80 per cent in one case. Further, the accuracy of the estimates remained high, keeping the ground truth within the 99 per cent confidence bounds for all cases.« less

Pb and Sr isotope measurements by inductively coupled plasma mass spectrometer: efficient time management for precision improvement

NASA Astrophysics Data System (ADS)

Monna, F.; Loizeau, J.-L.; Thomas, B. A.; Guéguen, C.; Favarger, P.-Y.

1998-08-01

One of the factors limiting the precision of inductively coupled plasma mass spectrometry is the counting statistics, which depend upon acquisition time and ion fluxes. In the present study, the precision of the isotopic measurements of Pb and Sr is examined. The time of measurement is optimally shared for each isotope, using a mathematical simulation, to provide the lowest theoretical analytical error. Different algorithms of mass bias correction are also taken into account and evaluated in term of improvement of overall precision. Several experiments allow a comparison of real conditions with theory. The present method significantly improves the precision, regardless of the instrument used. However, this benefit is more important for equipment which originally yields a precision close to that predicted by counting statistics. Additionally, the procedure is flexible enough to be easily adapted to other problems, such as isotopic dilution.

Theoretical distribution of gutta-percha within root canals filled using cold lateral compaction based on numeric calculus.

PubMed

Min, Yi; Song, Ying; Gao, Yuan; Dummer, Paul M H

2016-08-01

This study aimed to present a new method based on numeric calculus to provide data on the theoretical volume ratio of voids when using the cold lateral compaction technique in canals with various diameters and tapers. Twenty-one simulated mathematical root canal models were created with different tapers and sizes of apical diameter, and were filled with defined sizes of standardized accessory gutta-percha cones. The areas of each master and accessory gutta-percha cone as well as the depth of their insertion into the canals were determined mathematically in Microsoft Excel. When the first accessory gutta-percha cone had been positioned, the residual area of void was measured. The areas of the residual voids were then measured repeatedly upon insertion of additional accessary cones until no more could be inserted in the canal. The volume ratio of voids was calculated through measurement of the volume of the root canal and mass of gutta-percha cones. The theoretical volume ratio of voids was influenced by the taper of canal, the size of apical preparation and the size of accessory gutta-percha cones. Greater apical preparation size and larger taper together with the use of smaller accessory cones reduced the volume ratio of voids in the apical third. The mathematical model provided a precise method to determine the theoretical volume ratio of voids in root-filled canals when using cold lateral compaction.

Compact spectrometer for precision studies of multimode behavior in an extended-cavity diode laser

NASA Astrophysics Data System (ADS)

Roach, Timothy; Golemi, Josian; Krueger, Thomas

2016-05-01

We have built a compact, inexpensive, high-precision spectrometer and used it to investigate the tuning behavior of a grating stabilized extended-cavity diode laser (ECDL). A common ECDL design uses a laser chip with an uncoated (partially reflecting) front facet, and the laser output exhibits a complicated pattern of mode hops as the frequency is tuned, in some cases even showing chaotic dynamics. Our grating spectrometer (based on a design by White & Scholten) monitors a span of 4000 GHz (8 nm at 780 nm) with a linewidth of 3 GHz, which with line-splitting gives a precision of 0.02 GHz in determining the frequency of a laser mode. We have studied multimode operation of the ECDL, tracking two or three simultaneous chip cavity modes (spacing ~ 30 GHz) during tuning via current or piezo control of the external cavity. Simultaneous output on adjacent external cavity modes (spacing ~ 5 GHz) is monitored by measuring an increase in the spectral linewidth. Computer-control of the spectrometer (for line-fitting and averaging) and of the ECDL (electronic tuning) allows rapid collection of spectral data sets, which we will use to test mathematical simulation models of the non-linear laser cavity interactions.

D2 Delta Robot Structural Design and Kinematics Analysis

NASA Astrophysics Data System (ADS)

Yang, Xudong; wang, Song; Dong, Yu; Yang, Hai

2017-12-01

In this paper, a new type of Delta robot with only two degrees of freedom is proposed on the basis of multi - degree - of - freedom delta robot. In order to meet our application requirements, we have carried out structural design and analysis of the robot. Through SolidWorks modeling, combined with 3D printing technology to determine the final robot structure. In order to achieve the precise control of the robot, the kinematics analysis of the robot was carried out. The SimMechanics toolbox of MATLAB is used to establish the mechanism model, and the kinematics mathematical model is used to simulate the robot motion control in Matlab environment. Finally, according to the design mechanism, the working space of the robot is drawn by the graphic method, which lays the foundation for the motion control of the subsequent robot.

Modeling of Instrument Landing System (ILS) localizer signal on runway 25L at Los Angeles International Airport

NASA Technical Reports Server (NTRS)

Hueschen, Richard M.; Knox, Charles E.

1994-01-01

A joint NASA/FAA flight test has been made to record instrument landing system (ILS) localizer receiver signals for use in mathematically modeling the ILS localizer for future simulation studies and airplane flight tracking tasks. The flight test was conducted on a portion of the ILS localizer installed on runway 25L at the Los Angeles International Airport. The tests covered the range from 10 to 32 n.mi. from the localizer antenna. Precision radar tracking information was compared with the recorded localizer deviation data. Data analysis showed that the ILS signal centerline was offset to the left of runway centerline by 0.071 degrees and that no significant bends existed on the localizer beam. Suggested simulation models for the ILS localizer are formed from a statistical analysis.

The Measurand: The Problem of Frequency

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

Kirkham, Harold

The conceptual entity that metrologists term the measurand is a model selected to represent the physical entity being measured. In a world of digital measurements, it should be defined first mathematically, and only then put into words. Human linguistic processes lack the precision required when all we do is use labels. In this paper, reactive power and frequency are used as examples. The act of measurement finds the values of the coef-ficients of the model. In other words, it solves an equation. In a digital instrument, information about the quality of the fit between the physical entity being measured andmore » the conceptual model is often available. In essence the instrument can comment on the selection of the model. This comment should be reported as part of the statement of the result of the measurement, along with the declared value and the uncertainty.« less

Stabilizing effect of cannibalism in a two stages population model.

PubMed

Rault, Jonathan; Benoît, Eric; Gouzé, Jean-Luc

2013-03-01

In this paper we build a prey-predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage (larvae and adults) and present some general mathematical results. In the last part, we will assume that the dynamics of the prey is fast compared to the predator's one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result.

An overview of quantitative approaches in Gestalt perception.

PubMed

Jäkel, Frank; Singh, Manish; Wichmann, Felix A; Herzog, Michael H

2016-09-01

Gestalt psychology is often criticized as lacking quantitative measurements and precise mathematical models. While this is true of the early Gestalt school, today there are many quantitative approaches in Gestalt perception and the special issue of Vision Research "Quantitative Approaches in Gestalt Perception" showcases the current state-of-the-art. In this article we give an overview of these current approaches. For example, ideal observer models are one of the standard quantitative tools in vision research and there is a clear trend to try and apply this tool to Gestalt perception and thereby integrate Gestalt perception into mainstream vision research. More generally, Bayesian models, long popular in other areas of vision research, are increasingly being employed to model perceptual grouping as well. Thus, although experimental and theoretical approaches to Gestalt perception remain quite diverse, we are hopeful that these quantitative trends will pave the way for a unified theory. Copyright © 2016 Elsevier Ltd. All rights reserved.

New mechanistically based model for predicting reduction of biosolids waste by ozonation of return activated sludge.

PubMed

Isazadeh, Siavash; Feng, Min; Urbina Rivas, Luis Enrique; Frigon, Dominic

2014-04-15

Two pilot-scale activated sludge reactors were operated for 98 days to provide the necessary data to develop and validate a new mathematical model predicting the reduction of biosolids production by ozonation of the return activated sludge (RAS). Three ozone doses were tested during the study. In addition to the pilot-scale study, laboratory-scale experiments were conducted with mixed liquor suspended solids and with pure cultures to parameterize the biomass inactivation process during exposure to ozone. The experiments revealed that biomass inactivation occurred even at the lowest doses, but that it was not associated with extensive COD solubilization. For validation, the model was used to simulate the temporal dynamics of the pilot-scale operational data. Increasing the description accuracy of the inactivation process improved the precision of the model in predicting the operational data. Copyright © 2014 Elsevier B.V. All rights reserved.

Vibration transmission through rolling element bearings in geared rotor system, part 1. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Lim, Teik Chin

1989-01-01

A mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element description, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. This study clarifies this issue qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 model for the precision rolling element bearings from basic principles. The proposed bearing formulation is extended to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques. Eigensolution and forced harmonic response due to rotating mass unbalance or kinematic transmission error excitation for a number of examples are computed.

[Relations between biomedical variables: mathematical analysis or linear algebra?].

PubMed

Hucher, M; Berlie, J; Brunet, M

1977-01-01

The authors, after a short reminder of one pattern's structure, stress on the possible double approach of relations uniting the variables of this pattern: use of fonctions, what is within the mathematical analysis sphere, use of linear algebra profiting by matricial calculation's development and automatiosation. They precise the respective interests on these methods, their bounds and the imperatives for utilization, according to the kind of variables, of data, and the objective for work, understanding phenomenons or helping towards decision.

Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor

NASA Astrophysics Data System (ADS)

Ferrer, Sebastián; Lara, Martin

2010-05-01

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

The Application of Leap Motion in Astronaut Virtual Training

NASA Astrophysics Data System (ADS)

Qingchao, Xie; Jiangang, Chao

2017-03-01

With the development of computer vision, virtual reality has been applied in astronaut virtual training. As an advanced optic equipment to track hand, Leap Motion can provide precise and fluid tracking of hands. Leap Motion is suitable to be used as gesture input device in astronaut virtual training. This paper built an astronaut virtual training based Leap Motion, and established the mathematics model of hands occlusion. At last the ability of Leap Motion to handle occlusion was analysed. A virtual assembly simulation platform was developed for astronaut training, and occlusion gesture would influence the recognition process. The experimental result can guide astronaut virtual training.

Research on axisymmetric aspheric surface numerical design and manufacturing technology

NASA Astrophysics Data System (ADS)

Wang, Zhen-zhong; Guo, Yin-biao; Lin, Zheng

2006-02-01

The key technology for aspheric machining offers exact machining path and machining aspheric lens with high accuracy and efficiency, in spite of the development of traditional manual manufacturing into nowadays numerical control (NC) machining. This paper presents a mathematical model between virtual cone and aspheric surface equations, and discusses the technology of uniform wear of grinding wheel and error compensation in aspheric machining. Finally, a software system for high precision aspheric surface manufacturing is designed and realized, based on the mentioned above. This software system can work out grinding wheel path according to input parameters and generate machining NC programs of aspheric surfaces.

PLZT Ceramic Driving Rotary Micro-mirror Based on Photoelectric-electrostatic Mechanism

NASA Astrophysics Data System (ADS)

Tang, Yujuan; Yang, Zhong; Chen, Yusong; Wang, Xinjie

2017-12-01

Based on the anomalous photovoltaic effect of PLZT, a rotary micro-mirror driven by hybrid photoelectric-electrostatic actuation of PLZT ceramic is proposed. Firstly, the mathematical modelling of coupled multi-physics fields of PLZT ceramic is established during illumination and light off phases. Then, the relationship between the rotation angle and the photovoltage of PLZT ceramics is established. In addition, the feasibility of rotary micro-mirror with hybrid photoelectric-electrostatic driving is verified via closed-loop control for photo-induced voltage of PLZT ceramic. The experimental results show that the photo-induced voltage of PLZT ceramics has good dynamic control precision using on-off closed-loop control method.

Wire in the Cable-Driven System of Surgical Robot

NASA Astrophysics Data System (ADS)

Wang, X. F.; Lv, N.; Mu, H. Z.; Xue, L. J.

2017-07-01

During the evolution of the surgical robot, cable plays an important role. It translates motion and force precisely from surgeon’s hand to the tool’s tips. In the paper, the vertical wires, the composition of cable, are mathematically modeled from a geometric point of view. The cable structure and tension are analyzed according to the characteristics of wire screw twist. The structural equations of the wires in different positions are derived for both non-bent cable and bent cable, respectively. The bending moment formula of bent cable is also obtained. This will help researchers find suitable cable and design more matched pulley.

Modelling heterogeneity variances in multiple treatment comparison meta-analysis – Are informative priors the better solution?

PubMed Central

2013-01-01

Background Multiple treatment comparison (MTC) meta-analyses are commonly modeled in a Bayesian framework, and weakly informative priors are typically preferred to mirror familiar data driven frequentist approaches. Random-effects MTCs have commonly modeled heterogeneity under the assumption that the between-trial variance for all involved treatment comparisons are equal (i.e., the ‘common variance’ assumption). This approach ‘borrows strength’ for heterogeneity estimation across treatment comparisons, and thus, ads valuable precision when data is sparse. The homogeneous variance assumption, however, is unrealistic and can severely bias variance estimates. Consequently 95% credible intervals may not retain nominal coverage, and treatment rank probabilities may become distorted. Relaxing the homogeneous variance assumption may be equally problematic due to reduced precision. To regain good precision, moderately informative variance priors or additional mathematical assumptions may be necessary. Methods In this paper we describe four novel approaches to modeling heterogeneity variance - two novel model structures, and two approaches for use of moderately informative variance priors. We examine the relative performance of all approaches in two illustrative MTC data sets. We particularly compare between-study heterogeneity estimates and model fits, treatment effect estimates and 95% credible intervals, and treatment rank probabilities. Results In both data sets, use of moderately informative variance priors constructed from the pair wise meta-analysis data yielded the best model fit and narrower credible intervals. Imposing consistency equations on variance estimates, assuming variances to be exchangeable, or using empirically informed variance priors also yielded good model fits and narrow credible intervals. The homogeneous variance model yielded high precision at all times, but overall inadequate estimates of between-trial variances. Lastly, treatment rankings were similar among the novel approaches, but considerably different when compared with the homogenous variance approach. Conclusions MTC models using a homogenous variance structure appear to perform sub-optimally when between-trial variances vary between comparisons. Using informative variance priors, assuming exchangeability or imposing consistency between heterogeneity variances can all ensure sufficiently reliable and realistic heterogeneity estimation, and thus more reliable MTC inferences. All four approaches should be viable candidates for replacing or supplementing the conventional homogeneous variance MTC model, which is currently the most widely used in practice. PMID:23311298

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…

Differential forms for scientists and engineers

NASA Astrophysics Data System (ADS)

Blair Perot, J.; Zusi, Christopher J.

2014-01-01

This paper is a review of a number of mathematical concepts from differential geometry and exterior calculus that are finding increasing application in the numerical solution of partial differential equations. The objective of the paper is to introduce the scientist/ engineer to some of these ideas via a number of concrete examples in 2, 3, and 4 dimensions. The goal is not to explain these ideas with mathematical precision but to present concrete examples and enable a physical intuition of these concepts for those who are not mathematicians. The objective of this paper is to provide enough context so that scientist/engineers can interpret, implement, and understand other works which use these elegant mathematical concepts.

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling.

PubMed

Sumner, T; Shephard, E; Bogle, I D L

2012-09-07

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.

Probability bounds analysis for nonlinear population ecology models.

PubMed

Enszer, Joshua A; Andrei Măceș, D; Stadtherr, Mark A

2015-09-01

Mathematical models in population ecology often involve parameters that are empirically determined and inherently uncertain, with probability distributions for the uncertainties not known precisely. Propagating such imprecise uncertainties rigorously through a model to determine their effect on model outputs can be a challenging problem. We illustrate here a method for the direct propagation of uncertainties represented by probability bounds though nonlinear, continuous-time, dynamic models in population ecology. This makes it possible to determine rigorous bounds on the probability that some specified outcome for a population is achieved, which can be a core problem in ecosystem modeling for risk assessment and management. Results can be obtained at a computational cost that is considerably less than that required by statistical sampling methods such as Monte Carlo analysis. The method is demonstrated using three example systems, with focus on a model of an experimental aquatic food web subject to the effects of contamination by ionic liquids, a new class of potentially important industrial chemicals. Copyright © 2015. Published by Elsevier Inc.

Bayesian Action–Perception Computational Model: Interaction of Production and Recognition of Cursive Letters

PubMed Central

Gilet, Estelle; Diard, Julien; Bessière, Pierre

2011-01-01

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception–action loop, based on probabilistic modeling and Bayesian inference, which we call the Bayesian Action–Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using Bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments. PMID:21674043

Development and calibration of an accurate 6-degree-of-freedom measurement system with total station

NASA Astrophysics Data System (ADS)

Gao, Yang; Lin, Jiarui; Yang, Linghui; Zhu, Jigui

2016-12-01

To meet the demand of high-accuracy, long-range and portable use in large-scale metrology for pose measurement, this paper develops a 6-degree-of-freedom (6-DOF) measurement system based on total station by utilizing its advantages of long range and relative high accuracy. The cooperative target sensor, which is mainly composed of a pinhole prism, an industrial lens, a camera and a biaxial inclinometer, is designed to be portable in use. Subsequently, a precise mathematical model is proposed from the input variables observed by total station, imaging system and inclinometer to the output six pose variables. The model must be calibrated in two levels: the intrinsic parameters of imaging system, and the rotation matrix between coordinate systems of the camera and the inclinometer. Then corresponding approaches are presented. For the first level, we introduce a precise two-axis rotary table as a calibration reference. And for the second level, we propose a calibration method by varying the pose of a rigid body with the target sensor and a reference prism on it. Finally, through simulations and various experiments, the feasibilities of the measurement model and calibration methods are validated, and the measurement accuracy of the system is evaluated.

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

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

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

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

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

Precision of spiral-bevel gears

NASA Technical Reports Server (NTRS)

Litvin, F. L.; Goldrich, R. N.; Coy, J. J.; Zaretsky, E. V.

1982-01-01

The kinematic errors in spiral bevel gear trains caused by the generation of nonconjugate surfaces, by axial displacements of the gears during assembly, and by eccentricity of the assembled gears were determined. One mathematical model corresponds to the motion of the contact ellipse across the tooth surface, (geometry I) and the other along the tooth surface (geometry II). The following results were obtained: (1) kinematic errors induced by errors of manufacture may be minimized by applying special machine settings, the original error may be reduced by order of magnitude, the procedure is most effective for geometry 2 gears, (2) when trying to adjust the bearing contact pattern between the gear teeth for geometry 1 gears, it is more desirable to shim the gear axially; for geometry II gears, shim the pinion axially; (3) the kinematic accuracy of spiral bevel drives are most sensitive to eccentricities of the gear and less sensitive to eccentricities of the pinion. The precision of mounting accuracy and manufacture are most crucial for the gear, and less so for the pinion.

A self-synchronized high speed computational ghost imaging system: A leap towards dynamic capturing

NASA Astrophysics Data System (ADS)

Suo, Jinli; Bian, Liheng; Xiao, Yudong; Wang, Yongjin; Zhang, Lei; Dai, Qionghai

2015-11-01

High quality computational ghost imaging needs to acquire a large number of correlated measurements between the to-be-imaged scene and different reference patterns, thus ultra-high speed data acquisition is of crucial importance in real applications. To raise the acquisition efficiency, this paper reports a high speed computational ghost imaging system using a 20 kHz spatial light modulator together with a 2 MHz photodiode. Technically, the synchronization between such high frequency illumination and bucket detector needs nanosecond trigger precision, so the development of synchronization module is quite challenging. To handle this problem, we propose a simple and effective computational self-synchronization scheme by building a general mathematical model and introducing a high precision synchronization technique. The resulted efficiency is around 14 times faster than state-of-the-arts, and takes an important step towards ghost imaging of dynamic scenes. Besides, the proposed scheme is a general approach with high flexibility for readily incorporating other illuminators and detectors.

Can we use high precision metal isotope analysis to improve our understanding of cancer?

PubMed

Larner, Fiona

2016-01-01

High precision natural isotope analyses are widely used in geosciences to trace elemental transport pathways. The use of this analytical tool is increasing in nutritional and disease-related research. In recent months, a number of groups have shown the potential this technique has in providing new observations for various cancers when applied to trace metal metabolism. The deconvolution of isotopic signatures, however, relies on mathematical models and geochemical data, which are not representative of the system under investigation. In addition to relevant biochemical studies of protein-metal isotopic interactions, technological development both in terms of sample throughput and detection sensitivity of these elements is now needed to translate this novel approach into a mainstream analytical tool. Following this, essential background healthy population studies must be performed, alongside observational, cross-sectional disease-based studies. Only then can the sensitivity and specificity of isotopic analyses be tested alongside currently employed methods, and important questions such as the influence of cancer heterogeneity and disease stage on isotopic signatures be addressed.

A COMPUTATIONAL ANALYSIS OF BONE FORMATION IN THE CRANIAL VAULT USING A COUPLED REACTION-DIFFUSION-STRAIN MODEL

PubMed Central

LEE, CHANYOUNG; RICHTSMEIER, JOAN T.; KRAFT, REUBEN H.

2017-01-01

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing’s reaction-diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction-diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-diffusion model with structural mechanics. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provide precise three dimensional (3D) measures of murine cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures. PMID:29225392

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Mathematical 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.

Studies into the averaging problem: Macroscopic gravity and precision cosmology

NASA Astrophysics Data System (ADS)

Wijenayake, Tharake S.

2016-08-01

With the tremendous improvement in the precision of available astrophysical data in the recent past, it becomes increasingly important to examine some of the underlying assumptions behind the standard model of cosmology and take into consideration nonlinear and relativistic corrections which may affect it at percent precision level. Due to its mathematical rigor and fully covariant and exact nature, Zalaletdinov's macroscopic gravity (MG) is arguably one of the most promising frameworks to explore nonlinearities due to inhomogeneities in the real Universe. We study the application of MG to precision cosmology, focusing on developing a self-consistent cosmology model built on the averaging framework that adequately describes the large-scale Universe and can be used to study real data sets. We first implement an algorithmic procedure using computer algebra systems to explore new exact solutions to the MG field equations. After validating the process with an existing isotropic solution, we derive a new homogeneous, anisotropic and exact solution. Next, we use the simplest (and currently only) solvable homogeneous and isotropic model of MG and obtain an observable function for cosmological expansion using some reasonable assumptions on light propagation. We find that the principal modification to the angular diameter distance is through the change in the expansion history. We then linearize the MG field equations and derive a framework that contains large-scale structure, but the small scale inhomogeneities have been smoothed out and encapsulated into an additional cosmological parameter representing the averaging effect. We derive an expression for the evolution of the density contrast and peculiar velocities and integrate them to study the growth rate of large-scale structure. We find that increasing the magnitude of the averaging term leads to enhanced growth at late times. Thus, for the same matter content, the growth rate of large scale structure in the MG model is stronger than that of the standard model. Finally, we constrain the MG model using Cosmic Microwave Background temperature anisotropy data, the distance to supernovae data, the galaxy power spectrum, the weak lensing tomography shear-shear cross-correlations and the baryonic acoustic oscillations. We find that for this model the averaging density parameter is very small and does not cause any significant shift in the other cosmological parameters. However, it can lead to increased errors on some cosmological parameters such as the Hubble constant and the amplitude of the linear matter spectrum at the scale of 8h. {-1}Mpc. Further studiesare needed to explore other solutions and models of MG as well as their effects on precision cosmology.

Distributed collaborative probabilistic design of multi-failure structure with fluid-structure interaction using fuzzy neural network of regression

NASA Astrophysics Data System (ADS)

Song, Lu-Kai; Wen, Jie; Fei, Cheng-Wei; Bai, Guang-Chen

2018-05-01

To improve the computing efficiency and precision of probabilistic design for multi-failure structure, a distributed collaborative probabilistic design method-based fuzzy neural network of regression (FR) (called as DCFRM) is proposed with the integration of distributed collaborative response surface method and fuzzy neural network regression model. The mathematical model of DCFRM is established and the probabilistic design idea with DCFRM is introduced. The probabilistic analysis of turbine blisk involving multi-failure modes (deformation failure, stress failure and strain failure) was investigated by considering fluid-structure interaction with the proposed method. The distribution characteristics, reliability degree, and sensitivity degree of each failure mode and overall failure mode on turbine blisk are obtained, which provides a useful reference for improving the performance and reliability of aeroengine. Through the comparison of methods shows that the DCFRM reshapes the probability of probabilistic analysis for multi-failure structure and improves the computing efficiency while keeping acceptable computational precision. Moreover, the proposed method offers a useful insight for reliability-based design optimization of multi-failure structure and thereby also enriches the theory and method of mechanical reliability design.

Utilization of mathematics amongst healthcare students towards problem solving during their occupational safety health internship

NASA Astrophysics Data System (ADS)

Umasenan a/l Thanikasalam

2017-05-01

Occupational safety health is a multidisciplinary discipline concentrating on the safety, health and welfare of workers in the working place. Healthcare Students undergoing Occupational Safety Health internships are required to apply mathematical in areas such as safety legislation, safety behavior, ergonomics, chemical safety, OSH practices, industrial hygiene, risk management and safety health practices as problem solving. The aim of this paper is to investigate the level of mathematics and logic utilization from these students during their internship looking at areas of Hazard identification, Determining the population exposed to the hazard, Assessing the risk of the exposure to the hazards and Taking preventive and control. A total of 142 returning healthcare students from their Occupational Safety Health, internship were given a questionnaire to measure their perceptions towards mathematical and logic utilization. The overall results indicated a strong positive skewed result towards the use of Mathematics during their internship. The findings showed that mathematics were well delivered by the students during their internship. Mathematics could not be separated from OSH practice as a needed precision in quantifying safety, health an d welfare of workers in addition to empiricism.

Self-organization in the limb: a Turing mechanism for digit development.

PubMed

Cooper, Kimberly L

2015-06-01

The statistician George E. P. Box stated, 'Essentially all models are wrong, but some are useful.' (Box GEP, Draper NR: Empirical Model-Building and Response Surfaces. Wiley; 1987). Modeling biological processes is challenging for many of the reasons classically trained developmental biologists often resist the idea that black and white equations can explain the grayscale subtleties of living things. Although a simplified mathematical model of development will undoubtedly fall short of precision, a good model is exceedingly useful if it raises at least as many testable questions as it answers. Self-organizing Turing models that simulate the pattern of digits in the hand replicate events that have not yet been explained by classical approaches. The union of theory and experimentation has recently identified and validated the minimal components of a Turing network for digit pattern and triggered a cascade of questions that will undoubtedly be well-served by the continued merging of disciplines. Copyright © 2015 Elsevier Ltd. All rights reserved.

Basic research and data analysis for the National Geodetic Satellite Program and for the Earth and Ocean Physics Application Program

NASA Technical Reports Server (NTRS)

1974-01-01

Accomplishments in the continuing programs are reported. The data were obtained in support of the following broad objectives: (1) to provide a precise and accurate geometric description of the earth's surface; (2) to provide a precise and accurate mathematical description of the earth's gravitational field; and (3) to determine time variations of the geometry of the ocean surface, the solid earth, the gravity field, and other geophysical parameters.

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…

Natural Firing Patterns Imply Low Sensitivity of Synaptic Plasticity to Spike Timing Compared with Firing Rate

PubMed Central

Wallisch, Pascal; Ostojic, Srdjan

2016-01-01

Synaptic plasticity is sensitive to the rate and the timing of presynaptic and postsynaptic action potentials. In experimental protocols inducing plasticity, the imposed spike trains are typically regular and the relative timing between every presynaptic and postsynaptic spike is fixed. This is at odds with firing patterns observed in the cortex of intact animals, where cells fire irregularly and the timing between presynaptic and postsynaptic spikes varies. To investigate synaptic changes elicited by in vivo-like firing, we used numerical simulations and mathematical analysis of synaptic plasticity models. We found that the influence of spike timing on plasticity is weaker than expected from regular stimulation protocols. Moreover, when neurons fire irregularly, synaptic changes induced by precise spike timing can be equivalently induced by a modest firing rate variation. Our findings bridge the gap between existing results on synaptic plasticity and plasticity occurring in vivo, and challenge the dominant role of spike timing in plasticity. SIGNIFICANCE STATEMENT Synaptic plasticity, the change in efficacy of connections between neurons, is thought to underlie learning and memory. The dominant paradigm posits that the precise timing of neural action potentials (APs) is central for plasticity induction. This concept is based on experiments using highly regular and stereotyped patterns of APs, in stark contrast with natural neuronal activity. Using synaptic plasticity models, we investigated how irregular, in vivo-like activity shapes synaptic plasticity. We found that synaptic changes induced by precise timing of APs are much weaker than suggested by regular stimulation protocols, and can be equivalently induced by modest variations of the AP rate alone. Our results call into question the dominant role of precise AP timing for plasticity in natural conditions. PMID:27807166

Quantum interval-valued probability: Contextuality and the Born rule

NASA Astrophysics Data System (ADS)

Tai, Yu-Tsung; Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr

2018-05-01

We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and the Born rule. While foundational results such as the Kochen-Specker and Gleason theorems are valid in the context of infinite precision, they fail to hold in general in a world with limited resources. Here we employ an interval-valued framework to establish bounds on the validity of those theorems in realistic experimental environments. In this way, not only can we quantify the idea of finite-precision measurement within our theory, but we can also suggest a possible resolution of the Meyer-Mermin debate on the impact of finite-precision measurement on the Kochen-Specker theorem.

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…

Resimulation of noise: a precision estimator for least square error curve-fitting tested for axial strain time constant imaging

NASA Astrophysics Data System (ADS)

Nair, S. P.; Righetti, R.

2015-05-01

Recent elastography techniques focus on imaging information on properties of materials which can be modeled as viscoelastic or poroelastic. These techniques often require the fitting of temporal strain data, acquired from either a creep or stress-relaxation experiment to a mathematical model using least square error (LSE) parameter estimation. It is known that the strain versus time relationships for tissues undergoing creep compression have a non-linear relationship. In non-linear cases, devising a measure of estimate reliability can be challenging. In this article, we have developed and tested a method to provide non linear LSE parameter estimate reliability: which we called Resimulation of Noise (RoN). RoN provides a measure of reliability by estimating the spread of parameter estimates from a single experiment realization. We have tested RoN specifically for the case of axial strain time constant parameter estimation in poroelastic media. Our tests show that the RoN estimated precision has a linear relationship to the actual precision of the LSE estimator. We have also compared results from the RoN derived measure of reliability against a commonly used reliability measure: the correlation coefficient (CorrCoeff). Our results show that CorrCoeff is a poor measure of estimate reliability for non-linear LSE parameter estimation. While the RoN is specifically tested only for axial strain time constant imaging, a general algorithm is provided for use in all LSE parameter estimation.

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…

Representing the Earth's shape: the polemics surrounding Maupertuis's expedition to Lapland.

NASA Astrophysics Data System (ADS)

Terrall, M.

1992-06-01

Historical accounts of quantification in the physical sciences in the eighteenth century have often been described as a straightforward series of steps in a process of maturation, as instruments and standards advanced in precision. This paper calls into question the self-evidence nature of precision by investigating the production and uses of measurements. In the case of the dispute over the shape of the Earth, centered in Paris in the 1730s, the precision of measurements was a matter to be interpreted, attacked, defended, and represented. The whole messy business, undertaken by the participants to win consensus from their contemporaries, took place in the context of academic politics and the intellectual fashions of the salons and the court. All parties to the dispute claimed to be drawing on precision measurements; evaluating precision turned out to require the use of a range of intellectual, mathematical, instrumental, political, and textual resources. The alleged precision was then used to construct and defend rival scientific programs and practices.

The prediction of the flash point for binary aqueous-organic solutions.

PubMed

Liaw, Horng-Jang; Chiu, Yi-Yu

2003-07-18

A mathematical model, which may be used for predicting the flash point of aqueous-organic solutions, has been proposed and subsequently verified by experimentally-derived data. The results reveal that this model is able to precisely predict the flash point over the entire composition range of binary aqueous-organic solutions by way of utilizing the flash point data pertaining to the flammable component. The derivative of flash point with respect to composition (solution composition effect upon flash point) can be applied to process safety design/operation in order to identify as to whether the dilution of a flammable liquid solution with water is effective in reducing the fire and explosion hazard of the solution at a specified composition. Such a derivative equation was thus derived based upon the flash point prediction model referred to above and then verified by the application of experimentally-derived data.

Full-field 3D shape measurement of specular object having discontinuous surfaces

NASA Astrophysics Data System (ADS)

Zhang, Zonghua; Huang, Shujun; Gao, Nan; Gao, Feng; Jiang, Xiangqian

2017-06-01

This paper presents a novel Phase Measuring Deflectometry (PMD) method to measure specular objects having discontinuous surfaces. A mathematical model is established to directly relate the absolute phase and depth, instead of the phase and gradient. Based on the model, a hardware measuring system has been set up, which consists of a precise translating stage, a projector, a diffuser and a camera. The stage locates the projector and the diffuser together to a known position during measurement. By using the model-based and machine vision methods, system calibration is accomplished to provide the required parameters and conditions. The verification tests are given to evaluate the effectiveness of the developed system. 3D (Three-Dimensional) shapes of a concave mirror and a monolithic multi-mirror array having multiple specular surfaces have been measured. Experimental results show that the proposed method can obtain 3D shape of specular objects having discontinuous surfaces effectively

A survey of fuzzy logic monitoring and control utilisation in medicine.

PubMed

Mahfouf, M; Abbod, M F; Linkens, D A

2001-01-01

Intelligent systems have appeared in many technical areas, such as consumer electronics, robotics and industrial control systems. Many of these intelligent systems are based on fuzzy control strategies which describe complex systems mathematical models in terms of linguistic rules. Since the 1980s new techniques have appeared from which fuzzy logic has been applied extensively in medical systems. The justification for such intelligent systems driven solutions is that biological systems are so complex that the development of computerised systems within such environments is not always a straightforward exercise. In practice, a precise model may not exist for biological systems or it may be too difficult to model. In most cases fuzzy logic is considered to be an ideal tool as human minds work from approximate data, extract meaningful information and produce crisp solutions. This paper surveys the utilisation of fuzzy logic control and monitoring in medical sciences with an analysis of its possible future penetration.

Identity: a complex structure for researching students' academic behavior in science and mathematics

NASA Astrophysics Data System (ADS)

Aydeniz, Mehmet; Hodge, Lynn Liao

2011-06-01

This article is a response to Pike and Dunne's research. The focus of their analysis is on reflections of studying science post-16. Pike and Dunne draw attention to under enrollments in science, technology, engineering, and mathematics (STEM) fields, in particular, in the field of physics, chemistry and biology in the United Kingdom. We provide an analysis of how the authors conceptualize the problem of scientific career choices, the theoretical framework through which they study the problem, and the methodology they use to collect and analyze data. In addition, we examine the perspective they provide in light of new developments in the field of students' attitudes towards science and mathematics. More precisely, we draw attention to and explicate the authors' use of identity from the perspective of emerging theories that explore the relationships between the learner and culture in the context of science and mathematics.

Reflections on the Notion of Culture in the History of Mathematics: The Example of "Geometrical Equations".

PubMed

Lê, François

2016-09-01

Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system."

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

A real success in numerical modeling of dynamics of the Earth can be achieved only by multidisciplinary research teams of experts in geodynamics, applied and pure mathematics, and computer science. The success in numerical modeling is based on the following basic, but simple, rules. (i) People need simplicity most, but they understand intricacies best (B. Pasternak, writer). Start from a simple numerical model, which describes basic physical laws by a set of mathematical equations, and move then to a complex model. Never start from a complex model, because you cannot understand the contribution of each term of the equations to the modeled geophysical phenomenon. (ii) Study the numerical methods behind your computer code. Otherwise it becomes difficult to distinguish true and erroneous solutions to the geodynamic problem, especially when your problem is complex enough. (iii) Test your model versus analytical and asymptotic solutions, simple 2D and 3D model examples. Develop benchmark analysis of different numerical codes and compare numerical results with laboratory experiments. Remember that the numerical tool you employ is not perfect, and there are small bugs in every computer code. Therefore the testing is the most important part of your numerical modeling. (iv) Prove (if possible) or learn relevant statements concerning the existence, uniqueness and stability of the solution to the mathematical and discrete problems. Otherwise you can solve an improperly-posed problem, and the results of the modeling will be far from the true solution of your model problem. (v) Try to analyze numerical models of a geological phenomenon using as less as possible tuning model variables. Already two tuning variables give enough possibilities to constrain your model well enough with respect to observations. The data fitting sometimes is quite attractive and can take you far from a principal aim of your numerical modeling: to understand geophysical phenomena. (vi) If the number of tuning model variables are greater than two, test carefully the effect of each of the variables on the modeled phenomenon. Remember: With four exponents I can fit an elephant (E. Fermi, physicist). (vii) Make your numerical model as accurate as possible, but never put the aim to reach a great accuracy: Undue precision of computations is the first symptom of mathematical illiteracy (N. Krylov, mathematician). How complex should be a numerical model? A model which images any detail of the reality is as useful as a map of scale 1:1 (J. Robinson, economist). This message is quite important for geoscientists, who study numerical models of complex geodynamical processes. I believe that geoscientists will never create a model of the real Earth dynamics, but we should try to model the dynamics such a way to simulate basic geophysical processes and phenomena. Does a particular model have a predictive power? Each numerical model has a predictive power, otherwise the model is useless. The predictability of the model varies with its complexity. Remember that a solution to the numerical model is an approximate solution to the equations, which have been chosen in believe that they describe dynamic processes of the Earth. Hence a numerical model predicts dynamics of the Earth as well as the mathematical equations describe this dynamics. What methodological advances are still needed for testable geodynamic modeling? Inverse (time-reverse) numerical modeling and data assimilation are new methodologies in geodynamics. The inverse modeling can allow to test geodynamic models forward in time using restored (from present-day observations) initial conditions instead of unknown conditions.

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.

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik

2014-03-01

The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

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

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

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

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

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

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

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

Formal Darwinism, the individual-as-maximizing-agent analogy and bet-hedging

PubMed Central

Grafen, A.

1999-01-01

The central argument of The origin of species was that mechanical processes (inheritance of features and the differential reproduction they cause) can give rise to the appearance of design. The 'mechanical processes' are now mathematically represented by the dynamic systems of population genetics, and the appearance of design by optimization and game theory in which the individual plays the part of the maximizing agent. Establishing a precise individual-as-maximizing-agent (IMA) analogy for a population-genetics system justifies optimization approaches, and so provides a modern formal representation of the core of Darwinism. It is a hitherto unnoticed implication of recent population-genetics models that, contrary to a decades-long consensus, an IMA analogy can be found in models with stochastic environments (subject to a convexity assumption), in which individuals maximize expected reproductive value. The key is that the total reproductive value of a species must be considered as constant, so therefore reproductive value should always be calculated in relative terms. This result removes a major obstacle from the theoretical challenge to find a unifying framework which establishes the IMA analogy for all of Darwinian biology, including as special cases inclusive fitness, evolutionarily stable strategies, evolutionary life-history theory, age-structured models and sex ratio theory. This would provide a formal, mathematical justification of fruitful and widespread but 'intentional' terms in evolutionary biology, such as 'selfish', 'altruism' and 'conflict'.

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…

After Behaviourism, Navigationism?

ERIC Educational Resources Information Center

Moran, Sean

2008-01-01

Two previous articles in this journal advocate the greater use of a behaviourist methodology called "Precision Teaching" (PT). From a position located within virtue ethics, this article argues that the technical feat of raising narrowly defined performance in mathematics and other subjects is not sufficient justification for the…

An evaluation of models of bare soil evaporation formulated with different land surface boundary conditions and assumptions

NASA Astrophysics Data System (ADS)

Smits, Kathleen M.; Ngo, Viet V.; Cihan, Abdullah; Sakaki, Toshihiro; Illangasekare, Tissa H.

2012-12-01

Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance. However, there is no agreement on the best modeling methodology to determine evaporation under different atmospheric boundary conditions. Also, there is a lack of directly measured soil evaporation data for model validation to compare these methods to establish the validity of their mathematical formulations. Thus, a need exists to systematically compare evaporation estimates using existing methods to experimental observations. The goal of this work is to test different conceptual and mathematical formulations that are used to estimate evaporation from bare soils to critically investigate various formulations and surface boundary conditions. Such a comparison required the development of a numerical model that has the ability to incorporate these boundary conditions. For this model, we modified a previously developed theory that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. Precision data under well-controlled transient heat and wind boundary conditions were generated, and results from numerical simulations were compared with experimental data. Results demonstrate that the approaches based on different boundary conditions varied in their ability to capture different stages of evaporation. All approaches have benefits and limitations, and no one approach can be deemed most appropriate for every scenario. Comparisons of different formulations of the surface boundary condition validate the need for further research on heat and vapor transport processes in soil for better modeling accuracy.

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

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…

Psychoacoustic entropy theory and its implications for performance practice

NASA Astrophysics Data System (ADS)

Strohman, Gregory J.

This dissertation attempts to motivate, derive and imply potential uses for a generalized perceptual theory of musical harmony called psychoacoustic entropy theory. This theory treats the human auditory system as a physical system which takes acoustic measurements. As a result, the human auditory system is subject to all the appropriate uncertainties and limitations of other physical measurement systems. This is the theoretic basis for defining psychoacoustic entropy. Psychoacoustic entropy is a numerical quantity which indexes the degree to which the human auditory system perceives instantaneous disorder within a sound pressure wave. Chapter one explains the importance of harmonic analysis as a tool for performance practice. It also outlines the critical limitations for many of the most influential historical approaches to modeling harmonic stability, particularly when compared to available scientific research in psychoacoustics. Rather than analyze a musical excerpt, psychoacoustic entropy is calculated directly from sound pressure waves themselves. This frames psychoacoustic entropy theory in the most general possible terms as a theory of musical harmony, enabling it to be invoked for any perceivable sound. Chapter two provides and examines many widely accepted mathematical models of the acoustics and psychoacoustics of these sound pressure waves. Chapter three introduces entropy as a precise way of measuring perceived uncertainty in sound pressure waves. Entropy is used, in combination with the acoustic and psychoacoustic models introduced in chapter two, to motivate the mathematical formulation of psychoacoustic entropy theory. Chapter four shows how to use psychoacoustic entropy theory to analyze the certain types of musical harmonies, while chapter five applies the analytical tools developed in chapter four to two short musical excerpts to influence their interpretation. Almost every form of harmonic analysis invokes some degree of mathematical reasoning. However, the limited scope of most harmonic systems used for Western common practice music greatly simplifies the necessary level of mathematical detail. Psychoacoustic entropy theory requires a greater deal of mathematical complexity due to its sheer scope as a generalized theory of musical harmony. Fortunately, under specific assumptions the theory can take on vastly simpler forms. Psychoacoustic entropy theory appears to be highly compatible with the latest scientific research in psychoacoustics. However, the theory itself should be regarded as a hypothesis and this dissertation an experiment in progress. The evaluation of psychoacoustic entropy theory as a scientific theory of human sonic perception must wait for more rigorous future research.

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…

Controlled fire use in early humans might have triggered the evolutionary emergence of tuberculosis.

PubMed

Chisholm, Rebecca H; Trauer, James M; Curnoe, Darren; Tanaka, Mark M

2016-08-09

Tuberculosis (TB) is caused by the Mycobacterium tuberculosis complex (MTBC), a wildly successful group of organisms and the leading cause of death resulting from a single bacterial pathogen worldwide. It is generally accepted that MTBC established itself in human populations in Africa and that animal-infecting strains diverged from human strains. However, the precise causal factors of TB emergence remain unknown. Here, we propose that the advent of controlled fire use in early humans created the ideal conditions for the emergence of TB as a transmissible disease. This hypothesis is supported by mathematical modeling together with a synthesis of evidence from epidemiology, evolutionary genetics, and paleoanthropology.

Research on the Diesel Engine with Sliding Mode Variable Structure Theory

NASA Astrophysics Data System (ADS)

Ma, Zhexuan; Mao, Xiaobing; Cai, Le

2018-05-01

This study constructed the nonlinear mathematical model of the diesel engine high-pressure common rail (HPCR) system through two polynomial fitting which was treated as a kind of affine nonlinear system. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for affine nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrated that sliding-mode variable structure control algorithm shows favourable control performances which are overcoming the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

Inverting Image Data For Optical Testing And Alignment

NASA Technical Reports Server (NTRS)

Shao, Michael; Redding, David; Yu, Jeffrey W.; Dumont, Philip J.

1993-01-01

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

General Principles for Brain Design

NASA Astrophysics Data System (ADS)

Josephson, Brian D.

2006-06-01

The task of understanding how the brain works has met with only limited success since important design concepts are not as yet incorporated in the analysis. Relevant concepts can be uncovered by studying the powerful methodologies that have evolved in the context of computer programming, raising the question of how the concepts involved there can be realised in neural hardware. Insights can be gained in regard to such issues through the study of the role played by models and representation. These insights lead on to an appreciation of the mechanisms underlying subtle capacities such as those concerned with the use of language. A precise, essentially mathematical account of such capacities is in prospect for the future.

Construction Theory and Noise Analysis Method of Global CGCS2000 Coordinate Frame

NASA Astrophysics Data System (ADS)

Jiang, Z.; Wang, F.; Bai, J.; Li, Z.

2018-04-01

The definition, renewal and maintenance of geodetic datum has been international hot issue. In recent years, many countries have been studying and implementing modernization and renewal of local geodetic reference coordinate frame. Based on the precise result of continuous observation for recent 15 years from state CORS (continuously operating reference system) network and the mainland GNSS (Global Navigation Satellite System) network between 1999 and 2007, this paper studies the construction of mathematical model of the Global CGCS2000 frame, mainly analyzes the theory and algorithm of two-step method for Global CGCS2000 Coordinate Frame formulation. Finally, the noise characteristic of the coordinate time series are estimated quantitatively with the criterion of maximum likelihood estimation.

Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

NASA Astrophysics Data System (ADS)

Chakhmakhchyan, L.; Cerf, N. J.; Garcia-Patron, R.

2017-08-01

We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.

Production of Entanglement Entropy by Decoherence

NASA Astrophysics Data System (ADS)

Merkli, M.; Berman, G. P.; Sayre, R. T.; Wang, X.; Nesterov, A. I.

We examine the dynamics of entanglement entropy of all parts in an open system consisting of a two-level dimer interacting with an environment of oscillators. The dimer-environment interaction is almost energy conserving. We find the precise link between decoherence and production of entanglement entropy. We show that not all environment oscillators carry significant entanglement entropy and we identify the oscillator frequency regions which contribute to the production of entanglement entropy. For energy conserving dimer-environment interactions the models are explicitly solvable and our results hold for all dimer-environment coupling strengths. We carry out a mathematically rigorous perturbation theory around the energy conserving situation in the presence of small non-energy conserving interactions.

Precise determination of time to reach viral load set point after acute HIV-1 infection.

PubMed

Huang, Xiaojie; Chen, Hui; Li, Wei; Li, Haiying; Jin, Xia; Perelson, Alan S; Fox, Zoe; Zhang, Tong; Xu, Xiaoning; Wu, Hao

2012-12-01

The HIV viral load set point has long been used as a prognostic marker of disease progression and more recently as an end-point parameter in HIV vaccine clinical trials. The definition of set point, however, is variable. Moreover, the earliest time at which the set point is reached after the onset of infection has never been clearly defined. In this study, we obtained sequential plasma viral load data from 60 acutely HIV-infected Chinese patients among a cohort of men who have sex with men, mathematically determined viral load set point levels, and estimated time to attain set point after infection. We also compared the results derived from our models and that obtained from an empirical method. With novel uncomplicated mathematic model, we discovered that set points may vary from 21 to 119 days dependent on the patients' initial viral load trajectory. The viral load set points were 4.28 ± 0.86 and 4.25 ± 0.87 log10 copies per milliliter (P = 0.08), respectively, as determined by our model and an empirical method, suggesting an excellent agreement between the old and new methods. We provide a novel method to estimate viral load set point at the very early stage of HIV infection. Application of this model can accurately and reliably determine the set point, thus providing a new tool for physicians to better monitor early intervention strategies in acutely infected patients and scientists to rationally design preventative vaccine studies.

The study of precision measurement of pelvis spatial structure

NASA Astrophysics Data System (ADS)

Ma, Xiang; Ouyang, Jianfei; Qu, Xinghua

2010-03-01

Osteometry is fundamental for anthropometry. It provides the key technology and value to the study of palaeoanthropology, medicine, and criminal investigation. The traditional osteometry that has been widely accepted and used since 18th century has no longer met the information demand for modern research and application. It is significant and necessary to create an advanced 3-dimensional osteometry technique for anthropometry. This paper presents a new quick and accurate method to measure human pelvis through mathematical modeling. The pelvis is a complex combination of bones, which consists of three connected parts: hipbones, sacrum, and coccyx. There are over 40 items to be measured for the 1-dimension characteristics. In this paper, a combined measuring technology is developed for pelvis measurement. It uses machine vision systems and a portable measuring arm to obtain key geometry parameters of the pelvis. The mathematics models of the pelvis spatial structure and its parts are created through the process of data collecting, digging, assembling, and modeling. The experiment shows that the proposed technology can meet traditional osteometry and obtain entire 1D geometric parameters of the pelvis, such as maximum breadth and height, diameter of obstetric conjugata, inclination angle, and sakralneigungswinkel, etc. at the same time after modeling. Besides making the measurements above, the proposed technology can measure the geometry characteristics of pelvis and its parts, such as volume, surface area, curvature, and spatial structure, which are almost impossible for traditional technology. The overall measuring error is less than 0.1mm.

Shrinking microbubbles with microfluidics: mathematical modelling to control microbubble sizes.

PubMed

Salari, A; Gnyawali, V; Griffiths, I M; Karshafian, R; Kolios, M C; Tsai, S S H

2017-11-29

Microbubbles have applications in industry and life-sciences. In medicine, small encapsulated bubbles (<10 μm) are desirable because of their utility in drug/oxygen delivery, sonoporation, and ultrasound diagnostics. While there are various techniques for generating microbubbles, microfluidic methods are distinguished due to their precise control and ease-of-fabrication. Nevertheless, sub-10 μm diameter bubble generation using microfluidics remains challenging, and typically requires expensive equipment and cumbersome setups. Recently, our group reported a microfluidic platform that shrinks microbubbles to sub-10 μm diameters. The microfluidic platform utilizes a simple microbubble-generating flow-focusing geometry, integrated with a vacuum shrinkage system, to achieve microbubble sizes that are desirable in medicine, and pave the way to eventual clinical uptake of microfluidically generated microbubbles. A theoretical framework is now needed to relate the size of the microbubbles produced and the system's input parameters. In this manuscript, we characterize microbubbles made with various lipid concentrations flowing in solutions that have different interfacial tensions, and monitor the changes in bubble size along the microfluidic channel under various vacuum pressures. We use the physics governing the shrinkage mechanism to develop a mathematical model that predicts the resulting bubble sizes and elucidates the dominant parameters controlling bubble sizes. The model shows a good agreement with the experimental data, predicting the resulting microbubble sizes under different experimental input conditions. We anticipate that the model will find utility in enabling users of the microfluidic platform to engineer bubbles of specific sizes.

Blue light-mediated transcriptional activation and repression of gene expression in bacteria

PubMed Central

Jayaraman, Premkumar; Devarajan, Kavya; Chua, Tze Kwang; Zhang, Hanzhong; Gunawan, Erry; Poh, Chueh Loo

2016-01-01

Light-regulated modules offer unprecedented new ways to control cellular behavior in precise spatial and temporal resolution. The availability of such tools may dramatically accelerate the progression of synthetic biology applications. Nonetheless, current optogenetic toolbox of prokaryotes has potential issues such as lack of rapid and switchable control, less portable, low dynamic expression and limited parts. To address these shortcomings, we have engineered a novel bidirectional promoter system for Escherichia coli that can be induced or repressed rapidly and reversibly using the blue light dependent DNA-binding protein EL222. We demonstrated that by modulating the dosage of light pulses or intensity we could control the level of gene expression precisely. We show that both light-inducible and repressible system can function in parallel with high spatial precision in a single cell and can be switched stably between ON- and OFF-states by repetitive pulses of blue light. In addition, the light-inducible and repressible expression kinetics were quantitatively analysed using a mathematical model. We further apply the system, for the first time, to optogenetically synchronize two receiver cells performing different logic behaviors over time using blue light as a molecular clock signal. Overall, our modular approach layers a transformative platform for next-generation light-controllable synthetic biology systems in prokaryotes. PMID:27353329

[A plane-based hand-eye calibration method for surgical robots].

PubMed

Zeng, Bowei; Meng, Fanle; Ding, Hui; Liu, Wenbo; Wu, Di; Wang, Guangzhi

2017-04-01

In order to calibrate the hand-eye transformation of the surgical robot and laser range finder (LRF), a calibration algorithm based on a planar template was designed. A mathematical model of the planar template had been given and the approach to address the equations had been derived. Aiming at the problems of the measurement error in a practical system, we proposed a new algorithm for selecting coplanar data. This algorithm can effectively eliminate considerable measurement error data to improve the calibration accuracy. Furthermore, three orthogonal planes were used to improve the calibration accuracy, in which a nonlinear optimization for hand-eye calibration was used. With the purpose of verifying the calibration precision, we used the LRF to measure some fixed points in different directions and a cuboid's surfaces. Experimental results indicated that the precision of a single planar template method was (1.37±0.24) mm, and that of the three orthogonal planes method was (0.37±0.05) mm. Moreover, the mean FRE of three-dimensional (3D) points was 0.24 mm and mean TRE was 0.26 mm. The maximum angle measurement error was 0.4 degree. Experimental results show that the method presented in this paper is effective with high accuracy and can meet the requirements of surgical robot precise location.

Ultra-precision turning of complex spiral optical delay line

NASA Astrophysics Data System (ADS)

Zhang, Xiaodong; Li, Po; Fang, Fengzhou; Wang, Qichang

2011-11-01

Optical delay line (ODL) implements the vertical or depth scanning of optical coherence tomography, which is the most important factor affecting the scanning resolution and speed. The spinning spiral mirror is found as an excellent optical delay device because of the high-speed and high-repetition-rate. However, it is one difficult task to machine the mirror due to the special shape and precision requirement. In this paper, the spiral mirror with titled parabolic generatrix is proposed, and the ultra-precision turning method is studied for its machining using the spiral mathematic model. Another type of ODL with the segmental shape is also introduced and machined to make rotation balance for the mass equalization when scanning. The efficiency improvement is considered in details, including the rough cutting with the 5- axis milling machine, the machining coordinates unification, and the selection of layer direction in turning. The onmachine measuring method based on stylus gauge is designed to analyze the shape deviation. The air bearing is used as the measuring staff and the laser interferometer sensor as the position sensor, whose repeatability accuracy is proved up to 10nm and the stable feature keeps well. With this method developed, the complex mirror with nanometric finish of 10.7nm in Ra and the form error within 1um are achieved.

Theoretical and experimental research on machine tool servo system for ultra-precision position compensation on CNC lathe

NASA Astrophysics Data System (ADS)

Ma, Zhichao; Hu, Leilei; Zhao, Hongwei; Wu, Boda; Peng, Zhenxing; Zhou, Xiaoqin; Zhang, Hongguo; Zhu, Shuai; Xing, Lifeng; Hu, Huang

2010-08-01

The theories and techniques for improving machining accuracy via position control of diamond tool's tip and raising resolution of cutting depth on precise CNC lathes have been extremely focused on. A new piezo-driven ultra-precision machine tool servo system is designed and tested to improve manufacturing accuracy of workpiece. The mathematical model of machine tool servo system is established and the finite element analysis is carried out on parallel plate flexure hinges. The output position of diamond tool's tip driven by the machine tool servo system is tested via a contact capacitive displacement sensor. Proportional, integral, derivative (PID) feedback is also implemented to accommodate and compensate dynamical change owing cutting forces as well as the inherent non-linearity factors of the piezoelectric stack during cutting process. By closed loop feedback controlling strategy, the tracking error is limited to 0.8 μm. Experimental results have shown the proposed machine tool servo system could provide a tool positioning resolution of 12 nm, which is much accurate than the inherent CNC resolution magnitude. The stepped shaft of aluminum specimen with a step increment of cutting depth of 1 μm is tested, and the obtained contour illustrates the displacement command output from controller is accurately and real-time reflected on the machined part.

Tightly coupled integration of ionosphere-constrained precise point positioning and inertial navigation systems.

PubMed

Gao, Zhouzheng; Zhang, Hongping; Ge, Maorong; Niu, Xiaoji; Shen, Wenbin; Wickert, Jens; Schuh, Harald

2015-03-10

The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS.

Test-particle dynamics in general spherically symmetric black hole spacetimes

NASA Astrophysics Data System (ADS)

De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Rezzolla, Luciano

2018-05-01

To date, the most precise tests of general relativity have been achieved through pulsar timing, albeit in the weak-field regime. Since pulsars are some of the most precise and stable "clocks" in the Universe, present observational efforts are focused on detecting pulsars in the vicinity of supermassive black holes (most notably in the Galactic Centre), enabling pulsar timing to be used as an extremely precise probe of strong-field gravity. In this paper, a mathematical framework to describe test-particle dynamics in general black-hole spacetimes is presented and subsequently used to study a binary system comprising a pulsar orbiting a black hole. In particular, taking into account the parameterization of a general spherically symmetric black-hole metric, general analytic expressions for both the advance of the periastron and for the orbital period of a massive test particle are derived. Furthermore, these expressions are applied to four representative cases of solutions arising in both general relativity and in alternative theories of gravity. Finally, this framework is applied to the Galactic center S -stars and four distinct pulsar toy models. It is shown that by adopting a fully general-relativistic description of test-particle motion which is independent of any particular theory of gravity, observations of pulsars can help impose better constraints on alternative theories of gravity than is presently possible.

Therapy operating characteristic curves: tools for precision chemotherapy

PubMed Central

Barrett, Harrison H.; Alberts, David S.; Woolfenden, James M.; Caucci, Luca; Hoppin, John W.

2016-01-01

Abstract. The therapy operating characteristic (TOC) curve, developed in the context of radiation therapy, is a plot of the probability of tumor control versus the probability of normal-tissue complications as the overall radiation dose level is varied, e.g., by varying the beam current in external-beam radiotherapy or the total injected activity in radionuclide therapy. This paper shows how TOC can be applied to chemotherapy with the administered drug dosage as the variable. The area under a TOC curve (AUTOC) can be used as a figure of merit for therapeutic efficacy, analogous to the area under an ROC curve (AUROC), which is a figure of merit for diagnostic efficacy. In radiation therapy, AUTOC can be computed for a single patient by using image data along with radiobiological models for tumor response and adverse side effects. The mathematical analogy between response of observers to images and the response of tumors to distributions of a chemotherapy drug is exploited to obtain linear discriminant functions from which AUTOC can be calculated. Methods for using mathematical models of drug delivery and tumor response with imaging data to estimate patient-specific parameters that are needed for calculation of AUTOC are outlined. The implications of this viewpoint for clinical trials are discussed. PMID:27175376

A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

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

Lienert, Matthias, E-mail: lienert@math.lmu.de

2015-04-15

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to amore » relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.« less

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…

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service

PubMed Central

Al-hetar, Abdulaziz M.

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum. PMID:27855216

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service.

PubMed

Shamsan, Zaid Ahmed; Al-Hetar, Abdulaziz M

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum.

General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

NASA Astrophysics Data System (ADS)

De Vincenzo, Salvatore; Sánchez, Carlet

2018-05-01

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.

Rolling friction and energy dissipation in a spinning disc

PubMed Central

Ma, Daolin; Liu, Caishan; Zhao, Zhen; Zhang, Hongjian

2014-01-01

This paper presents the results of both experimental and theoretical investigations for the dynamics of a steel disc spinning on a horizontal rough surface. With a pair of high-speed cameras, a stereoscopic vision method is adopted to perform omnidirectional measurements for the temporal evolution of the disc's motion. The experiment data allow us to detail the dynamics of the disc, and consequently to quantify its energy. From our experimental observations, it is confirmed that rolling friction is a primary factor responsible for the dissipation of the energy. Furthermore, a mathematical model, in which the rolling friction is characterized by a resistance torque proportional to the square of precession rate, is also proposed. By employing the model, we perform qualitative analysis and numerical simulations. Both of them provide results that precisely agree with our experimental findings. PMID:25197246

Inhibition, Conflict Detection, and Number Conservation

ERIC Educational Resources Information Center

Lubin, Amélie; Simon, Grégory; Houdé, Olivier; De Neys, Wim

2015-01-01

The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

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)…

Metal Carbon Eutectics to Extend the Use of the Fixed-Point Technique in Precision IR Thermometry

NASA Astrophysics Data System (ADS)

Battuello, M.; Girard, F.; Florio, M.

2008-06-01

The high-temperature extension of the fixed-point technique for primary calibration of precision infrared (IR) thermometers was investigated both through mathematical simulations and laboratory investigations. Simulations were performed with Co C (1,324°C) and Pd C (1, 492°C) eutectic fixed points, and a precision IR thermometer was calibrated from the In point (156.5985°C) up to the Co C point. Mathematical simulations suggested the possibility of directly deriving the transition temperature of the Co C and Pd C points by extrapolating the calibration derived from fixed-point measurements from In to the Cu point. Both temperatures, as a result of the low uncertainty associated with the In Cu calibration and the high number of fixed points involved in the calibration process, can be derived with an uncertainty of 0.11°C for Co C and 0.18°C for Pd C. A transition temperature of 1,324.3°C for Co C was determined from the experimental verification, a value higher than, but compatible with, the one proposed by the thermometry community for inclusion as a secondary reference point for ITS-90 dissemination, i.e., 1,324.0°C.

The Approximate Number System and its Relation to Early Math Achievement: Evidence from the Preschool Years

PubMed Central

Bonny, Justin W.; Lourenco, Stella F.

2012-01-01

Humans rely on two main systems of quantification - one is non-symbolic and involves approximate number representations (known as the approximate number system or ANS), the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations, which, importantly, have been shown to relate to symbolic math competence, even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement, but, critically, that this relation was non-linear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such non-linearity are discussed. PMID:23201156

The approximate number system and its relation to early math achievement: evidence from the preschool years.

PubMed

Bonny, Justin W; Lourenco, Stella F

2013-03-01

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed. Copyright © 2012 Elsevier Inc. All rights reserved.

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.

Property-Based Software Engineering Measurement

NASA Technical Reports Server (NTRS)

Briand, Lionel; Morasca, Sandro; Basili, Victor R.

1995-01-01

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysis, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact, and rigorous, because it is based on precise mathematical concepts. This framework defines several important measurement concepts (size, length, complexity, cohesion, coupling). It is not intended to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalism and properties we introduce are convenient and intuitive. In addition, we have reviewed the literature on this subject and compared it with our work. This framework contributes constructively to a firmer theoretical ground of software measurement.

Property-Based Software Engineering Measurement

NASA Technical Reports Server (NTRS)

Briand, Lionel C.; Morasca, Sandro; Basili, Victor R.

1997-01-01

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts, regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysts, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact and rigorous, because it is based on precise mathematical concepts. We use this framework to propose definitions of several important measurement concepts (size, length, complexity, cohesion, coupling). It does not intend to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalisms and properties we introduce are convenient and intuitive. This framework contributes constructively to a firmer theoretical ground of software measurement.

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

PubMed

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

2016-01-01

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

Effects of Finger Counting on Numerical Development – The Opposing Views of Neurocognition and Mathematics Education

PubMed Central

Moeller, Korbinian; Martignon, Laura; Wessolowski, Silvia; Engel, Joachim; Nuerk, Hans-Christoph

2011-01-01

Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis, or “finger sense,” enhances mathematical skills. Therefore neurocognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development. However, research in mathematics education recommends fostering mentally based numerical representations so as to induce children to abandon finger counting. More precisely, mathematics education recommends first using finger counting, then concrete structured representations and, finally, mental representations of numbers to perform numerical operations. Taken together, these results reveal an important debate between neurocognitive and mathematics education research concerning the benefits and detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be discussed. PMID:22144969

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.…

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Cognitive and attitudinal predictors related to graphing achievement among pre-service elementary teachers

NASA Astrophysics Data System (ADS)

Szyjka, Sebastian P.

The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers' performance on line graphing. Predictors included Illinois teacher education basic skills sub-component scores in reading comprehension and mathematics, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. This study also determined the strength of the relationship between each prospective predictor variable and the line graphing performance variable, as well as the extent to which measures of attitude towards science, mathematics and graphing mediated relationships between scores on mathematics, reading, logical thinking and line graphing. Ninety-four pre-service elementary education teachers enrolled in two different elementary science methods courses during the spring 2009 semester at Southern Illinois University Carbondale participated in this study. Each subject completed five different instruments designed to assess science, mathematics and graphing attitudes as well as logical thinking and graphing ability. Sixty subjects provided copies of primary basic skills score reports that listed subset scores for both reading comprehension and mathematics. The remaining scores were supplied by a faculty member who had access to a database from which the scores were drawn. Seven subjects, whose scores could not be found, were eliminated from final data analysis. Confirmatory factor analysis (CFA) was conducted in order to establish validity and reliability of the Questionnaire of Attitude Toward Line Graphs in Science (QALGS) instrument. CFA tested the statistical hypothesis that the five main factor structures within the Questionnaire of Attitude Toward Statistical Graphs (QASG) would be maintained in the revised QALGS. Stepwise Regression Analysis with backward elimination was conducted in order to generate a parsimonious and precise predictive model. This procedure allowed the researcher to explore the relationships among the affective and cognitive variables that were included in the regression analysis. The results for CFA indicated that the revised QALGS measure was sound in its psychometric properties when tested against the QASG. Reliability statistics indicated that the overall reliability for the 32 items in the QALGS was .90. The learning preferences construct had the lowest reliability (.67), while enjoyment (.89), confidence (.86) and usefulness (.77) constructs had moderate to high reliabilities. The first four measurement models fit the data well as indicated by the appropriate descriptive and statistical indices. However, the fifth measurement model did not fit the data well statistically, and only fit well with two descriptive indices. The results addressing the research question indicated that mathematical and logical thinking ability were significant predictors of line graph performance among the remaining group of variables. These predictors accounted for 41% of the total variability on the line graph performance variable. Partial correlation coefficients indicated that mathematics ability accounted for 20.5% of the variance on the line graphing performance variable when removing the effect of logical thinking. The logical thinking variable accounted for 4.7% of the variance on the line graphing performance variable when removing the effect of mathematics ability.

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;…

[Gaston Bachelard anagogical reverie and surrational at stake].

PubMed

Castellana, Mario

2015-01-01

The latest studies on epistemological thought of Gaston Bachelard, especially in France and Italy, they are highlighting some fundamental issues, such as creative and propulsive assigned to mathematics in the construction of physical reality. The studies of Bachelard on the quantum mechanics of the '30s, and especially on the theoretical physics of Paul Dirac, introduced a particular concept of "anagogical reverie" precisely in order to understand the increasingly abstract and creative thinking of mathematics in the various levels of physical reality. In the wake of what Federigo Enriques called "mathematical poetry", Bachelard comes to propose a real "nouménologie mathématique" which characterizes the contemporary scientific thought and which provides the basis epistemic appropriate to understand the 'rational effectiveness' of mathematics and the real meaning of their application to the real. For these reasons, Bachelard in the '30s used a new term to describe his rationalist engagement, the "surrationalisme", just to understand in depth what Enriques called the "implicit philosophy" in sciences, the "pensée des sciences", where mathematics, thanks to the "anagogical reverie", put in place continue "enjeux" of the rational.

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.

Evaluating the Impact of Global Warming on Water Balance of Maize by High-precision Controlled Experiment and MLCan model

NASA Astrophysics Data System (ADS)

Ma, Y.; Song, X.; Kumar, P.; Wu, Y.; Woo, D.; Le, P. V.; Ma, C.

2016-12-01

Increased temperature affects the agricultural hydrologic cycle not only by changing precipitation levels, evapotranspiration and the magnitude and timing of run-off, but also by impacting water flows and soil water dynamics. Accurate prediction of hydrologic change under global warming requires high-precision experiment and mathematical model to determine water interaction between interfaces in the soil-plant-atmosphere continuum. In this study, the weighting lysimeter and chamber were coupled to monitor water balance component dynamics of maize under controlled ambient temperature and elevated temperature of 2°C conditions. A mechanistic multilayer canopy-soil-root system model (MLCan) was used to predict hydrologic fluxes variation under different elevated temperature scenarios after calibration with experimental results. The results showed that maize growth period reduced 8 days under increased temperature of 2°C. The mean daily evapotranspiration, soil water storage change, and drainage was 2.66 mm, -2.75 mm, and 0.22 mm under controlled temperature condition, respectively. When temperature was elevated by 2°C, the average daily ET for maize significantly increased about 6.7% (p<0.05). However, there were non-significant impacts of increased temperature on the daily soil water storage change and drainage (p>0.05). Quantification of changes in water balance components induced by temperature increase for maize is critical for optimizing irrigation water management practices and improving water use efficiency.

Quantitative approaches to energy and glucose homeostasis: machine learning and modelling for precision understanding and prediction

PubMed Central

Murphy, Kevin G.; Jones, Nick S.

2018-01-01

Obesity is a major global public health problem. Understanding how energy homeostasis is regulated, and can become dysregulated, is crucial for developing new treatments for obesity. Detailed recording of individual behaviour and new imaging modalities offer the prospect of medically relevant models of energy homeostasis that are both understandable and individually predictive. The profusion of data from these sources has led to an interest in applying machine learning techniques to gain insight from these large, relatively unstructured datasets. We review both physiological models and machine learning results across a diverse range of applications in energy homeostasis, and highlight how modelling and machine learning can work together to improve predictive ability. We collect quantitative details in a comprehensive mathematical supplement. We also discuss the prospects of forecasting homeostatic behaviour and stress the importance of characterizing stochasticity within and between individuals in order to provide practical, tailored forecasts and guidance to combat the spread of obesity. PMID:29367240

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…

The Equivalence of Precession Phenomena in Metric Theories of Gravity

NASA Technical Reports Server (NTRS)

Krisher, Timothy P.

1997-01-01

The requirement of general covariance imparts to metric theories of gravity, such as general relavity, important structural features. A precise mathematical form results, ensuring that computation of observable physical effects in the theory gives the same answers independently of the chosen system of coordinates.

Evaluation, Instruction and Policy Making. IIEP Seminar Paper: 9.

ERIC Educational Resources Information Center

Bloom, Benjamin S.

Recently, educational evaluation has attempted to use the precision, objectivity, and mathematical rigor of the psychological measurement field as well as to find ways in which instrumentation and data utilization could more directly be related to educational institutions, educational processes, and educational purposes. The linkages between…

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

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

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

PubMed

Ganusov, Vitaly V

2016-01-01

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

Pre-service mathematics teachers' attitudes towards learning English: A case study in Yogyakarta

NASA Astrophysics Data System (ADS)

Setyaningrum, Wahyu

2017-08-01

This study investigated attitudes of pre-service mathematics teachers towards English as one of the subject at the university. It is a qualitative study in which questionnaire and face-to-face interview were employed to collect the data. The participants of this study were sixty students of mathematics education department at one of the university in Yogyakarta. The main research question was concern with how pre-service mathematics teachers perceive the importance of learning English. This study found that most of the participants perceive English as an important language that should be acquired by mathematics teachers. Their beliefs about the importance of English were mostly due to instrumental orientation rather than integrative orientation, such as getting a good job, getting a scholarship and understanding learning sources that are written in English. The data also revealed some obstacles faced by pre-service mathematics teachers in learning English as an additional language for them. The main obstacles were related to the differences between English for mathematics and English in daily life including its vocabulary and structure. Most of the participants argued that several mathematics vocabularies had precise meaning and different from daily English. In addition, they found difficult to understand some sentences used in the paper journal due to its structure. This study therefore, provided an insight into the pre-service mathematics teachers' perception and obstacles when learning English that could be use in improving pre-service teachers' education.

Soil physics: a Moroccan perspective

NASA Astrophysics Data System (ADS)

Lahlou, Sabah; Mrabet, Rachid; Ouadia, Mohamed

2004-06-01

Research on environmental pollution and degradation of soil and water resources is now of highest priority worldwide. To address these problems, soil physics should be conceived as a central core to this research. This paper objectives are to: (1) address the role and importance of soil physics, (2) demonstrate progress in this discipline, and (3) present various uses of soil physics in research, environment and industry. The study of dynamic processes at and within the soil vadose zone (flow, dispersion, transport, sedimentation, etc.), and ephemeral phenomena (deformation, compaction, etc.), form an area of particular interest in soil physics. Soil physics has changed considerably over time. These changes are due to needed precision in data collection for accurate interpretation of space and time variation of soil properties. Soil physics interacts with other disciplines and sciences such as hydro(geo)logy, agronomy, environment, micro-meteorology, pedology, mathematics, physics, water sciences, etc. These interactions prompted the emergence of advanced theories and comprehensive mechanisms of most natural processes, development of new mathematical tools (modeling and computer simulation, fractals, geostatistics, transformations), creation of high precision instrumentation (computer assisted, less time constraint, increased number of measured parameters) and the scale sharpening of physical measurements which ranges from micro to watershed. The environment industry has contributed to an enlargement of many facets of soil physics. In other words, research demand in soil physics has increased considerably to satisfy specific and environmental problems (contamination of water resources, global warming, etc.). Soil physics research is still at an embryonic stage in Morocco. Consequently, soil physicists can take advantage of developments occurring overseas, and need to build up a database of soil static and dynamic properties and to revise developed models to meet our conditions. Large, but special, investment is required to promote research programs in soil physics, which consider developments in this discipline and respect Moroccan needs. These programs will be highlighted herein.

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…

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

NASA Astrophysics Data System (ADS)

Fiorini, Rodolfo A.; Dacquino, Gianfranco F.

2004-12-01

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

An algebra-based method for inferring gene regulatory networks.

PubMed

Vera-Licona, Paola; Jarrah, Abdul; Garcia-Puente, Luis David; McGee, John; Laubenbacher, Reinhard

2014-03-26

The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used. This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network. Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.

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…

Influence of Waveform Characteristics on LiDAR Ranging Accuracy and Precision

PubMed Central

Yang, Bingwei; Xie, Xinhao; Li, Duan

2018-01-01

Time of flight (TOF) based light detection and ranging (LiDAR) is a technology for calculating distance between start/stop signals of time of flight. In lab-built LiDAR, two ranging systems for measuring flying time between start/stop signals include time-to-digital converter (TDC) that counts time between trigger signals and analog-to-digital converter (ADC) that processes the sampled start/stop pulses waveform for time estimation. We study the influence of waveform characteristics on range accuracy and precision of two kinds of ranging system. Comparing waveform based ranging (WR) with analog discrete return system based ranging (AR), a peak detection method (WR-PK) shows the best ranging performance because of less execution time, high ranging accuracy, and stable precision. Based on a novel statistic mathematical method maximal information coefficient (MIC), WR-PK precision has a high linear relationship with the received pulse width standard deviation. Thus keeping the received pulse width of measuring a constant distance as stable as possible can improve ranging precision. PMID:29642639

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…

Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.

PubMed

Ozaktas, Haldun M; Yüksel, Serdar; Kutay, M Alper

2002-08-01

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.

Fabrication of micro-lens array on convex surface by meaning of micro-milling

NASA Astrophysics Data System (ADS)

Zhang, Peng; Du, Yunlong; Wang, Bo; Shan, Debin

2014-08-01

In order to develop the application of the micro-milling technology, and to fabricate ultra-precision optical surface with complex microstructure, in this paper, the primary experimental research on micro-milling complex microstructure array is carried out. A complex microstructure array surface with vary parameters is designed, and the mathematic model of the surface is set up and simulated. For the fabrication of the designed microstructure array surface, a micro three-axis ultra-precision milling machine tool is developed, aerostatic guideway drove directly by linear motor is adopted in order to guarantee the enough stiffness of the machine, and novel numerical control strategy with linear encoders of 5nm resolution used as the feedback of the control system is employed to ensure the extremely high motion control accuracy. With the help of CAD/CAM technology, convex micro lens array on convex spherical surface with different scales on material of polyvinyl chloride (PVC) and pure copper is fabricated using micro tungsten carbide ball end milling tool based on the ultra-precision micro-milling machine. Excellent nanometer-level micro-movement performance of the axis is proved by motion control experiment. The fabrication is nearly as the same as the design, the characteristic scale of the microstructure is less than 200μm and the accuracy is better than 1μm. It prove that ultra-precision micro-milling technology based on micro ultra-precision machine tool is a suitable and optional method for micro manufacture of microstructure array surface on different kinds of materials, and with the development of micro milling cutter, ultraprecision micro-milling complex microstructure surface will be achieved in future.

Exact event-driven implementation for recurrent networks of stochastic perfect integrate-and-fire neurons.

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Precision of spiral-bevel gears

NASA Technical Reports Server (NTRS)

Litvin, F. L.; Goldrich, R. N.; Coy, J. J.; Zaretsky, E. V.

1983-01-01

The kinematic errors in spiral bevel gear trains caused by the generation of nonconjugate surfaces, by axial displacements of the gears during assembly, and by eccentricity of the assembled gears were determined. One mathematical model corresponds to the motion of the contact ellipse across the tooth surface, (geometry I) and the other along the tooth surface (geometry II). The following results were obtained: (1) kinematic errors induced by errors of manufacture may be minimized by applying special machine settings, the original error may be reduced by order of magnitude, the procedure is most effective for geometry 2 gears, (2) when trying to adjust the bearing contact pattern between the gear teeth for geometry I gears, it is more desirable to shim the gear axially; for geometry II gears, shim the pinion axially; (3) the kinematic accuracy of spiral bevel drives are most sensitive to eccentricities of the gear and less sensitive to eccentricities of the pinion. The precision of mounting accuracy and manufacture are most crucial for the gear, and less so for the pinion. Previously announced in STAR as N82-30552

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.

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…

Mathematics Placement at the University of Illinois

ERIC Educational Resources Information Center

Ahlgren Reddy, Alison; Harper, Marc

2013-01-01

Data from the ALEKS-based placement program at the University of Illinois is presented visually in several ways. The placement exam (an ALEKS assessment) contains precise item-specific information and the data show many interesting properties of the student populations of the placement courses, which include Precalculus, Calculus, and Business…

Astonishment: A Post-Constructivist Investigation into Mathematics as Passion

ERIC Educational Resources Information Center

Roth, Wolff-Michael

2017-01-01

Constructivist learning theories have become the dominant ideology in educational circles, in part, because there is a primacy on the agential individual with its definite identity. However, precisely because "to construct" is a "transitive" verb, it occludes the fact that in learning and development, we come to know something…

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).

Scalable nanohelices for predictive studies and enhanced 3D visualization.

PubMed

Meagher, Kwyn A; Doblack, Benjamin N; Ramirez, Mercedes; Davila, Lilian P

2014-11-12

Spring-like materials are ubiquitous in nature and of interest in nanotechnology for energy harvesting, hydrogen storage, and biological sensing applications. For predictive simulations, it has become increasingly important to be able to model the structure of nanohelices accurately. To study the effect of local structure on the properties of these complex geometries one must develop realistic models. To date, software packages are rather limited in creating atomistic helical models. This work focuses on producing atomistic models of silica glass (SiO₂) nanoribbons and nanosprings for molecular dynamics (MD) simulations. Using an MD model of "bulk" silica glass, two computational procedures to precisely create the shape of nanoribbons and nanosprings are presented. The first method employs the AWK programming language and open-source software to effectively carve various shapes of silica nanoribbons from the initial bulk model, using desired dimensions and parametric equations to define a helix. With this method, accurate atomistic silica nanoribbons can be generated for a range of pitch values and dimensions. The second method involves a more robust code which allows flexibility in modeling nanohelical structures. This approach utilizes a C++ code particularly written to implement pre-screening methods as well as the mathematical equations for a helix, resulting in greater precision and efficiency when creating nanospring models. Using these codes, well-defined and scalable nanoribbons and nanosprings suited for atomistic simulations can be effectively created. An added value in both open-source codes is that they can be adapted to reproduce different helical structures, independent of material. In addition, a MATLAB graphical user interface (GUI) is used to enhance learning through visualization and interaction for a general user with the atomistic helical structures. One application of these methods is the recent study of nanohelices via MD simulations for mechanical energy harvesting purposes.

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.

Inferring Mathematical Equations Using Crowdsourcing.

PubMed

Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw

2015-01-01

Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.

Inferring Mathematical Equations Using Crowdsourcing

PubMed Central

Wasik, Szymon

2015-01-01

Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game—so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players. PMID:26713846

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

PubMed Central

2013-01-01

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

Flow discharge prediction in compound channels using linear genetic programming

NASA Astrophysics Data System (ADS)

Azamathulla, H. Md.; Zahiri, A.

2012-08-01

SummaryFlow discharge determination in rivers is one of the key elements in mathematical modelling in the design of river engineering projects. Because of the inundation of floodplains and sudden changes in river geometry, flow resistance equations are not applicable for compound channels. Therefore, many approaches have been developed for modification of flow discharge computations. Most of these methods have satisfactory results only in laboratory flumes. Due to the ability to model complex phenomena, the artificial intelligence methods have recently been employed for wide applications in various fields of water engineering. Linear genetic programming (LGP), a branch of artificial intelligence methods, is able to optimise the model structure and its components and to derive an explicit equation based on the variables of the phenomena. In this paper, a precise dimensionless equation has been derived for prediction of flood discharge using LGP. The proposed model was developed using published data compiled for stage-discharge data sets for 394 laboratories, and field of 30 compound channels. The results indicate that the LGP model has a better performance than the existing models.

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

On the necessity of U-shaped learning.

PubMed

Carlucci, Lorenzo; Case, John

2013-01-01

A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism versus nativism) are often judged on their ability of modeling or accounting for U-shaped behavior. The prior literature is mostly occupied with explaining how U-shaped behavior occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behavior? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research. Copyright © 2013 Cognitive Science Society, Inc.

Mathematical modeling of fed-batch fermentation of Schizochytrium sp. FJU-512 growth and DHA production using a shift control strategy.

PubMed

Zhang, Mingliang; Wu, Weibin; Guo, Xiaolei; Weichen, You; Qi, Feng; Jiang, Xianzhang; Huang, Jianzhong

2018-03-01

To obtain high-cell-density cultures of Schizochytrium sp. FJU-512 for DHA production, two stages of fermentation strategy were used and carbon/nitrogen ratio, DO and temperature were controlled at different levels. The final dry cell weight, total lipid production and DHA yield in 15 l bioreactor reached 103.9, 37.2 and 16.0 g/l, respectively. For the further study of microbial growth and DHA production dynamics, we established a set of kinetic models for the fed-batch production of DHA by Schizochytrium sp. FJU-512 in 15 and 100 l fermenters and a compensatory parameter n was integrated into the model in order to find the optimal mathematical equations. A modified Logistic model was proposed to fit the cell growth data and the following kinetic parameters were obtained: µ m  = 0.0525/h, X m  = 100 g/l and n  = 4.1717 for the 15 l bioreactor, as well as µ m  = 0.0382/h, X m  = 107.4371 g/l and n  = 10 for the 100 l bioreactor. The Luedeking-Piret equations were utilized to model DHA production, yielding values of α  = 0.0648 g/g and β  = 0.0014 g/g/h for the 15 l bioreactor, while the values of α and β obtained for the 100 l fermentation were 0.0209 g/g and 0.0030 g/g/h. The predicted results compared with experimental data showed that the established models had a good fitting precision and were able to exactly depict the dynamic features of the DHA production process.

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.

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.

Formulation of topical bioadhesive gel of aceclofenac using 3-level factorial design.

PubMed

Singh, Sanjay; Parhi, Rabinarayan; Garg, Anuj

2011-01-01

The objective of this work was to develop bioadhesive topical gel of Aceclofenac with the help of response-surface approach. Experiments were performed according to a 3-level factorial design to evaluate the effects of two independent variables [amount of Poloxamer 407 (PL-407 = X1) and hydroxypropylmethyl cellulose K100 M (HPMC = X2)] on the bioadhesive character of gel, rheological property of gel (consistency index), and in-vitro drug release. The best model was selected to fit the data. Mathematical equation was generated by Design Expert® software for the model which assists in determining the effect of independent variables. Response surface plots were also generated by the software for analyzing effect of the independent variables on the response. Quadratic model was found to be the best for all the responses. Both independent variable (X1 and X2) were found to have synergistic effect on bioadhesion (Y1) but the effect of HPMC was more pronounced than PL-407. Consistency index was enhanced by increasing the level of both independent variables. An antagonistic effect of both independent variables was found on cumulative percentage release of drug in 2 (Y3) and 8 h (Y4). Both independent variables approximately equally contributed the antagonistic effect on Y3 whereas antagonistic effect of HPMC was more pronounced than PL-407. The effect of formulation variables on the product characteristics can be easily predicted and precisely interpreted by using a 3-level factorial experimental design and generated quadratic mathematical equations.

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,…

An Improved Azimuth Angle Estimation Method with a Single Acoustic Vector Sensor Based on an Active Sonar Detection System.

PubMed

Zhao, Anbang; Ma, Lin; Ma, Xuefei; Hui, Juan

2017-02-20

In this paper, an improved azimuth angle estimation method with a single acoustic vector sensor (AVS) is proposed based on matched filtering theory. The proposed method is mainly applied in an active sonar detection system. According to the conventional passive method based on complex acoustic intensity measurement, the mathematical and physical model of this proposed method is described in detail. The computer simulation and lake experiments results indicate that this method can realize the azimuth angle estimation with high precision by using only a single AVS. Compared with the conventional method, the proposed method achieves better estimation performance. Moreover, the proposed method does not require complex operations in frequencydomain and achieves computational complexity reduction.

Birefringence dispersion compensation demodulation algorithm for polarized low-coherence interferometry.

PubMed

Wang, Shuang; Liu, Tiegen; Jiang, Junfeng; Liu, Kun; Yin, Jinde; Wu, Fan

2013-08-15

A demodulation algorithm based on the birefringence dispersion characteristics for a polarized low-coherence interferometer is proposed. With the birefringence dispersion parameter taken into account, the mathematical model of the polarized low-coherence interference fringes is established and used to extract phase shift information between the measured coherence envelope center and the zero-order fringe, which eliminates the interferometric 2 π ambiguity of locating the zero-order fringe. A pressure measurement experiment using an optical fiber Fabry-Perot pressure sensor was carried out to verify the effectiveness of the proposed algorithm. The experiment result showed that the demodulation precision was 0.077 kPa in the range of 210 kPa, which was improved by 23 times compared to the traditional envelope detection method.

CFRP composite mirrors for space telescopes and their micro-dimensional stability

NASA Astrophysics Data System (ADS)

Utsunomiya, Shin; Kamiya, Tomohiro; Shimizu, Ryuzo

2010-07-01

Ultra-lightweight and high-accuracy CFRP (carbon fiber reinforced plastics) mirrors for space telescopes were fabricated to demonstrate their feasibility for light wavelength applications. The CTE (coefficient of thermal expansion) of the all- CFRP sandwich panels was tailored to be smaller than 1×10-7/K. The surface accuracy of mirrors of 150 mm in diameter was 1.8 um RMS as fabricated and the surface smoothness was improved to 20 nm RMS by using a replica technique. Moisture expansion was considered the largest in un-predictable surface preciseness errors. The moisture expansion affected not only homologous shape change but also out-of-plane distortion especially in unsymmetrical compositions. Dimensional stability due to the moisture expansion was compared with a structural mathematical model.

Theory research of seam recognition and welding torch pose control based on machine vision

NASA Astrophysics Data System (ADS)

Long, Qiang; Zhai, Peng; Liu, Miao; He, Kai; Wang, Chunyang

2017-03-01

At present, the automation requirement of the welding become higher, so a method of the welding information extraction by vision sensor is proposed in this paper, and the simulation with the MATLAB has been conducted. Besides, in order to improve the quality of robot automatic welding, an information retrieval method for welding torch pose control by visual sensor is attempted. Considering the demands of welding technology and engineering habits, the relative coordinate systems and variables are strictly defined, and established the mathematical model of the welding pose, and verified its feasibility by using the MATLAB simulation in the paper, these works lay a foundation for the development of welding off-line programming system with high precision and quality.

Systematic modelling and design evaluation of unperturbed tumour dynamics in xenografts.

PubMed

Parra Guillen, Zinnia P Patricia; Mangas Sanjuan, Victor; Garcia-Cremades, Maria; Troconiz, Inaki F; Mo, Gary; Pitou, Celine; Iversen, Philip W; Wallin, Johan E

2018-04-24

Xenograft mice are largely used to evaluate the efficacy of oncological drugs during preclinical phases of drug discovery and development. Mathematical models provide a useful tool to quantitatively characterise tumour growth dynamics and also optimise upcoming experiments. To the best of our knowledge, this is the first report where unperturbed growth of a large set of tumour cell lines (n=28) has been systematically analysed using the model proposed by Simeoni in the context of non-linear mixed effect (NLME). Exponential growth was identified as the governing mechanism in the majority of the cell lines, with constant rate values ranging from 0.0204 to 0.203 day -1 No common patterns could be observed across tumour types, highlighting the importance of combining information from different cell lines when evaluating drug activity. Overall, typical model parameters were precisely estimated using designs where tumour size measurements were taken every two days. Moreover, reducing the number of measurement to twice per week, or even once per week for cell lines with low growth rates, showed little impact on parameter precision. However, in order to accurately characterise parameter variability (i.e. relative standard errors below 50%), a sample size of at least 50 mice is needed. This work illustrates the feasibility to systematically apply NLME models to characterise tumour growth in drug discovery and development, and constitutes a valuable source of data to optimise experimental designs by providing an a priori sampling window and minimising the number of samples required. The American Society for Pharmacology and Experimental Therapeutics.

A hybrid fuzzy logic and extreme learning machine for improving efficiency of circulating water systems in power generation plant

NASA Astrophysics Data System (ADS)

Aziz, Nur Liyana Afiqah Abdul; Siah Yap, Keem; Afif Bunyamin, Muhammad

2013-06-01

This paper presents a new approach of the fault detection for improving efficiency of circulating water system (CWS) in a power generation plant using a hybrid Fuzzy Logic System (FLS) and Extreme Learning Machine (ELM) neural network. The FLS is a mathematical tool for calculating the uncertainties where precision and significance are applied in the real world. It is based on natural language which has the ability of "computing the word". The ELM is an extremely fast learning algorithm for neural network that can completed the training cycle in a very short time. By combining the FLS and ELM, new hybrid model, i.e., FLS-ELM is developed. The applicability of this proposed hybrid model is validated in fault detection in CWS which may help to improve overall efficiency of power generation plant, hence, consuming less natural recourses and producing less pollutions.

Cell-Free Optogenetic Gene Expression System.

PubMed

Jayaraman, Premkumar; Yeoh, Jing Wui; Jayaraman, Sudhaghar; Teh, Ai Ying; Zhang, Jingyun; Poh, Chueh Loo

2018-04-20

Optogenetic tools provide a new and efficient way to dynamically program gene expression with unmatched spatiotemporal precision. To date, their vast potential remains untapped in the field of cell-free synthetic biology, largely due to the lack of simple and efficient light-switchable systems. Here, to bridge the gap between cell-free systems and optogenetics, we studied our previously engineered one component-based blue light-inducible Escherichia coli promoter in a cell-free environment through experimental characterization and mathematical modeling. We achieved >10-fold dynamic expression and demonstrated rapid and reversible activation of the target gene to generate oscillatory response. The deterministic model developed was able to recapitulate the system behavior and helped to provide quantitative insights to optimize dynamic response. This in vitro optogenetic approach could be a powerful new high-throughput screening technology for rapid prototyping of complex biological networks in both space and time without the need for chemical induction.

Joint U.S./Japan Conference on Adaptive Structures, 1st, Maui, HI, Nov. 13-15, 1990, Proceedings

NASA Technical Reports Server (NTRS)

Wada, Ben K. (Editor); Fanson, James L. (Editor); Miura, Koryo (Editor)

1991-01-01

The present volume of adaptive structures discusses the development of control laws for an orbiting tethered antenna/reflector system test scale model, the sizing of active piezoelectric struts for vibration suppression on a space-based interferometer, the control design of a space station mobile transporter with multiple constraints, and optimum configuration control of an intelligent truss structure. Attention is given to the formulation of full state feedback for infinite order structural systems, robustness issues in the design of smart structures, passive piezoelectric vibration damping, shape control experiments with a functional model for large optical reflectors, and a mathematical basis for the design optimization of adaptive trusses in precision control. Topics addressed include approaches to the optimal adaptive geometries of intelligent truss structures, the design of an automated manufacturing system for tubular smart structures, the Sandia structural control experiments, and the zero-gravity dynamics of space structures in parabolic aircraft flight.

Joint U.S./Japan Conference on Adaptive Structures, 1st, Maui, HI, Nov. 13-15, 1990, Proceedings

NASA Astrophysics Data System (ADS)

Wada, Ben K.; Fanson, James L.; Miura, Koryo

1991-11-01

The present volume of adaptive structures discusses the development of control laws for an orbiting tethered antenna/reflector system test scale model, the sizing of active piezoelectric struts for vibration suppression on a space-based interferometer, the control design of a space station mobile transporter with multiple constraints, and optimum configuration control of an intelligent truss structure. Attention is given to the formulation of full state feedback for infinite order structural systems, robustness issues in the design of smart structures, passive piezoelectric vibration damping, shape control experiments with a functional model for large optical reflectors, and a mathematical basis for the design optimization of adaptive trusses in precision control. Topics addressed include approaches to the optimal adaptive geometries of intelligent truss structures, the design of an automated manufacturing system for tubular smart structures, the Sandia structural control experiments, and the zero-gravity dynamics of space structures in parabolic aircraft flight.

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.

Routine OGTT: a robust model including incretin effect for precise identification of insulin sensitivity and secretion in a single individual.

PubMed

De Gaetano, Andrea; Panunzi, Simona; Matone, Alice; Samson, Adeline; Vrbikova, Jana; Bendlova, Bela; Pacini, Giovanni

2013-01-01

In order to provide a method for precise identification of insulin sensitivity from clinical Oral Glucose Tolerance Test (OGTT) observations, a relatively simple mathematical model (Simple Interdependent glucose/insulin MOdel SIMO) for the OGTT, which coherently incorporates commonly accepted physiological assumptions (incretin effect and saturating glucose-driven insulin secretion) has been developed. OGTT data from 78 patients in five different glucose tolerance groups were analyzed: normal glucose tolerance (NGT), impaired glucose tolerance (IGT), impaired fasting glucose (IFG), IFG+IGT, and Type 2 Diabetes Mellitus (T2DM). A comparison with the 2011 Salinari (COntinuos GI tract MOdel, COMO) and the 2002 Dalla Man (Dalla Man MOdel, DMMO) models was made with particular attention to insulin sensitivity indices ISCOMO, ISDMMO and kxgi (the insulin sensitivity index for SIMO). ANOVA on kxgi values across groups resulted significant overall (P<0.001), and post-hoc comparisons highlighted the presence of three different groups: NGT (8.62×10(-5)±9.36×10(-5) min(-1)pM(-1)), IFG (5.30×10(-5)±5.18×10(-5)) and combined IGT, IFG+IGT and T2DM (2.09×10(-5)±1.95×10(-5), 2.38×10(-5)±2.28×10(-5) and 2.38×10(-5)±2.09×10(-5) respectively). No significance was obtained when comparing ISCOMO or ISDMMO across groups. Moreover, kxgi presented the lowest sample average coefficient of variation over the five groups (25.43%), with average CVs for ISCOMO and ISDMMO of 70.32% and 57.75% respectively; kxgi also presented the strongest correlations with all considered empirical measures of insulin sensitivity. While COMO and DMMO appear over-parameterized for fitting single-subject clinical OGTT data, SIMO provides a robust, precise, physiologically plausible estimate of insulin sensitivity, with which habitual empirical insulin sensitivity indices correlate well. The kxgi index, reflecting insulin secretion dependency on glycemia, also significantly differentiates clinically diverse subject groups. The SIMO model may therefore be of value for the quantification of glucose homeostasis from clinical OGTT data.

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.

Theory and applications survey of decentralized control methods

NASA Technical Reports Server (NTRS)

Athans, M.

1975-01-01

A nonmathematical overview is presented of trends in the general area of decentralized control strategies which are suitable for hierarchical systems. Advances in decentralized system theory are closely related to advances in the so-called stochastic control problem with nonclassical information pattern. The basic assumptions and mathematical tools pertaining to the classical stochastic control problem are outlined. Particular attention is devoted to pitfalls in the mathematical problem formulation for decentralized control. Major conclusions are that any purely deterministic approach to multilevel hierarchical dynamic systems is unlikely to lead to realistic theories or designs, that the flow of measurements and decisions in a decentralized system should not be instantaneous and error-free, and that delays in information exchange in a decentralized system lead to reasonable approaches to decentralized control. A mathematically precise notion of aggregating information is not yet available.

Study ethnomathematics of aboge (alif, rebo, wage) calendar as determinant of the great days of Islam and traditional ceremony in Cirebon Kasepuhan Palace

NASA Astrophysics Data System (ADS)

Syahrin, Muhammad Alfi; Turmudi, Puspita, Entit

2016-02-01

This research attempts to show about the relationship between mathematics and culture. Paradigm that emerged currently, that mathematics is an abstract concept and difficult, therefore mathematics is not favored by most students. In the reality, indirectly mathematics is present in a culture of a society. Ethnomathematics study is a study to examine how does a group of people in a particular culture understand, express, and use the concepts and practices of culture that depicted mathematically. This research was conducted in Cirebon precisely in Kasepuhan Palace, which was in RW 04, Kasepuhan village, Lemah Wungkuk district, Cirebon city, West Java. The focus of the study and research purposes was the application of aboge (alif rebo wage) calendar as the calculation of days and the calendar rules determine the time of days, great days of Islam and traditional ceremony in Kasepuhan Palace. Qualitative methods with the principles of ethnography such as studies in ethnomathematics i.e observation, interviews, documentation and fieldnotes were used in this research. The findings of this ethnomathematics study show that the determining great days of Islam and the days of palace traditional ceremony have a close relationship with the counts and principles in mathematics. This study provides recommendations that mathematics is closely related to culture due to ethnomathematics.

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

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

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

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

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

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

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

Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

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

2016-01-01

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

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

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

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

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

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

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

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

Implementing multiresolution models and families of models: from entity-level simulation to desktop stochastic models and "repro" models

NASA Astrophysics Data System (ADS)

McEver, Jimmie; Davis, Paul K.; Bigelow, James H.

2000-06-01

We have developed and used families of multiresolution and multiple-perspective models (MRM and MRMPM), both in our substantive analytic work for the Department of Defense and to learn more about how such models can be designed and implemented. This paper is a brief case history of our experience with a particular family of models addressing the use of precision fires in interdicting and halting an invading army. Our models were implemented as closed-form analytic solutions, in spreadsheets, and in the more sophisticated AnalyticaTM environment. We also drew on an entity-level simulation for data. The paper reviews the importance of certain key attributes of development environments (visual modeling, interactive languages, friendly use of array mathematics, facilities for experimental design and configuration control, statistical analysis tools, graphical visualization tools, interactive post-processing, and relational database tools). These can go a long way towards facilitating MRMPM work, but many of these attributes are not yet widely available (or available at all) in commercial model-development tools--especially for use with personal computers. We conclude with some lessons learned from our experience.

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

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

2013-01-01

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

Comparison of learning models based on mathematics logical intelligence in affective domain

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

Measurement precision of the anaerobic threshold by means of a portable calorimeter.

PubMed

Nogueira, Fernando dos Santos; Pompeu, Fernando Augusto Monteiro Sabóia

2010-09-01

Many methods are used for determining the Anaerobic Threshold (AT) by means of sophisticated ergospirometer. To test the AT variation, detected by mathematical models and visual inspection, when low cost ergospirometer is used and intended for clinical application. Seventy nine apparently healthy subjects were volunteers in this study; from these, 57 men. The VO₂(max) and the ventilatory threshold were determined by indirect, open-circuit calorimetry. The electro-enzymatic method was used for analyzing the lactacidemia and direct determination of the Lactate Threshold (LT). The AT was determined by two mathematical methods (MM(RSS) and MM(slope)), based on the gases exchange, and by the log-log visual method, for determining the LT. Two independent investigators determined the AT through visual inspection of three graphs, considering two methods (AT₋(a)= V-slope, EqV; and AT₋(b) = V-slope, EqV and ExCO₂). The data were analyzed by means of parametric statistics for determining the differences between AT₋(a) versus ExCO₂, MM(RSS) and MM(slope); AT-b versus MM(RSS) and MM(slope); and LT versus AT₋(a), AT₋(b), MM(RSS) and MM(slope). The MM(slope) was the only method that presented a significant difference between the AT₋(a) and AT₋(b) (p=0.001), with CV% >15. LT versus MM(slope) did not present significant difference (p=0.274), however, it was observed a high CV (24%). It was concluded that with the low cost equipment, the MM(RSS) and AT₋(a) methods can be used for determining the TAn. The MM(slope) method did not present satisfactory precision to be employed with this equipment.

Pixelized Measurement of (99m)Tc-HDP Micro Particles Formed in Gamma Correction Phantom Pinhole Scan: a Reference Study.

PubMed

Jung, Joo-Young; Cheon, Gi Jeong; Lee, Yun-Sang; Ha, Seunggyun; Chae, Mi-Hye; Chung, Yong-An; Yoon, Do Kyun; Bahk, Yong-Whee

2016-09-01

Currently, traumatic bone diseases are diagnosed by assessing the micro (99m)Tc-hydroxymethylene diphosphonate (HDP) uptake in injured trabeculae with ongoing osteoneogenesis demonstrated by gamma correction pinhole scan (GCPS). However, the mathematic size quantification of micro-uptake is not yet available. We designed and performed this phantom-based study to set up an in-vitro model of the mathematical calculation of micro-uptake by the pixelized measurement. The micro (99m)Tc-HDP deposits used in this study were spontaneously formed both in a large standard flood and small house-made dish phantoms. The processing was as follows: first, phantoms were flooded with distilled water and (99m)Tc-HDP was therein injected to induce micro (99m)Tc-HDP deposition; second, the deposits were scanned using parallel-hole and pinhole collimator to generally survey (99m)Tc-HDP deposition pattern; and third, the scans underwent gamma correction (GC) to discern individual deposits for size measurement. In original naïve scans, tracer distribution was simply nebulous in appearance and, hence, could not be measured. Impressively, however, GCPS could discern individual micro deposits so that they were calculated by pixelized measurement. Phantoms naturally formed micro (99m)Tc-HDP deposits that are analogous to (99m)Tc-HDP uptake on in-vivo bone scan. The smallest one we measured was 0.414 mm. Flooded phantoms and therein injected (99m)Tc-HDP form nebulous micro (99m)Tc-HDP deposits that are rendered discernible by GCPB and precisely calculable using pixelized measurement. This method can be used for precise quantitative and qualitative diagnosis of bone and joint diseases at the trabecular level.

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

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

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

Mathematical modelling in developmental biology.

PubMed

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

2013-06-01

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

Mathematical models for plant-herbivore interactions

USGS Publications Warehouse

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

A model-updating procedure to stimulate piezoelectric transducers accurately.

PubMed

Piranda, B; Ballandras, S; Steichen, W; Hecart, B

2001-09-01

The use of numerical calculations based on finite element methods (FEM) has yielded significant improvements in the simulation and design of piezoelectric transducers piezoelectric transducer utilized in acoustic imaging. However, the ultimate precision of such models is directly controlled by the accuracy of material characterization. The present work is dedicated to the development of a model-updating technique adapted to the problem of piezoelectric transducer. The updating process is applied using the experimental admittance of a given structure for which a finite element analysis is performed. The mathematical developments are reported and then applied to update the entries of a FEM of a two-layer structure (a PbZrTi-PZT-ridge glued on a backing) for which measurements were available. The efficiency of the proposed approach is demonstrated, yielding the definition of a new set of constants well adapted to predict the structure response accurately. Improvement of the proposed approach, consisting of the updating of material coefficients not only on the admittance but also on the impedance data, is finally discussed.

Systems biology derived source-sink mechanism of BMP gradient formation

PubMed Central

Zinski, Joseph; Bu, Ye; Wang, Xu; Dou, Wei

2017-01-01

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development. PMID:28826472

Systems biology derived source-sink mechanism of BMP gradient formation.

PubMed

Zinski, Joseph; Bu, Ye; Wang, Xu; Dou, Wei; Umulis, David; Mullins, Mary C

2017-08-09

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development.

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

NASA Astrophysics Data System (ADS)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Tightly Coupled Integration of Ionosphere-Constrained Precise Point Positioning and Inertial Navigation Systems

PubMed Central

Gao, Zhouzheng; Zhang, Hongping; Ge, Maorong; Niu, Xiaoji; Shen, Wenbin; Wickert, Jens; Schuh, Harald

2015-01-01

The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS. PMID:25763647

A theoretical approach to evaluate the release rate of acetaminophen from erosive wax matrix dosage forms.

PubMed

Agata, Yasuyoshi; Iwao, Yasunori; Shiino, Kai; Miyagishima, Atsuo; Itai, Shigeru

2011-07-29

To predict drug dissolution and understand the mechanisms of drug release from wax matrix dosage forms containing glyceryl monostearate (GM; a wax base), aminoalkyl methacrylate copolymer E (AMCE; a pH-dependent functional polymer), and acetaminophen (APAP; a model drug), we tried to derive a novel mathematical model with respect to erosion and diffusion theory. Our model exhibited good agreement with the whole set of experimentally obtained values pertaining to APAP release at pH 4.0 and pH 6.5. In addition, this model revealed that the eroding speed of wax matrices was strongly influenced by the loading content of AMCE, but not that of APAP, and that the diffusion coefficient increased as APAP loading decreased and AMCE loading increased, thus directly defining the physicochemical properties of erosion and diffusion. Therefore, this model might prove a useful equation for the precise prediction of dissolution and for understanding the mechanisms of drug release from wax matrix dosage forms. Copyright © 2011 Elsevier B.V. All rights reserved.

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

PubMed

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

2018-04-01

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

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

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

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

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

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

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

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

PubMed

Gilbert, Scott F

2018-01-31

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

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

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

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

Mathematical modeling and full-scale shaking table tests for multi-curve buckling restrained braces

NASA Astrophysics Data System (ADS)

Tsai, C. S.; Lin, Yungchang; Chen, Wenshin; Su, H. C.

2009-09-01

Buckling restrained braces (BRBs) have been widely applied in seismic mitigation since they were introduced in the 1970s. However, traditional BRBs have several disadvantages caused by using a steel tube to envelope the mortar to prevent the core plate from buckling, such as: complex interfaces between the materials used, uncertain precision, and time consumption during the manufacturing processes. In this study, a new device called the multi-curve buckling restrained brace (MC-BRB) is proposed to overcome these disadvantages. The new device consists of a core plate with multiple neck portions assembled to form multiple energy dissipation segments, and the enlarged segment, lateral support elements and constraining elements to prevent the BRB from buckling. The enlarged segment located in the middle of the core plate can be welded to the lateral support and constraining elements to increase buckling resistance and to prevent them from sliding during earthquakes. Component tests and a series of shaking table tests on a full-scale steel structure equipped with MC-BRBs were carried out to investigate the behavior and capability of this new BRB design for seismic mitigation. The experimental results illustrate that the MC-BRB possesses a stable mechanical behavior under cyclic loadings and provides good protection to structures during earthquakes. Also, a mathematical model has been developed to simulate the mechanical characteristics of BRBs.

X-ray microbeam stand-alone facility for cultured cells irradiation

NASA Astrophysics Data System (ADS)

Bożek, Sebastian; Bielecki, Jakub; Wiecheć, Anna; Lekki, Janusz; Stachura, Zbigniew; Pogoda, Katarzyna; Lipiec, Ewelina; Tkocz, Konrad; Kwiatek, Wojciech M.

2017-03-01

The article describes an X-ray microbeam standalone facility dedicated for irradiation of living cultured cells. The article can serve as an advice for such facilities construction, as it begins from engineering details, through mathematical modeling and experimental procedures, ending up with preliminary experimental results and conclusions. The presented system consists of an open type X-ray tube with microfocusing down to about 2 μm, an X-ray focusing system with optical elements arranged in the nested Kirckpatrick-Baez (or Montel) geometry, a sample stand and an optical microscope with a scientific digital CCD camera. For the beam visualisation an X-ray sensitive CCD camera and a spectral detector are used, as well as a scintillator screen combined with the microscope. A method of precise one by one irradiation of previously chosen cells is presented, as well as a fast method of uniform irradiation of a chosen sample area. Mathematical models of beam and cell with calculations of kerma and dose are presented. The experiments on dose-effect relationship, kinetics of DNA double strand breaks repair, as well as micronuclei observation were performed on PC-3 (Prostate Cancer) cultured cells. The cells were seeded and irradiated on Mylar foil, which covered a hole drilled in the Petri dish. DNA lesions were visualised with γ-H2AX marker combined with Alexa Fluor 488 fluorescent dye.

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

PubMed

Hoskinson, Anne-Marie

2010-01-01

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

Thomas L. Griffiths: Award for Distinguished Scientific Early Career Contributions to Psychology

ERIC Educational Resources Information Center

American Psychologist, 2012

2012-01-01

Presents a short biography of one of the winners of the American Psychological Association's Award for Distinguished Scientific Early Career Contributions to Psychology (2012). Thomas L. Griffiths won the award for bringing mathematical precision to the deepest questions in human learning, reasoning, and concept formation. In his pioneering work,…

Early-Years Teachers' Concept Images and Concept Definitions: Triangles, Circles, and Cylinders

ERIC Educational Resources Information Center

Tsamir, Pessia; Tirosh, Dina; Levenson, Esther; Barkai, Ruthi; Tabach, Michal

2015-01-01

This study investigates practicing early-years teachers' concept images and concept definitions for triangles, circles, and cylinders. Teachers were requested to define each figure and then to identify various examples and non-examples of the figure. Teachers' use of correct and precise mathematical language and reference to critical and…

Metric Measurement. A Course to Reduce Math Anxiety and Sex-Role Stereotyping in Elementary Education.

ERIC Educational Resources Information Center

City Univ. of New York, Flushing, NY. Queens Coll.

This Teacher Education and Mathematics (TEAM) content module focuses on metric measurement. Topics addressed include decimal structure and prefixes, precision in measurement, reference measures, United States customary and metric systems, volume, area, and conversion. The module consists of: (1) an instructor's text; (2) an instructor's guide and…

Arithmetic Abilities in Children with Developmental Dyslexia: Performance on French ZAREKI-R Test

ERIC Educational Resources Information Center

De Clercq-Quaegebeur, Maryse; Casalis, Séverine; Vilette, Bruno; Lemaitre, Marie-Pierre; Vallée, Louis

2018-01-01

A high comorbidity between reading and arithmetic disabilities has already been reported. The present study aims at identifying more precisely patterns of arithmetic performance in children with developmental dyslexia, defined with severe and specific criteria. By means of a standardized test of achievement in mathematics ("Calculation and…

Crabtree, William (1610-44)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Instrument-maker and astronomer, born in Broughton, Lancashire, England, studied sunspots, made precise observations of the planets, including a transit of Venus. Crabtree collaborated with HORROCKS who predicted the transit. Horrocks described his friend Crabtree as `a man who has few superiors in mathematical learning' and described how awestruck Crabtree had been on perceiving the little disc ...

The Common Core State Standards for Mathematics and College Readiness

ERIC Educational Resources Information Center

Kamin, David C.

2016-01-01

The Common Core State Standards were created with college and career readiness in mind to help prepare students to succeed upon graduation from high school. In this article, I examine college readiness as it has been described by both university mathematicians and educational researchers to precisely discern what will foster success in collegiate…

Simulation of Left Atrial Function Using a Multi-Scale Model of the Cardiovascular System

PubMed Central

Pironet, Antoine; Dauby, Pierre C.; Paeme, Sabine; Kosta, Sarah; Chase, J. Geoffrey; Desaive, Thomas

2013-01-01

During a full cardiac cycle, the left atrium successively behaves as a reservoir, a conduit and a pump. This complex behavior makes it unrealistic to apply the time-varying elastance theory to characterize the left atrium, first, because this theory has known limitations, and second, because it is still uncertain whether the load independence hypothesis holds. In this study, we aim to bypass this uncertainty by relying on another kind of mathematical model of the cardiac chambers. In the present work, we describe both the left atrium and the left ventricle with a multi-scale model. The multi-scale property of this model comes from the fact that pressure inside a cardiac chamber is derived from a model of the sarcomere behavior. Macroscopic model parameters are identified from reference dog hemodynamic data. The multi-scale model of the cardiovascular system including the left atrium is then simulated to show that the physiological roles of the left atrium are correctly reproduced. This include a biphasic pressure wave and an eight-shaped pressure-volume loop. We also test the validity of our model in non basal conditions by reproducing a preload reduction experiment by inferior vena cava occlusion with the model. We compute the variation of eight indices before and after this experiment and obtain the same variation as experimentally observed for seven out of the eight indices. In summary, the multi-scale mathematical model presented in this work is able to correctly account for the three roles of the left atrium and also exhibits a realistic left atrial pressure-volume loop. Furthermore, the model has been previously presented and validated for the left ventricle. This makes it a proper alternative to the time-varying elastance theory if the focus is set on precisely representing the left atrial and left ventricular behaviors. PMID:23755183

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

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

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

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

Mathematical models of behavior of individual animals.

PubMed

Tsibulsky, Vladimir L; Norman, Andrew B

2007-01-01

This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

High-Precision Simulation of the Gravity Field of Rapidly-Rotating Barotropes in Hydrostatic Equilibrium

NASA Astrophysics Data System (ADS)

Hubbard, W. B.

2013-12-01

The so-called theory of figures (TOF) uses potential theory to solve for the structure of highly distorted rotating liquid planets in hydrostatic equilibrium. TOF is noteworthy both for its antiquity (Maclaurin 1742) and its mathematical complexity. Planned high-precision gravity measurements near the surfaces of Jupiter and Saturn (possibly detecting signals ~ microgal) will place unprecedented requirements on TOF, not because one expects hydrostatic equilibrium to that level, but because nonhydrostatic components in the surface gravity, at expected levels ~ 1 milligal, must be referenced to precise hydrostatic-equilibrium models. The Maclaurin spheroid is both a useful test of numerical TOF codes (Hubbard 2012, ApJ Lett 756:L15), and an approach to an efficient TOF code for arbitrary barotropes of variable density (Hubbard 2013, ApJ 768:43). For the latter, one trades off vertical resolution by replacing a continuous barotropic pressure-density relation with a stairstep relation, corresponding to N concentric Maclaurin spheroids (CMS), each of constant density. The benefit of this trade-off is that two-dimensional integrals over the mass distributions at each interface are reduced to one-dimensional integrals, quickly and accurately evaluated by Gaussian quadrature. The shapes of the spheroids comprise N level surfaces within the planet and at its surface, are gravitationally coupled to each other, and are found by self-consistent iteration, relaxing to a final configuration to within the computer's precision limits. The angular and radial variation of external gravity (using the usual geophysical expansion in multipole moments) can be found to the limit of typical floating point precision (~ 1.e-14), much better than the expected noise/signal for either the Juno or Cassini gravity experiments. The stairstep barotrope can be adjusted to fit a prescribed continuous or discontinuous interior barotrope, and can be made to approximate it to any required precision by increasing N. One can insert a higher density of CMSs toward the surface of an interior model in order to more accurately model high-order gravitational moments. The magnitude of high-order moments predicted by TOF declines geometrically with order number, and falls below the magnitude of expected non-hydrostatic terms produced by interior dynamics at ~ order 10 and above. Juno's sensitivity is enough to detect tidal gravity signals from Galilean satellites. The CMS method can be generalized to predict tidal zonal and tesseral terms consistent with an interior model fitted to measured zonal harmonics. For this purpose, two-dimensional Gaussian quadrature is necessary at each CMS interface. However, once the model is relaxed to equilibrium, one need not refit the model to the average zonal harmonics because of the smallness of the tidal terms. I will describe how the CMS method has been validated through comparisons with standard TOF models for which fully or partially analytic solutions exist, as well as through consistency checks. At this stage in software development in preparation for Jupiter orbit, we are focused on increasing the speed of the code in order to more efficiently search the parameter space of acceptable Jupiter interior models, as well as to interface it with advanced hydrogen-helium equations of state.

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.

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

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

USGS Publications Warehouse

Kuniansky, Eve L.

2014-01-01

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

Modelling the balance between quiescence and cell death in normal and tumour cell populations.

PubMed

Spinelli, Lorenzo; Torricelli, Alessandro; Ubezio, Paolo; Basse, Britta

2006-08-01

When considering either human adult tissues (in vivo) or cell cultures (in vitro), cell number is regulated by the relationship between quiescent cells, proliferating cells, cell death and other controls of cell cycle duration. By formulating a mathematical description we see that even small alterations of this relationship may cause a non-growing population to start growing with doubling times characteristic of human tumours. Our model consists of two age structured partial differential equations for the proliferating and quiescent cell compartments. Model parameters are death rates from and transition rates between these compartments. The partial differential equations can be solved for the steady-age distributions, giving the distribution of the cells through the cell cycle, dependent on specific model parameter values. Appropriate formulas can then be derived for various population characteristic quantities such as labelling index, proliferation fraction, doubling time and potential doubling time of the cell population. Such characteristic quantities can be estimated experimentally, although with decreasing precision from in vitro, to in vivo experimental systems and to the clinic. The model can be used to investigate the effects of a single alteration of either quiescence or cell death control on the growth of the whole population and the non-trivial dependence of the doubling time and other observable quantities on particular underlying cell cycle scenarios of death and quiescence. The model indicates that tumour evolution in vivo is a sequence of steady-states, each characterised by particular death and quiescence rate functions. We suggest that a key passage of carcinogenesis is a loss of the communication between quiescence, death and cell cycle machineries, causing a defect in their precise, cell cycle dependent relationship.

Optimization of controlled processes in combined-cycle plant (new developments and researches)

NASA Astrophysics Data System (ADS)

Tverskoy, Yu S.; Muravev, I. K.

2017-11-01

All modern complex technical systems, including power units of TPP and nuclear power plants, work in the system-forming structure of multifunctional APCS. The development of the modern APCS mathematical support allows bringing the automation degree to the solution of complex optimization problems of equipment heat-mass-exchange processes in real time. The difficulty of efficient management of a binary power unit is related to the need to solve jointly at least three problems. The first problem is related to the physical issues of combined-cycle technologies. The second problem is determined by the criticality of the CCGT operation to changes in the regime and climatic factors. The third problem is related to a precise description of a vector of controlled coordinates of a complex technological object. To obtain a joint solution of this complex of interconnected problems, the methodology of generalized thermodynamic analysis, methods of the theory of automatic control and mathematical modeling are used. In the present report, results of new developments and studies are shown. These results allow improving the principles of process control and the automatic control systems structural synthesis of power units with combined-cycle plants that provide attainable technical and economic efficiency and operational reliability of equipment.

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

ERIC Educational Resources Information Center

Al Duwairi, Ahmed

2013-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

The use of mathematical models in teaching wastewater treatment engineering.

PubMed

Morgenroth, E; Arvin, E; Vanrolleghem, P

2002-01-01

Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available.

A manufacturing error measurement methodology for a rotary vector reducer cycloidal gear based on a gear measuring center

NASA Astrophysics Data System (ADS)

Li, Tianxing; Zhou, Junxiang; Deng, Xiaozhong; Li, Jubo; Xing, Chunrong; Su, Jianxin; Wang, Huiliang

2018-07-01

A manufacturing error of a cycloidal gear is the key factor affecting the transmission accuracy of a robot rotary vector (RV) reducer. A methodology is proposed to realize the digitized measurement and data processing of the cycloidal gear manufacturing error based on the gear measuring center, which can quickly and accurately measure and evaluate the manufacturing error of the cycloidal gear by using both the whole tooth profile measurement and a single tooth profile measurement. By analyzing the particularity of the cycloidal profile and its effect on the actual meshing characteristics of the RV transmission, the cycloid profile measurement strategy is planned, and the theoretical profile model and error measurement model of cycloid-pin gear transmission are established. Through the digital processing technology, the theoretical trajectory of the probe and the normal vector of the measured point are calculated. By means of precision measurement principle and error compensation theory, a mathematical model for the accurate calculation and data processing of manufacturing error is constructed, and the actual manufacturing error of the cycloidal gear is obtained by the optimization iterative solution. Finally, the measurement experiment of the cycloidal gear tooth profile is carried out on the gear measuring center and the HEXAGON coordinate measuring machine, respectively. The measurement results verify the correctness and validity of the measurement theory and method. This methodology will provide the basis for the accurate evaluation and the effective control of manufacturing precision of the cycloidal gear in a robot RV reducer.

Computational Psychiatry: towards a mathematically informed understanding of mental illness

PubMed Central

Huys, Quentin J M; Roiser, Jonathan P

2016-01-01

Computational Psychiatry aims to describe the relationship between the brain's neurobiology, its environment and mental symptoms in computational terms. In so doing, it may improve psychiatric classification and the diagnosis and treatment of mental illness. It can unite many levels of description in a mechanistic and rigorous fashion, while avoiding biological reductionism and artificial categorisation. We describe how computational models of cognition can infer the current state of the environment and weigh up future actions, and how these models provide new perspectives on two example disorders, depression and schizophrenia. Reinforcement learning describes how the brain can choose and value courses of actions according to their long-term future value. Some depressive symptoms may result from aberrant valuations, which could arise from prior beliefs about the loss of agency (‘helplessness’), or from an inability to inhibit the mental exploration of aversive events. Predictive coding explains how the brain might perform Bayesian inference about the state of its environment by combining sensory data with prior beliefs, each weighted according to their certainty (or precision). Several cortical abnormalities in schizophrenia might reduce precision at higher levels of the inferential hierarchy, biasing inference towards sensory data and away from prior beliefs. We discuss whether striatal hyperdopaminergia might have an adaptive function in this context, and also how reinforcement learning and incentive salience models may shed light on the disorder. Finally, we review some of Computational Psychiatry's applications to neurological disorders, such as Parkinson's disease, and some pitfalls to avoid when applying its methods. PMID:26157034

Approximate number and approximate time discrimination each correlate with school math abilities in young children.

PubMed

Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

2016-01-01

What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright © 2015 Elsevier B.V. All rights reserved.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology.

PubMed

Rajagopal, Vijay; Holmes, William R; Lee, Peter Vee Sin

2018-03-01

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models. © 2017 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc.