Effects of rotor model degradation on the accuracy of rotorcraft real time simulation

NASA Technical Reports Server (NTRS)

Houck, J. A.; Bowles, R. L.

1976-01-01

The effects are studied of degrading a rotating blade element rotor mathematical model to meet various real-time simulation requirements of rotorcraft. Three methods of degradation were studied: reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments, (2) reduction of number of blades, and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which the rotating blade element rotor mathematical model should not be used.

Mathematically precocious and female: Self-efficacy and STEM course choices among high achieving middle grade students

NASA Astrophysics Data System (ADS)

Burt, Stacey M.

The problem addressed in this project is the lack of mathematically gifted females choosing to pursue advanced science, technology, engineering, and mathematics (STEM) courses in secondary education due to deficiencies in self-efficacy. The purpose of this project was to study the effects of a child-guided robotics program as it relates to the self-efficacy of mathematically gifted 6th grade female students and their future course choices in the advanced STEM content areas. This mixed-model study utilized a STEM attitude survey, artifacts, interviews, field notes, and standardized tests as measurement tools. Significance was found between genders in the treatment group for the standardized science scores, indicating closure in the achievement gap. Research suggests that STEM enrichment is beneficial for mathematically gifted females.

Advances in multi-scale modeling of solidification and casting processes

NASA Astrophysics Data System (ADS)

Liu, Baicheng; Xu, Qingyan; Jing, Tao; Shen, Houfa; Han, Zhiqiang

2011-04-01

The development of the aviation, energy and automobile industries requires an advanced integrated product/process R&D systems which could optimize the product and the process design as well. Integrated computational materials engineering (ICME) is a promising approach to fulfill this requirement and make the product and process development efficient, economic, and environmentally friendly. Advances in multi-scale modeling of solidification and casting processes, including mathematical models as well as engineering applications are presented in the paper. Dendrite morphology of magnesium and aluminum alloy of solidification process by using phase field and cellular automaton methods, mathematical models of segregation of large steel ingot, and microstructure models of unidirectionally solidified turbine blade casting are studied and discussed. In addition, some engineering case studies, including microstructure simulation of aluminum casting for automobile industry, segregation of large steel ingot for energy industry, and microstructure simulation of unidirectionally solidified turbine blade castings for aviation industry are discussed.

Modeling and simulation of the flow field in the electrolysis of magnesium

NASA Astrophysics Data System (ADS)

Sun, Ze; Zhang, He-Nan; Li, Ping; Li, Bing; Lu, Gui-Min; Yu, Jian-Guo

2009-05-01

A three-dimensional mathematical model was developed to describe the flow field in the electrolysis cell of the molten magnesium salt, where the model of the three-phase flow was coupled with the electric field force. The mathematical model was validated against the experimental data of the cold model in the electrolysis cell of zinc sulfate with 2 mol/L concentration. The flow field of the cold model was measured by particle image velocimetry, a non-intrusive visualization experimental technique. The flow field in the advanced diaphragmless electrolytic cell of the molten magnesium salt was investigated by the simulations with the mathematical model.

VTI Driving Simulator: Mathematical Model of a Four-wheeled Vehicle for Simulation in Real Time. VTI Rapport 267A.

ERIC Educational Resources Information Center

Nordmark, Staffan

1984-01-01

This report contains a theoretical model for describing the motion of a passenger car. The simulation program based on this model is used in conjunction with an advanced driving simulator and run in real time. The mathematical model is complete in the sense that the dynamics of the engine, transmission and steering system is described in some…

Mathematical description of drug-target interactions: application to biologics that bind to targets with two binding sites.

PubMed

Gibiansky, Leonid; Gibiansky, Ekaterina

2018-02-01

The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

Computational aspects of real-time simulation of rotary-wing aircraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Houck, J. A.

1976-01-01

A study was conducted to determine the effects of degrading a rotating blade element rotor mathematical model suitable for real-time simulation of rotorcraft. Three methods of degradation were studied, reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments; (2) reduction of number of blades; and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which a different rotor mathematical model should be used.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

PubMed Central

Boianelli, Alessandro; Nguyen, Van Kinh; Ebensen, Thomas; Schulze, Kai; Wilk, Esther; Sharma, Niharika; Stegemann-Koniszewski, Sabine; Bruder, Dunja; Toapanta, Franklin R.; Guzmán, Carlos A.; Meyer-Hermann, Michael; Hernandez-Vargas, Esteban A.

2015-01-01

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization. PMID:26473911

Modeling Influenza Virus Infection: A Roadmap for Influenza Research.

PubMed

Boianelli, Alessandro; Nguyen, Van Kinh; Ebensen, Thomas; Schulze, Kai; Wilk, Esther; Sharma, Niharika; Stegemann-Koniszewski, Sabine; Bruder, Dunja; Toapanta, Franklin R; Guzmán, Carlos A; Meyer-Hermann, Michael; Hernandez-Vargas, Esteban A

2015-10-12

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

Mathematical modeling for Phase I cancer trials: A study of metronomic vinorelbine for advanced non-small cell lung cancer (NSCLC) and mesothelioma patients.

PubMed

Barlesi, Fabrice; Imbs, Diane-Charlotte; Tomasini, Pascale; Greillier, Laurent; Galloux, Melissa; Testot-Ferry, Albane; Garcia, Mélanie; Elharrar, Xavier; Pelletier, Annick; André, Nicolas; Mascaux, Céline; Lacarelle, Bruno; Cheikh, Raouf El; Serre, Raphaël; Ciccolini, Joseph; Barbolosi, Dominique

2017-07-18

Using mathematical modelling allows to select a treatment's regimen across infinite possibilities. Here, we report the phase I assessment of a new schedule for metronomic vinorelbine in treating refractory advanced NSCLC and mesothelioma patients. Overall, 13 patients were screened and 12 were treated (50% male, median age: 68yrs), including 9 NSCLC patients. All patients received at least one week (3 doses) of treatment. At data cut-off, the median length of treatment was 6.5 weeks (1-32+). All the patients presented with at least one adverse event (AE) and six patients with a severe AE (SAE). One partial response and 5 stable diseases were observed. The median OS was 6.4 months (95% CI, 4.8 to 12 months). The median and mean vinorelbine's AUC were 122 ng/ml*h and 159 ng/ml*h, respectively, with the higher plasmatic vinorelbine exposure associated with the best ORR (difference of AUC comparison between responders and non-responders, p-value 0.017). The mathematical modelling determined the administration of vinorelbine, 60 mg on Day 1, 30 mg on Day 2 and 60 mg on Day 4 weekly until progression, as the best schedule. Advanced NSCLC or mesothelioma patients progressing after standard treatment were eligible for the trial. NCT02555007. Responses with acceptable safety profile were observed in heavily pretreated NSCLC and mesothelioma patients using oral vinorelbine at this metronomic dosage based on a mathematic modeling. This study demonstrates the feasibility of this new type of approach, as mathematical modeling may help to rationally decide the better regimen to be clinically tested across infinite possibilities.

CSP - The 19th European Conference on Mathematics for Industry (ECMI 2016)

DTIC Science & Technology

2017-03-02

Quality physics in game cinematics. Conclusions Most significant advance reported The ECMI 2016 exceeded by far the expectations of the Organizing... games . 15. SUBJECT TERMS Industrial mathematics; numerical simulation ; optimization; modelling; innovation. 16. SECURITY CLASSIFICATION OF: 17

Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

ERIC Educational Resources Information Center

Minor, Elizabeth Covay

2016-01-01

Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

Cognitive correlates of performance in advanced mathematics.

PubMed

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

ERIC Educational Resources Information Center

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2014-08-28

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

Connecting Advanced and Secondary Mathematics

ERIC Educational Resources Information Center

Murray, Eileen; Baldinger, Erin; Wasserman, Nicholas; Broderick, Shawn; White, Diana

2017-01-01

There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers…

Integrated network analysis and effective tools in plant systems biology

PubMed Central

Fukushima, Atsushi; Kanaya, Shigehiko; Nishida, Kozo

2014-01-01

One of the ultimate goals in plant systems biology is to elucidate the genotype-phenotype relationship in plant cellular systems. Integrated network analysis that combines omics data with mathematical models has received particular attention. Here we focus on the latest cutting-edge computational advances that facilitate their combination. We highlight (1) network visualization tools, (2) pathway analyses, (3) genome-scale metabolic reconstruction, and (4) the integration of high-throughput experimental data and mathematical models. Multi-omics data that contain the genome, transcriptome, proteome, and metabolome and mathematical models are expected to integrate and expand our knowledge of complex plant metabolisms. PMID:25408696

Mathematical modelling of skeletal repair.

PubMed

MacArthur, B D; Please, C P; Taylor, M; Oreffo, R O C

2004-01-23

Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

Mathematics and the surgeon.

PubMed Central

Crank, J.

1976-01-01

The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed. PMID:942167

Exemplarity in Mathematics Education: From a Romanticist Viewpoint to a Modern Hermeneutical One

ERIC Educational Resources Information Center

Patronis, Tasos; Spanos, Dimitris

2013-01-01

This paper proposes a setting of "exemplarity" different from the already known one, which is basically a Romanticist philosophical setting. Our general aim is to describe and explore the nature of some "exemplary themes" and "interpretive models" in advanced mathematics teaching and learning. In order to do so, we…

TIMSS Advanced 2008 Assessment Frameworks

ERIC Educational Resources Information Center

Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka

2006-01-01

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

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

PubMed

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

2016-01-01

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

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Bridging the divide: a model-data approach to Polar and Alpine microbiology.

PubMed

Bradley, James A; Anesio, Alexandre M; Arndt, Sandra

2016-03-01

Advances in microbial ecology in the cryosphere continue to be driven by empirical approaches including field sampling and laboratory-based analyses. Although mathematical models are commonly used to investigate the physical dynamics of Polar and Alpine regions, they are rarely applied in microbial studies. Yet integrating modelling approaches with ongoing observational and laboratory-based work is ideally suited to Polar and Alpine microbial ecosystems given their harsh environmental and biogeochemical characteristics, simple trophic structures, distinct seasonality, often difficult accessibility, geographical expansiveness and susceptibility to accelerated climate changes. In this opinion paper, we explain how mathematical modelling ideally complements field and laboratory-based analyses. We thus argue that mathematical modelling is a powerful tool for the investigation of these extreme environments and that fully integrated, interdisciplinary model-data approaches could help the Polar and Alpine microbiology community address some of the great research challenges of the 21st century (e.g. assessing global significance and response to climate change). However, a better integration of field and laboratory work with model design and calibration/validation, as well as a stronger focus on quantitative information is required to advance models that can be used to make predictions and upscale processes and fluxes beyond what can be captured by observations alone. © FEMS 2016.

Bridging the divide: a model-data approach to Polar and Alpine microbiology

PubMed Central

Bradley, James A.; Anesio, Alexandre M.; Arndt, Sandra

2016-01-01

Advances in microbial ecology in the cryosphere continue to be driven by empirical approaches including field sampling and laboratory-based analyses. Although mathematical models are commonly used to investigate the physical dynamics of Polar and Alpine regions, they are rarely applied in microbial studies. Yet integrating modelling approaches with ongoing observational and laboratory-based work is ideally suited to Polar and Alpine microbial ecosystems given their harsh environmental and biogeochemical characteristics, simple trophic structures, distinct seasonality, often difficult accessibility, geographical expansiveness and susceptibility to accelerated climate changes. In this opinion paper, we explain how mathematical modelling ideally complements field and laboratory-based analyses. We thus argue that mathematical modelling is a powerful tool for the investigation of these extreme environments and that fully integrated, interdisciplinary model-data approaches could help the Polar and Alpine microbiology community address some of the great research challenges of the 21st century (e.g. assessing global significance and response to climate change). However, a better integration of field and laboratory work with model design and calibration/validation, as well as a stronger focus on quantitative information is required to advance models that can be used to make predictions and upscale processes and fluxes beyond what can be captured by observations alone. PMID:26832206

Near-earth orbital guidance and remote sensing

NASA Technical Reports Server (NTRS)

Powers, W. F.

1972-01-01

The curriculum of a short course in remote sensing and parameter optimization is presented. The subjects discussed are: (1) basics of remote sensing and the user community, (2) multivariant spectral analysis, (3) advanced mathematics and physics of remote sensing, (4) the atmospheric environment, (5) imaging sensing, and (6)nonimaging sensing. Mathematical models of optimization techniques are developed.

Cognitive Correlates of Performance in Advanced Mathematics

ERIC Educational Resources Information Center

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-01-01

Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

Mathematical Model of the Jet Engine Fuel System

NASA Astrophysics Data System (ADS)

Klimko, Marek

2015-05-01

The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.

Towards predictive models of the human gut microbiome

PubMed Central

2014-01-01

The intestinal microbiota is an ecosystem susceptible to external perturbations such as dietary changes and antibiotic therapies. Mathematical models of microbial communities could be of great value in the rational design of microbiota-tailoring diets and therapies. Here, we discuss how advances in another field, engineering of microbial communities for wastewater treatment bioreactors, could inspire development of mechanistic mathematical models of the gut microbiota. We review the current state-of-the-art in bioreactor modeling and current efforts in modeling the intestinal microbiota. Mathematical modeling could benefit greatly from the deluge of data emerging from metagenomic studies, but data-driven approaches such as network inference that aim to predict microbiome dynamics without explicit mechanistic knowledge seem better suited to model these data. Finally, we discuss how the integration of microbiome shotgun sequencing and metabolic modeling approaches such as flux balance analysis may fulfill the promise of a mechanistic model of the intestinal microbiota. PMID:24727124

Mathematical modelling of prostate cancer growth and its application to hormone therapy.

PubMed

Tanaka, Gouhei; Hirata, Yoshito; Goldenberg, S Larry; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-11-13

Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on- and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

PubMed

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

Current advancements and challenges in soil-root interactions modelling

NASA Astrophysics Data System (ADS)

Schnepf, Andrea; Huber, Katrin; Abesha, Betiglu; Meunier, Felicien; Leitner, Daniel; Roose, Tiina; Javaux, Mathieu; Vanderborght, Jan; Vereecken, Harry

2015-04-01

Roots change their surrounding soil chemically, physically and biologically. This includes changes in soil moisture and solute concentration, the exudation of organic substances into the rhizosphere, increased growth of soil microorganisms, or changes in soil structure. The fate of water and solutes in the root zone is highly determined by these root-soil interactions. Mathematical models of soil-root systems in combination with non-invasive techniques able to characterize root systems are a promising tool to understand and predict the behaviour of water and solutes in the root zone. With respect to different fields of applications, predictive mathematical models can contribute to the solution of optimal control problems in plant recourse efficiency. This may result in significant gains in productivity, efficiency and environmental sustainability in various land use activities. Major challenges include the coupling of model parameters of the relevant processes with the surrounding environment such as temperature, nutrient concentration or soil water content. A further challenge is the mathematical description of the different spatial and temporal scales involved. This includes in particular the branched structures formed by root systems or the external mycelium of mycorrhizal fungi. Here, reducing complexity as well as bridging between spatial scales is required. Furthermore, the combination of experimental and mathematical techniques may advance the field enormously. Here, the use of root system, soil and rhizosphere models is presented through a number of modelling case studies, including image based modelling of phosphate uptake by a root with hairs, model-based optimization of root architecture for phosphate uptake from soil, upscaling of rhizosphere models, modelling root growth in structured soil, and the effect of root hydraulic architecture on plant water uptake efficiency and drought resistance.

Current Advancements and Challenges in Soil-Root Interactions Modelling

NASA Astrophysics Data System (ADS)

Schnepf, A.; Huber, K.; Abesha, B.; Meunier, F.; Leitner, D.; Roose, T.; Javaux, M.; Vanderborght, J.; Vereecken, H.

2014-12-01

Roots change their surrounding soil chemically, physically and biologically. This includes changes in soil moisture and solute concentration, the exudation of organic substances into the rhizosphere, increased growth of soil microorganisms, or changes in soil structure. The fate of water and solutes in the root zone is highly determined by these root-soil interactions. Mathematical models of soil-root systems in combination with non-invasive techniques able to characterize root systems are a promising tool to understand and predict the behaviour of water and solutes in the root zone. With respect to different fields of applications, predictive mathematical models can contribute to the solution of optimal control problems in plant recourse efficiency. This may result in significant gains in productivity, efficiency and environmental sustainability in various land use activities. Major challenges include the coupling of model parameters of the relevant processes with the surrounding environment such as temperature, nutrient concentration or soil water content. A further challenge is the mathematical description of the different spatial and temporal scales involved. This includes in particular the branched structures formed by root systems or the external mycelium of mycorrhizal fungi. Here, reducing complexity as well as bridging between spatial scales is required. Furthermore, the combination of experimental and mathematical techniques may advance the field enormously. Here, the use of root system, soil and rhizosphere models is presented through a number of modelling case studies, including image based modelling of phosphate uptake by a root with hairs, model-based optimization of root architecture for phosphate uptake from soil, upscaling of rhizosphere models, modelling root growth in structured soil, and the effect of root hydraulic architecture on plant water uptake efficiency and drought resistance.

The Impact of Advanced Curriculum on the Achievement of Mathematically Promising Elementary Students

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Carroll, Susan R.; Sheffield, Linda Jensen

2009-01-01

The primary aim of Project M[superscript 3]: Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in…

On the Modeling of Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Fiore, Daniel

2016-07-01

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into the effect of process parameters on final properties. This article describes the application of a 2-D mathematical VAR model presented at previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in a Ti-6Al-4V ingot is discussed. Model predictions are validated against published data from a industrial size ingot, and results of a parametric study on particle dissolution are also discussed.

Desegregating undergraduate mathematics and biology--interdisciplinary instruction with emphasis on ongoing biomedical research.

PubMed

Robeva, Raina

2009-01-01

The remarkable advances in the field of biology in the last decade, specifically in the areas of biochemistry, genetics, genomics, proteomics, and systems biology, have demonstrated how critically important mathematical models and methods are in addressing questions of vital importance for these disciplines. There is little doubt that the need for utilizing and developing mathematical methods for biology research will only grow in the future. The rapidly increasing demand for scientists with appropriate interdisciplinary skills and knowledge, however, is not being reflected in the way undergraduate mathematics and biology courses are structured and taught in most colleges and universities nationwide. While a number of institutions have stepped forward and addressed this need by creating and offering interdisciplinary courses at the juncture of mathematics and biology, there are still many others at which there is little, if any, interdisciplinary interaction between the curricula. This chapter describes an interdisciplinary course and a textbook in mathematical biology developed collaboratively by faculty from Sweet Briar College and the University of Virginia School of Medicine. The course and textbook are designed to provide a bridge between the mathematical and biological sciences at the lower undergraduate level. The course is developed for and is being taught in a liberal arts setting at Sweet Briar College, Virginia, but some of the advanced modules are used in a course at the University of Virginia for advanced undergraduate and beginning graduate students. The individual modules are relatively independent and can be used as stand-alone projects in conventional mathematics and biology courses. Except for the introductory material, the course and textbook topics are based on current biomedical research.

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

NASA Astrophysics Data System (ADS)

Díaz, Verónica; Poblete, Alvaro

2017-07-01

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

Evaluation of a Constrained Facet Analysis Efficiency Model for Identifying the Efficiency of Medical Treatment Facilities in the Army Medical Department

DTIC Science & Technology

1990-07-31

examples on their use is available with the PASS User Documentation Manual. 2 The data structure of PASS requires a three- lvel organizational...files, and missing control variables. A specific problem noted involved the absence of 8087 mathematical co-processor on the target IBM-XT 21 machine...System, required an operational understanding of the advanced mathematical technique used in the model. Problems with the original release of the PASS

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

PubMed Central

Bucksch, Alexander; Atta-Boateng, Acheampong; Azihou, Akomian F.; Battogtokh, Dorjsuren; Baumgartner, Aly; Binder, Brad M.; Braybrook, Siobhan A.; Chang, Cynthia; Coneva, Viktoirya; DeWitt, Thomas J.; Fletcher, Alexander G.; Gehan, Malia A.; Diaz-Martinez, Diego Hernan; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Klein, Laura L.; Leiboff, Samuel; Li, Mao; Lynch, Jonathan P.; Maizel, Alexis; Maloof, Julin N.; Markelz, R. J. Cody; Martinez, Ciera C.; Miller, Laura A.; Mio, Washington; Palubicki, Wojtek; Poorter, Hendrik; Pradal, Christophe; Price, Charles A.; Puttonen, Eetu; Reese, John B.; Rellán-Álvarez, Rubén; Spalding, Edgar P.; Sparks, Erin E.; Topp, Christopher N.; Williams, Joseph H.; Chitwood, Daniel H.

2017-01-01

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics. PMID:28659934

Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future

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

Brown, D L; Bell, J; Estep, D

2008-02-15

Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as themore » high-performance computers on which these codes run. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception. Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those that involve the energy, environmental and national security needs of the country. As the capability of high-performance computers continues to increase, the types of questions that can be answered by applying this huge computational power become more varied and more complex. It will be essential that we find new ways to develop and apply the mathematics necessary to enable the new scientific and engineering discoveries that are needed. In August 2007, a panel of experts in applied, computational and statistical mathematics met for a day and a half in Berkeley, California to understand the mathematical developments required to meet the future science and engineering needs of the DOE. It is important to emphasize that the panelists were not asked to speculate only on advances that might be made in their own research specialties. Instead, the guidance this panel was given was to consider the broad science and engineering challenges that the DOE faces and identify the corresponding advances that must occur across the field of mathematics for these challenges to be successfully addressed. As preparation for the meeting, each panelist was asked to review strategic planning and other informational documents available for one or more of the DOE Program Offices, including the Offices of Science, Nuclear Energy, Fossil Energy, Environmental Management, Legacy Management, Energy Efficiency & Renewable Energy, Electricity Delivery & Energy Reliability and Civilian Radioactive Waste Management as well as the National Nuclear Security Administration. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: (1) Can we predict the operating characteristics of a clean coal power plant? (2) How stable is the plasma containment in a tokamak? (3) How quickly is climate change occurring and what are the uncertainties in the predicted time scales? (4) How quickly can an introduced bio-weapon contaminate the agricultural environment in the US? (5) How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types? (6) How quickly can the United States recover if part of the power grid became inoperable? (7) What are optimal locations and communication protocols for sensing devices in a remote-sensing network? (8) How can new materials be designed with a specified desirable set of properties? In comparing and contrasting these and other questions of importance to DOE, the panel found that while the scientific breadth of the requirements is enormous, a central theme emerges: Scientists are being asked to identify or provide technology, or to give expert analysis to inform policy-makers that requires the scientific understanding of increasingly complex physical and engineered systems. In addition, as the complexity of the systems of interest increases, neither experimental observation nor mathematical and computational modeling alone can access all components of the system over the entire range of scales or conditions needed to provide the required scientific understanding.« less

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

NASA Technical Reports Server (NTRS)

Bekey, G. A.

1971-01-01

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

Adding structure to the transition process to advanced mathematical activity

NASA Astrophysics Data System (ADS)

Engelbrecht, Johann

2010-03-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.

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.

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

NASA Technical Reports Server (NTRS)

Aiken, E. W.

1980-01-01

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

[Research advances in mathematical model of coniferous trees cold hardiness].

PubMed

Zhang, Gang; Wang, Ai-Fang

2007-07-01

Plant cold hardiness has complicated attributes. This paper introduced the research advances in establishing the dynamic models of coniferous trees cold hardiness, with the advantages and disadvantages of the models presented and the further studies suggested. In the models established initially, temperature was concerned as the only environmental factor affecting the cold hardiness, and the concept of stationary level of cold hardiness was introduced. Due to the obvious prediction errors of these models, the stationary level of cold hardiness was modeled later by assuming the existence of an additive effect of temperature and photoperiod on the increase of cold hardiness. Furthermore, the responses of the annual development phases for cold hardiness to environment were considered. The model researchers have paid more attention to the additive effect models, and run some experiments to test the additivity principle. However, the research results on Scots pine (Pinus sylvestris) indicated that its organs did not support the presumption of an additive response of cold hardiness by temperature and photoperiod, and the interaction between environmental factors should be taken into account. The mathematical models of cold hardiness need to be developed and improved.

Preparing and Supporting Black Students to Enroll and Achieve in Advanced Mathematics Classes in Middle School: A Case Study

ERIC Educational Resources Information Center

Cobbs, Joyce Bernice

2014-01-01

The literature on minority student achievement indicates that Black students are underrepresented in advanced mathematics courses. Advanced mathematics courses offer students the opportunity to engage with challenging curricula, experience rigorous instruction, and interact with quality teachers. The middle school years are particularly…

Teacher Questioning and Invitations to Participate in Advanced Mathematics Lectures

ERIC Educational Resources Information Center

Paoletti, Teo; Krupnik, Victoria; Papadopoulos, Dimitrios; Olsen, Joseph; Fukawa-Connelly, Tim; Weber, Keith

2018-01-01

We were interested in exploring the extent to which advanced mathematics lecturers provide students with opportunities to play a role in considering or generating course content. To do this, we examined the questioning practices of 11 lecturers who taught advanced mathematics courses at the university level. Because we are unaware of other studies…

The link between middle school mathematics course placement and achievement.

PubMed

Domina, Thurston

2014-01-01

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. © 2014 The Author. Child Development © 2014 Society for Research in Child Development, Inc.

A Simple Mechanical Model for the Isotropic Harmonic Oscillator

ERIC Educational Resources Information Center

Nita, Gelu M.

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

Bearing capacity analysis and design of highway base materials reinforced with geofabrics.

DOT National Transportation Integrated Search

2005-06-01

The primary objective of this study was to develop and implement mathematical bearing capacity models originally proposed by Hopkins (1988, 1991) and Slepak and Hopkins (1993; 1995). These advanced models, which are based on limit equilibrium and are...

Research Area 3 - Mathematical Sciences: Multiscale Modeling of the Mechanics of Advanced Energetic Materials Relevant to Detonation Prediction

DTIC Science & Technology

2015-08-24

new energetic materials with enhanced energy release rates and reduced sensitivity to unintentional detonation . The following results have been...Mechanics of Advanced Energetic Materials Relevant to Detonation Prediction The views, opinions and/or findings contained in this report are those of the...modeling, molecular simulations, detonation prediction REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

2014-07-01

Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

Development and validation of a blade-element mathematical model for the AH-64A Apache helicopter

NASA Technical Reports Server (NTRS)

Mansur, M. Hossein

1995-01-01

A high-fidelity blade-element mathematical model for the AH-64A Apache Advanced Attack Helicopter has been developed by the Aeroflightdynamics Directorate of the U.S. Army's Aviation and Troop Command (ATCOM) at Ames Research Center. The model is based on the McDonnell Douglas Helicopter Systems' (MDHS) Fly Real Time (FLYRT) model of the AH-64A (acquired under contract) which was modified in-house and augmented with a blade-element-type main-rotor module. This report describes, in detail, the development of the rotor module, and presents some results of an extensive validation effort.

Kinetic modeling of plant metabolism and its predictive power: peppermint essential oil biosynthesis as an example.

PubMed

Lange, Bernd Markus; Rios-Estepa, Rigoberto

2014-01-01

The integration of mathematical modeling with analytical experimentation in an iterative fashion is a powerful approach to advance our understanding of the architecture and regulation of metabolic networks. Ultimately, such knowledge is highly valuable to support efforts aimed at modulating flux through target pathways by molecular breeding and/or metabolic engineering. In this article we describe a kinetic mathematical model of peppermint essential oil biosynthesis, a pathway that has been studied extensively for more than two decades. Modeling assumptions and approximations are described in detail. We provide step-by-step instructions on how to run simulations of dynamic changes in pathway metabolites concentrations.

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

PubMed

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

2010-01-01

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

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

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

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

Use of CAS in Secondary School: A Factor Influencing the Transition to University-Level Mathematics?

ERIC Educational Resources Information Center

Varsavsky, Cristina

2012-01-01

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…

How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

ERIC Educational Resources Information Center

Weber, Keith

2009-01-01

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

Adding Structure to the Transition Process to Advanced Mathematical Activity

ERIC Educational Resources Information Center

Engelbrecht, Johann

2010-01-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…

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

PubMed

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

2013-11-18

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

Modeling energy expenditure in children and adolescents using quantile regression

USDA-ARS?s Scientific Manuscript database

Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in energy expenditure (EE). Study objective is to apply quantile regression (QR) to predict EE and determine quantile-dependent variation in covariate effects in nonobese and obes...

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling

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

Erickson, Keesha E.; Rukhlenko, Oleksii S.; Posner, Richard G.

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisitionmore » of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.« less

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling

DOE PAGES

Erickson, Keesha E.; Rukhlenko, Oleksii S.; Posner, Richard G.; ...

2018-03-05

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisitionmore » of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.« less

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling.

PubMed

Erickson, Keesha E; Rukhlenko, Oleksii S; Posner, Richard G; Hlavacek, William S; Kholodenko, Boris N

2018-03-05

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisition of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1991-01-01

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

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

TIMSS Advanced 2015 Assessment Frameworks

ERIC Educational Resources Information Center

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the last of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the second of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

Which Advanced Mathematics Courses Influence ACT Score? A State Level Analysis of the Iowa Class of 2012

ERIC Educational Resources Information Center

Grinstead, Mary L.

2013-01-01

This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…

Methods of Technological Forecasting,

DTIC Science & Technology

1977-05-01

Trend Extrapolation Progress Curve Analogy Trend Correlation Substitution Analysis or Substitution Growth Curves Envelope Curve Advances in the State of...the Art Technological Mapping Contextual Mapping Matrix Input-Output Analysis Mathematical Models Simulation Models Dynamic Modelling. CHAPTER IV...Generation Interaction between Needs and Possibilities Map of the Technological Future — (‘ross- Impact Matri x Discovery Matrix Morphological Analysis

Interdisciplinary education - a predator-prey model for developing a skill set in mathematics, biology and technology

NASA Astrophysics Data System (ADS)

van der Hoff, Quay

2017-08-01

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in biological phenomena, find it difficult to master the complex systems encountered in biology. In short, the biologists do not have enough mathematics and the mathematicians are not being taught enough biology. The need for interdisciplinary curricula that includes disciplines such as biology, physical science, and mathematics is widely recognized, but has not been widely implemented. In this paper, it is suggested that students develop a skill set of ecology, mathematics and technology to encourage working across disciplinary boundaries. To illustrate such a skill set, a predator-prey model that contains self-limiting factors for both predator and prey is suggested. The general idea of dynamics, is introduced and students are encouraged to discover the applicability of this approach to more complex biological systems. The level of mathematics and technology required is not advanced; therefore, it is ideal for inclusion in a senior-level or introductory graduate-level course for students interested in mathematical biology.

Omics, microbial modeling, and food safety information infrastructure: a food safety perspective

USDA-ARS?s Scientific Manuscript database

Over the last three decades, advances in a variety of cutting-edge “omics” technologies, including genomics, proteomics, and metabolomics, as well as in molecular and mathematical modeling approaches have provided the ability to more easily determine and interpret the mechanisms underlying pathogene...

Use of CAS in secondary school: a factor influencing the transition to university-level mathematics?

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2012-01-01

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one where students learn and are examined with a computer algebra system (CAS) and another where students can only use scientific calculators. This study compares the performance of 1240 students as they transitioned to traditional university-level mathematics and according to whether they learned intermediate mathematics with or without the assistance of a CAS. This study concludes that students without CAS show a slight advantage, but the most important factor affecting student performance is the uptake of advanced-level mathematics studies in secondary school.

Understanding intratumor heterogeneity by combining genome analysis and mathematical modeling.

PubMed

Niida, Atsushi; Nagayama, Satoshi; Miyano, Satoru; Mimori, Koshi

2018-04-01

Cancer is composed of multiple cell populations with different genomes. This phenomenon called intratumor heterogeneity (ITH) is supposed to be a fundamental cause of therapeutic failure. Therefore, its principle-level understanding is a clinically important issue. To achieve this goal, an interdisciplinary approach combining genome analysis and mathematical modeling is essential. For example, we have recently performed multiregion sequencing to unveil extensive ITH in colorectal cancer. Moreover, by employing mathematical modeling of cancer evolution, we demonstrated that it is possible that this ITH is generated by neutral evolution. In this review, we introduce recent advances in a research field related to ITH and also discuss strategies for exploiting novel findings on ITH in a clinical setting. © 2018 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.

System identification of propagating wave segments in excitable media and its application to advanced control

NASA Astrophysics Data System (ADS)

Katsumata, Hisatoshi; Konishi, Keiji; Hara, Naoyuki

2018-04-01

The present paper proposes a scheme for controlling wave segments in excitable media. This scheme consists of two phases: in the first phase, a simple mathematical model for wave segments is derived using only the time series data of input and output signals for the media; in the second phase, the model derived in the first phase is used in an advanced control technique. We demonstrate with numerical simulations of the Oregonator model that this scheme performs better than a conventional control scheme.

Life on the Number Line: Routes to Understanding Fraction Magnitude for Students With Difficulties Learning Mathematics.

PubMed

Gersten, Russell; Schumacher, Robin F; Jordan, Nancy C

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.

Response of advance lodgepole pine regeneration to overstory removal in eastern Idaho

Treesearch

Tanya E. Lewis Murphy; David L. Adams; Dennis E. Ferguson

1999-01-01

Twenty-two stands of advance lodgepole pine released with overstory removal were sampled to determine height growth response. Tree and site characteristics correlated with release response were identified, and a mathematical model was developed to predict height growth in years 6 through 10 after release as a function of residual overstory basal area, height at release...

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

Recent Advances in the Edge-Function Method 1979-1980

DTIC Science & Technology

1980-07-30

the residuals are within the limits within which an engineer can specify the boundary conditions of the problem, then the corresponding Mathematical ...truncation lvel . The consistent preference shown by the solver routine for verteA functions as opposed to polar functions reinforces the expectations of...Accordingly,each solution zr_.-4_des a Mathematical Model for the given physical problem- R.M.S. values provide a practical criterion for the enai--er to

Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models II: The Role of Quantum Affine Symmetry

NASA Astrophysics Data System (ADS)

Jimbo, Michio

2013-03-01

Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

A Computational Model of Fraction Arithmetic

ERIC Educational Resources Information Center

Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Student Learning and Perceptions in a Flipped Linear Algebra Course

ERIC Educational Resources Information Center

Love, Betty; Hodge, Angie; Grandgenett, Neal; Swift, Andrew W.

2014-01-01

The traditional lecture style of teaching has long been the norm in college science, technology, engineering, and mathematics (STEM) courses, but an innovative teaching model, facilitated by recent advances in technology, is gaining popularity across college campuses. This new model inverts or "flips" the usual classroom paradigm, in…

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

PubMed

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-09-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

AISI/DOE Advanced Process Control Program Vol. 3 of 6 Microstructure Engineering in Hot Strip Mills, Part 1 of 2: Integrated Mathematical Model

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

J.K. Brimacombe; I.V. Samarasekera; E.B. Hawbolt

1999-07-31

This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evolution and mechanical properties of steel strip in a hot-strip mill. This achievement results from a joint research effort that is part of the American Iron and Steel Institute's (AIS) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American Steelmakers.

Air breathing engine/rocket trajectory optimization

NASA Technical Reports Server (NTRS)

Smith, V. K., III

1979-01-01

This research has focused on improving the mathematical models of the air-breathing propulsion systems, which can be mated with the rocket engine model and incorporated in trajectory optimization codes. Improved engine simulations provided accurate representation of the complex cycles proposed for advanced launch vehicles, thereby increasing the confidence in propellant use and payload calculations. The versatile QNEP (Quick Navy Engine Program) was modified to allow treatment of advanced turboaccelerator cycles using hydrogen or hydrocarbon fuels and operating in the vehicle flow field.

ECOLOGICAL THEORY. A general consumer-resource population model.

PubMed

Lafferty, Kevin D; DeLeo, Giulio; Briggs, Cheryl J; Dobson, Andrew P; Gross, Thilo; Kuris, Armand M

2015-08-21

Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model. Copyright © 2015, American Association for the Advancement of Science.

Advanced Mathematical Thinking

ERIC Educational Resources Information Center

Dubinsky, Ed; McDonald, Michael A.; Edwards, Barbara S.

2005-01-01

In this article we propose the following definition for advanced mathematical thinking: Thinking that requires deductive and rigorous reasoning about mathematical notions that are not entirely accessible to us through our five senses. We argue that this definition is not necessarily tied to a particular kind of educational experience; nor is it…

Rotor systems research aircraft simulation mathematical model

NASA Technical Reports Server (NTRS)

Houck, J. A.; Moore, F. L.; Howlett, J. J.; Pollock, K. S.; Browne, M. M.

1977-01-01

An analytical model developed for evaluating and verifying advanced rotor concepts is discussed. The model was used during in both open loop and real time man-in-the-loop simulation during the rotor systems research aircraft design. Future applications include: pilot training, preflight of test programs, and the evaluation of promising concepts before their implementation on the flight vehicle.

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the third of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the first of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the third of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first of the two chapters in this text deals with equations, inequalities and radicals.…

Computational Toxicology at the US EPA

EPA Science Inventory

Computational toxicology is the application of mathematical and computer models to help assess chemical hazards and risks to human health and the environment. Supported by advances in informatics, high-throughput screening (HTS) technologies, and systems biology, EPA is developin...

Reproducible research in vadose zone sciences

USDA-ARS?s Scientific Manuscript database

A significant portion of present-day soil and Earth science research is computational, involving complex data analysis pipelines, advanced mathematical and statistical models, and sophisticated computer codes. Opportunities for scientific progress are greatly diminished if reproducing and building o...

Mathematics Content Coverage and Student Learning in Kindergarten

PubMed Central

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2017-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998–99 and 2010–11 school years, they continued to place more emphasis on basic content. We find that time on advanced content is positively associated with student learning, whereas time on basic content has a negative association with learning. We argue that increased exposure to more advanced mathematics content could benefit the vast majority of kindergartners. PMID:29353913

The application of virtual prototyping methods to determine the dynamic parameters of mobile robot

NASA Astrophysics Data System (ADS)

Kurc, Krzysztof; Szybicki, Dariusz; Burghardt, Andrzej; Muszyńska, Magdalena

2016-04-01

The paper presents methods used to determine the parameters necessary to build a mathematical model of an underwater robot with a crawler drive. The parameters present in the dynamics equation will be determined by means of advanced mechatronic design tools, including: CAD/CAE software andMES modules. The virtual prototyping process is described as well as the various possible uses (design adaptability) depending on the optional accessories added to the vehicle. A mathematical model is presented to show the kinematics and dynamics of the underwater crawler robot, essential for the design stage.

Conditional Inference and Advanced Mathematical Study: Further Evidence

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2009-01-01

In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…

Gestures and Insight in Advanced Mathematical Thinking

ERIC Educational Resources Information Center

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

2011-01-01

What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

Modeling the Role of Priming in Executive Control: Cognitive and Neural Constraints

DTIC Science & Technology

2012-01-24

theoretical and empirical advances in our understanding of cognitive control. We discovered new phenomena and developed theories to account for them. We...developed theories of cognitive control and visual attention that integrated mathematical psychology with cognitive science and with neuroscience. We...significant theoretical and empirical advances in our understanding of cognitive control. We discovered new phenomena and developed theories to account

Mathematical modeling and SAR simulation multifunction SAR technology efforts

NASA Technical Reports Server (NTRS)

Griffin, C. R.; Estes, J. M.

1981-01-01

The orbital SAR (synthetic aperture radar) simulation data was used in several simulation efforts directed toward advanced SAR development. Efforts toward simulating an operational radar, simulation of antenna polarization effects, and simulation of SAR images at serveral different wavelengths are discussed. Avenues for improvements in the orbital SAR simulation and its application to the development of advanced digital radar data processing schemes are indicated.

Using Computational and Mechanical Models to Study Animal Locomotion

PubMed Central

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

2012-01-01

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

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the fourth of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Information modeling system for blast furnace control

NASA Astrophysics Data System (ADS)

Spirin, N. A.; Gileva, L. Y.; Lavrov, V. V.

2016-09-01

Modern Iron & Steel Works as a rule are equipped with powerful distributed control systems (DCS) and databases. Implementation of DSC system solves the problem of storage, control, protection, entry, editing and retrieving of information as well as generation of required reporting data. The most advanced and promising approach is to use decision support information technologies based on a complex of mathematical models. The model decision support system for control of blast furnace smelting is designed and operated. The basis of the model system is a complex of mathematical models created using the principle of natural mathematical modeling. This principle provides for construction of mathematical models of two levels. The first level model is a basic state model which makes it possible to assess the vector of system parameters using field data and blast furnace operation results. It is also used to calculate the adjustment (adaptation) coefficients of the predictive block of the system. The second-level model is a predictive model designed to assess the design parameters of the blast furnace process when there are changes in melting conditions relative to its current state. Tasks for which software is developed are described. Characteristics of the main subsystems of the blast furnace process as an object of modeling and control - thermal state of the furnace, blast, gas dynamic and slag conditions of blast furnace smelting - are presented.

The 1982 Goddard Space Flight Center Battery Workshop

NASA Technical Reports Server (NTRS)

Halpert, G. (Editor)

1983-01-01

Various topics concerned with advanced battery technology are addressed including lithium cell and battery safety developments, mathematical modelling, charge control of aerospace power systems, and the application of nickel hydrogen cells/batteries vis-a-vis nickel cadmium cells/batteries.

Recent advances in mathematical modeling of nitrous oxides emissions from wastewater treatment processes.

PubMed

Ni, Bing-Jie; Yuan, Zhiguo

2015-12-15

Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. Copyright © 2015 Elsevier Ltd. All rights reserved.

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls

PubMed Central

2016-01-01

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls’ STEM participation. PMID:27100631

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls.

PubMed

Stoet, Gijsbert; Bailey, Drew H; Moore, Alex M; Geary, David C

2016-01-01

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls' STEM participation.

Modelling with Difference Equations Supported by GeoGebra: Exploring the Kepler Problem

ERIC Educational Resources Information Center

Kovacs, Zoltan

2010-01-01

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Why Do Students Drop Advanced Mathematics?

ERIC Educational Resources Information Center

Horn, Ilana

2004-01-01

Students, especially black, Latino and Native American youth and students of low socio-economic status drop out of advanced mathematics. Teachers must coordinate their expectations, their knowledge of students and their teaching practices in order to stop struggling students from dropping out of advanced math classes.

Application of a Model for Simulating the Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Tripp, David W.; Fiore, Daniel

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into system dynamics and to predict the effect of process modifications or upsets on final properties. This article describes the application of a 2-D mathematical VAR model presented in previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in Ti-6Al-4V ingots will be discussed. Model predictions were first validated against the measured characteristics of industrially produced ingots, and process inputs and model formulation were adjusted to match macro-etched pool shapes. The results are compared to published data in the literature. Finally, the model is used to examine ingot chemistry during successive VAR melts.

Informal Content and Student Note-Taking in Advanced Mathematics Classes

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo

2017-01-01

This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…

Gender Differences in the Use and Benefit of Advanced Learning Technologies for Mathematics

ERIC Educational Resources Information Center

Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park

2013-01-01

We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…

Contradictions between and within School and University Activity Systems Helping to Explain Students' Difficulty with Advanced Mathematics

ERIC Educational Resources Information Center

Jooganah, Kamila; Williams, Julian S.

2016-01-01

This article explores how contradictions, as framed by activity theory (Engeström, 1987), can explain first-year undergraduate students' experiences of learning advanced mathematics. Analysing qualitative interview and observational data of students and lecturers based in one university mathematics department, we argue that contradictions between…

Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Champredon, David; Earn, David J. D.

2016-09-01

Mechanistic mathematical modelling of the population dynamics of infectious diseases has advanced tremendously over the last few decades [1-6]. Transmission models have been applied to countless diseases of public health importance, including seasonal and pandemic influenza [7], childhood diseases such as measles [8,9] and whooping cough [10], vector transmitted diseases such as malaria [11] and dengue [12], and waterborne diseases such as cholera [13-15]. Much attention in recent years has been directed to emergent diseases such as SARS [16], new subtypes of influenza [17,18], Ebola [19,20], and Zika [21], for which an understanding of early outbreak dynamics is critical.

Digital Avionics Information System (DAIS): Life Cycle Cost Impact Modeling System Reliability, Maintainability, and Cost Model (RMCM)--Description. Users Guide. Final Report.

ERIC Educational Resources Information Center

Goclowski, John C.; And Others

The Reliability, Maintainability, and Cost Model (RMCM) described in this report is an interactive mathematical model with a built-in sensitivity analysis capability. It is a major component of the Life Cycle Cost Impact Model (LCCIM), which was developed as part of the DAIS advanced development program to be used to assess the potential impacts…

Advanced Combustion Numerics and Modeling - FY18 First Quarter Report

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

Whitesides, R. A.; Killingsworth, N. J.; McNenly, M. J.

This project is focused on early stage research and development of numerical methods and models to improve advanced engine combustion concepts and systems. The current focus is on development of new mathematics and algorithms to reduce the time to solution for advanced combustion engine design using detailed fuel chemistry. The research is prioritized towards the most time-consuming workflow bottlenecks (computer and human) and accuracy gaps that slow ACS program members. Zero-RK, the fast and accurate chemical kinetics solver software developed in this project, is central to the research efforts and continues to be developed to address the current and emergingmore » needs of the engine designers, engine modelers and fuel mechanism developers.« less

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Simulation modelling for new gas turbine fuel controller creation.

NASA Astrophysics Data System (ADS)

Vendland, L. E.; Pribylov, V. G.; Borisov, Yu A.; Arzamastsev, M. A.; Kosoy, A. A.

2017-11-01

State of the art gas turbine fuel flow control systems are based on throttle principle. Major disadvantage of such systems is that they require high pressure fuel intake. Different approach to fuel flow control is to use regulating compressor. And for this approach because of controller and gas turbine interaction a specific regulating compressor is required. Difficulties emerge as early as the requirement definition stage. To define requirements for new object, his properties must be known. Simulation modelling helps to overcome these difficulties. At the requirement definition stage the most simplified mathematical model is used. Mathematical models will get more complex and detailed as we advance in planned work. If future adjusting of regulating compressor physical model to work with virtual gas turbine and physical control system is planned.

What's Working: Program Factors Influencing California Community College Basic Skills Mathematics Students' Advancement to Transfer Level

ERIC Educational Resources Information Center

Fiero, Diane M.

2013-01-01

Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…

Incentivizing Advanced Mathematics Study at Upper Secondary Level: The Case of Bonus Points in Ireland

ERIC Educational Resources Information Center

Treacy, Páraic Thomas

2018-01-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant…

Unsteady Aerodynamic Modeling in Roll for the NASA Generic Transport Model

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.

2012-01-01

Reducing the impact of loss-of-control conditions on commercial transport aircraft is a primary goal of the NASA Aviation Safety Program. One aspect in developing the supporting technologies is to improve the aerodynamic models that represent these adverse conditions. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. In this paper, a more general mathematical model is proposed for the subscale NASA Generic Transport Model (GTM) that covers both low and high angles of attack. Particular attention is devoted to the stall region where full-scale transports have demonstrated a tendency for roll instability. The complete aerodynamic model was estimated from dynamic wind-tunnel data. Advanced computational methods are used to improve understanding and visualize the flow physics within the region where roll instability is a factor.

A mathematical model for simulating noise suppression of lined ejectors

NASA Technical Reports Server (NTRS)

Watson, Willie R.

1994-01-01

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support

NASA Technical Reports Server (NTRS)

Cruthirds, John E.

2003-01-01

A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.

Improving the Graduate School Experience for Women in Mathematics: the Edge Program

NASA Astrophysics Data System (ADS)

Bozeman, Sylvia T.; Hughes, Rhonda J.

For over a decade, Spelman College and Bryn Mawr College have collaborated on initiatives designed to increase the presence of women, with a special focus on women of color, in the upper ranks of mathematical science. The most recent initiative is the EDGE Program (Enhancing Diversity in Graduate Education), which addresses this challenge by attempting to decrease the loss of talent from U.S. graduate programs. To this end, the program provides structures that help women make successful transitions from undergraduate into graduate mathematics programs, redirect or refocus their ambitions when programs are inappropriate or unsuitable, and, ultimately, enable them to "accumulate advantages" that will empower them and foster success in their careers. A broader goal of this program is to diversify the mathematics community by creating models for mathematics programs that allow people from all backgrounds and cultures to thrive, advance, and contribute to the profession.

Microwave Brightness Of Land Surfaces From Outer Space

NASA Technical Reports Server (NTRS)

Kerr, Yann H.; Njoku, Eni G.

1991-01-01

Mathematical model approximates microwave radiation emitted by land surfaces traveling to microwave radiometer in outer space. Applied to measurements made by Scanning Multichannel Microwave Radiometer (SMMR). Developed for interpretation of microwave imagery of Earth to obtain distributions of various chemical, physical, and biological characteristics across its surface. Intended primarily for use in mapping moisture content of soil and fraction of Earth covered by vegetation. Advanced Very-High-Resolution Radiometer (AVHRR), provides additional information on vegetative cover, thereby making possible retrieval of soil-moisture values from SMMR measurements. Possible to monitor changes of land surface during intervals of 5 to 10 years, providing significant data for mathematical models of evolution of climate.

Advanced High School Biology in an Era of Rapid Change: A Summary of the Biology Panel Report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

ERIC Educational Resources Information Center

Wood, William B.

2002-01-01

A recently released National Research Council (NRC) report, "Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools", evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study,…

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

PubMed

Agur, Zvia; Elishmereni, Moran; Kheifetz, Yuri

2014-01-01

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

Some observations on the interdigitation of advances in medical science and mathematics.

PubMed

Glamore, Michael James; West, James L; O'leary, James Patrick

2013-12-01

The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.

Resampling and Distribution of the Product Methods for Testing Indirect Effects in Complex Models

ERIC Educational Resources Information Center

Williams, Jason; MacKinnon, David P.

2008-01-01

Recent advances in testing mediation have found that certain resampling methods and tests based on the mathematical distribution of 2 normal random variables substantially outperform the traditional "z" test. However, these studies have primarily focused only on models with a single mediator and 2 component paths. To address this limitation, a…

Models of determining deformations

NASA Astrophysics Data System (ADS)

Gladilin, V. N.

2016-12-01

In recent years, a lot of functions designed to determine deformation values that occur mostly as a result of settlement of structures and industrial equipment. Some authors suggest such advanced mathematical functions approximating deformations as general methods for the determination of deformations. The article describes models of deformations as physical processes. When comparing static, cinematic and dynamic models, it was found that the dynamic model reflects the deformation of structures and industrial equipment most reliably.

A Mathematics Software Database Update.

ERIC Educational Resources Information Center

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Innovations in Science and Mathematics Education: Advanced Designs for Technologies of Learning.

ERIC Educational Resources Information Center

Jacobson, Michael J., Ed.; Kozma, Robert B., Ed.

This collection of essays consists of current work that addresses the challenge not just to put the newest technologies in schools, but to identify advanced ways to design and use these new technologies to advance learning. These essays are intended for science and mathematics educators, educational and cognitive researchers, instructional…

Highlights from TIMSS and TIMSS Advanced 2015: Mathematics and Science Achievement of U.S. Students in Grades 4 and 8 and in Advanced Courses at the End of High School in an International Context. NCES 2017-002

ERIC Educational Resources Information Center

Stephens, Maria; Landeros, Katherine; Perkins, Robert; Tang, Judy H.

2016-01-01

The Trends in International Mathematics and Science Study (TIMSS) 2015 is the sixth administration of this international comparative study since 1995 when first administered. TIMSS is used to compare over time the mathematics and science knowledge and skills of fourth- and eighth-graders. TIMSS is designed to align broadly with mathematics and…

Effects of Advance Organiser Strategy during Instruction on Secondary School Students' Mathematics Achievement in Kenya's Nakuru District

ERIC Educational Resources Information Center

Githua, Bernard N.; Nyabwa, Rachel Angela

2008-01-01

Students have continued to perform poorly in KCSE examinations in certain mathematics topics taught in secondary schools in Kenya. One such topic is commercial arithmetic. Successful teaching of mathematics depends partly on correct use of teaching methods in classroom settings. This study sought to examine how the use of advance organisers during…

Factors Contributing to Rural High School Students' Participation in Advanced Mathematics Courses. Working Paper No. 34

ERIC Educational Resources Information Center

Anderson, Rick

2006-01-01

The focus of this paper is a group of rural high school students and the factors that contributed to their participation in mathematics classes beyond those minimally required for high school graduation. The author follows Gutierrez (2002) in referring to participation as course taking, particularly in elective and advanced mathematics classes.…

Gender Differences in the Effects of a Utility-Value Intervention to Help Parents Motivate Adolescents in Mathematics and Science

ERIC Educational Resources Information Center

Rozek, Christopher S.; Hyde, Janet S.; Svoboda, Ryan C.; Hulleman, Chris S.; Harackiewicz, Judith M.

2015-01-01

A foundation in science, technology, engineering, and mathematics (STEM) education is critical for students' college and career advancement, but many U.S. students fail to take advanced mathematics and science classes in high school. Research has neglected the potential role of parents in enhancing students' motivation for pursuing STEM courses.…

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

An implementation framework for wastewater treatment models requiring a minimum programming expertise.

PubMed

Rodríguez, J; Premier, G C; Dinsdale, R; Guwy, A J

2009-01-01

Mathematical modelling in environmental biotechnology has been a traditionally difficult resource to access for researchers and students without programming expertise. The great degree of flexibility required from model implementation platforms to be suitable for research applications restricts their use to programming expert users. More user friendly software packages however do not normally incorporate the necessary flexibility for most research applications. This work presents a methodology based on Excel and Matlab-Simulink for both flexible and accessible implementation of mathematical models by researchers with and without programming expertise. The models are almost fully defined in an Excel file in which the names and values of the state variables and parameters are easily created. This information is automatically processed in Matlab to create the model structure and almost immediate model simulation, after only a minimum Matlab code definition, is possible. The framework proposed also provides programming expert researchers with a highly flexible and modifiable platform on which to base more complex model implementations. The method takes advantage of structural generalities in most mathematical models of environmental bioprocesses while enabling the integration of advanced elements (e.g. heuristic functions, correlations). The methodology has already been successfully used in a number of research studies.

Advanced Math? Write!

ERIC Educational Resources Information Center

Brandenburg, Sister M. Luka

2002-01-01

High-school mathematics teacher in Rock Island, Illinois, describes plan for using writing assignment to improve student understanding of advanced mathematics. Plan includes the following elements: Start small, be firm with students, make writing assignments count, and inform colleagues. (PKP)

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.

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

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

NASA Astrophysics Data System (ADS)

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

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

An Empirical Investigation of Differences between Mathematics Specialists and Non-Specialists at the High School Level in Cyprus: A Logistic Regression Approach

ERIC Educational Resources Information Center

Papanastasiou, Elena C.; Zembylas, Michalinos

2006-01-01

The data obtained from high-school seniors for the Third International Mathematics and Science Study (TIMSS) for the country of Cyprus appear to be contradictory. Although Cypriot students did not perform well in mathematics in elementary school, middle school, and in the non-advanced sectors of high school, students in advanced mathematics…

Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

ERIC Educational Resources Information Center

Hillman, Thomas

2014-01-01

This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey

ERIC Educational Resources Information Center

Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith

2016-01-01

We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…

Three-dimensional ray-tracing model for the study of advanced refractive errors in keratoconus.

PubMed

Schedin, Staffan; Hallberg, Per; Behndig, Anders

2016-01-20

We propose a numerical three-dimensional (3D) ray-tracing model for the analysis of advanced corneal refractive errors. The 3D modeling was based on measured corneal elevation data by means of Scheimpflug photography. A mathematical description of the measured corneal surfaces from a keratoconus (KC) patient was used for the 3D ray tracing, based on Snell's law of refraction. A model of a commercial intraocular lens (IOL) was included in the analysis. By modifying the posterior IOL surface, it was shown that the imaging quality could be significantly improved. The RMS values were reduced by approximately 50% close to the retina, both for on- and off-axis geometries. The 3D ray-tracing model can constitute a basis for simulation of customized IOLs that are able to correct the advanced, irregular refractive errors in KC.

Advanced scatter search approach and its application in a sequencing problem of mixed-model assembly lines in a case company

NASA Astrophysics Data System (ADS)

Liu, Qiong; Wang, Wen-xi; Zhu, Ke-ren; Zhang, Chao-yong; Rao, Yun-qing

2014-11-01

Mixed-model assembly line sequencing is significant in reducing the production time and overall cost of production. To improve production efficiency, a mathematical model aiming simultaneously to minimize overtime, idle time and total set-up costs is developed. To obtain high-quality and stable solutions, an advanced scatter search approach is proposed. In the proposed algorithm, a new diversification generation method based on a genetic algorithm is presented to generate a set of potentially diverse and high-quality initial solutions. Many methods, including reference set update, subset generation, solution combination and improvement methods, are designed to maintain the diversification of populations and to obtain high-quality ideal solutions. The proposed model and algorithm are applied and validated in a case company. The results indicate that the proposed advanced scatter search approach is significant for mixed-model assembly line sequencing in this company.

Vistas in applied mathematics: Numerical analysis, atmospheric sciences, immunology

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

Balakrishnan, A.V.; Dorodnitsyn, A.A.; Lions, J.L.

1986-01-01

Advances in the theory and application of numerical modeling techniques are discussed in papers contributed, primarily by Soviet scientists, on the occasion of the 60th birthday of Gurii I. Marchuk. Topics examined include splitting techniques for computations of industrial flows, the mathematical foundations of the k-epsilon turbulence model, splitting methods for the solution of the incompressible Navier-Stokes equations, the approximation of inhomogeneous hyperbolic boundary-value problems, multigrid methods, and the finite-element approximation of minimal surfaces. Consideration is given to dynamic modeling of moist atmospheres, satellite observations of the earth radiation budget and the problem of energy-active ocean regions, a numerical modelmore » of the biosphere for use with GCMs, and large-scale modeling of ocean circulation. Also included are several papers on modeling problems in immunology.« less

A transformative model for undergraduate quantitative biology education.

PubMed

Usher, David C; Driscoll, Tobin A; Dhurjati, Prasad; Pelesko, John A; Rossi, Louis F; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions.

A Transformative Model for Undergraduate Quantitative Biology Education

PubMed Central

Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions. PMID:20810949

Driven by History: Mathematics Education Reform

ERIC Educational Resources Information Center

Permuth, Steve; Dalzell, Nicole

2013-01-01

The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…

Developing a Network of and for Geometric Reasoning

ERIC Educational Resources Information Center

Mamolo, Ami; Ruttenberg-Rozen, Robyn; Whiteley, Walter

2015-01-01

In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…

On Popular Response to Violence During Insurgencies

DTIC Science & Technology

2012-04-11

function”, Advances in Computational Mathematics 5: 329–359. [5] Deitchman, S. J. (1962), “A Lanchester model of guerrilla warfare,” Operartions Re...Intelligence in Counterinsurgency Operations – A Best Case Scenario”, Operations Research, V. 57, pp 578-585. [11] Lanchester , F. W., (1916), Aircraft in

Advanced computer techniques for inverse modeling of electric current in cardiac tissue

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

Hutchinson, S.A.; Romero, L.A.; Diegert, C.F.

1996-08-01

For many years, ECG`s and vector cardiograms have been the tools of choice for non-invasive diagnosis of cardiac conduction problems, such as found in reentrant tachycardia or Wolff-Parkinson-White (WPW) syndrome. Through skillful analysis of these skin-surface measurements of cardiac generated electric currents, a physician can deduce the general location of heart conduction irregularities. Using a combination of high-fidelity geometry modeling, advanced mathematical algorithms and massively parallel computing, Sandia`s approach would provide much more accurate information and thus allow the physician to pinpoint the source of an arrhythmia or abnormal conduction pathway.

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Origins of the brain networks for advanced mathematics in expert mathematicians

PubMed Central

Amalric, Marie; Dehaene, Stanislas

2016-01-01

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124

Origins of the brain networks for advanced mathematics in expert mathematicians.

PubMed

Amalric, Marie; Dehaene, Stanislas

2016-05-03

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

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

PubMed

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

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

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

NASA Technical Reports Server (NTRS)

Clayton, Joseph P.; Tinker, Michael L.

1991-01-01

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

Advanced Multi-Physics (AMP)

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

Philip, Bobby

2012-06-01

The Advanced Multi-Physics (AMP) code, in its present form, will allow a user to build a multi-physics application code for existing mechanics and diffusion operators and extend them with user-defined material models and new physics operators. There are examples that demonstrate mechanics, thermo-mechanics, coupled diffusion, and mechanical contact. The AMP code is designed to leverage a variety of mathematical solvers (PETSc, Trilinos, SUNDIALS, and AMP solvers) and mesh databases (LibMesh and AMP) in a consistent interchangeable approach.

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.

Encouraging Young Women to Stay in the Mathematics Pipeline: Mathematics Camps for Young Women

ERIC Educational Resources Information Center

Chacon, Paul; Soto-Johnson, Hortensia

2003-01-01

For two summers, week-long residential mathematics programs were held for high school women, with the primary goal of encouraging them to continue their study of mathematics. The activities were designed to rekindle their excitement about mathematics and to support the idea that women should learn advanced mathematics. This paper reports the…

Advanced Mathematical Thinking and Students' Mathematical Learning: Reflection from Students' Problem-Solving in Mathematics Classroom

ERIC Educational Resources Information Center

Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree

2016-01-01

Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

Advanced Mathematical Modeling of Sonar-Induced Bubble Growth and Coalescence in Humans and Marine Mammals

DTIC Science & Technology

2008-09-01

under high amplitude acoustic excitation, and which explicitly accounts for mass flux across the bubble wall. The thermometric conductivity Xg of the...where Kgo is the thermal conductivity at the reference temperature Tg0. Introducing the reference thermometric conductivity for a gas with reference

76 FR 6795 - Statement of Organization, Functions, and Delegations of Authority; Office of the National...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-02-08

... Coordinator; (2) applies research methodologies to perform evaluation studies of health information technology grant programs; and, (3) applies advanced mathematical or quantitative modeling to the U.S. health care... remaining items in the paragraph accordingly: ``(1) Applying research methodologies to perform evaluation...

Software Partitioning Schemes for Advanced Simulation Computer Systems. Final Report.

ERIC Educational Resources Information Center

Clymer, S. J.

Conducted to design software partitioning techniques for use by the Air Force to partition a large flight simulator program for optimal execution on alternative configurations, this study resulted in a mathematical model which defines characteristics for an optimal partition, and a manually demonstrated partitioning algorithm design which…

Mathematical models for the early detection and treatment of colorectal cancer.

PubMed

Harper, P R; Jones, S K

2005-05-01

Colorectal cancer is a major cause of death for men and women in the Western world. When the cancer is detected through an awareness of the symptoms by a patient, typically it is at an advanced stage. It is possible to detect cancer at an early stage through screening and the marked differences in survival for early and late stages provide the incentive for the primary prevention or early detection of colorectal cancer. This paper considers mathematical models for colorectal cancer screening together with models for the treatment of patients. Illustrative results demonstrate that detailed attention to the processes involved in diseases, interventions and treatment enable us to combine data and expert knowledge from various sources. Thus a detailed operational model is a very useful tool in helping to make decisions about screening at national and local levels.

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.

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

NASA Astrophysics Data System (ADS)

Paniconi, Claudio; Putti, Mario

2015-09-01

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

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

TIMSS Advanced 2015 and Advanced Placement Calculus & Physics. A Framework Analysis. Research in Review 2016-1

ERIC Educational Resources Information Center

Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele

2016-01-01

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

Using explanatory crop models to develop simple tools for Advanced Life Support system studies

NASA Technical Reports Server (NTRS)

Cavazzoni, J.

2004-01-01

System-level analyses for Advanced Life Support require mathematical models for various processes, such as for biomass production and waste management, which would ideally be integrated into overall system models. Explanatory models (also referred to as mechanistic or process models) would provide the basis for a more robust system model, as these would be based on an understanding of specific processes. However, implementing such models at the system level may not always be practicable because of their complexity. For the area of biomass production, explanatory models were used to generate parameters and multivariable polynomial equations for basic models that are suitable for estimating the direction and magnitude of daily changes in canopy gas-exchange, harvest index, and production scheduling for both nominal and off-nominal growing conditions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Career Advancement Outcomes in Academic Science, Technology, Engineering and Mathematics (STEM): Gender, Mentoring Resources, and Homophily

NASA Astrophysics Data System (ADS)

Lee, Sang Eun

This dissertation examines gender differences in career advancement outcomes among academic science, technology, engineering and mathematics (STEM) scientists. In particular, this research examines effects of gender, PhD advisors and postdoctoral supervisors mentoring resources and gender homophily in the mentoring dyads on the career advancement outcomes at early career stages. Female academic scientists have disadvantages in the career progress in the academic STEM. They tend to fall behind throughout their career paths and to leave the field compared to their male colleagues. Researchers have found that gender differences in the career advancement are shaped by gender-biased evaluations derived from gender stereotypes. Other studies demonstrate the positive impacts of mentoring and gender homophily in the mentoring dyads. To add greater insights to the current findings of female academic scientists' career disadvantages, this dissertation investigates comprehensive effects of gender, mentoring, and gender homophily in the mentoring dyads on female scientists' career advancement outcomes in academic science. Based on the Status Characteristics Theory, the concept of mentoring, Social Capital Theory, and Ingroup Bias Theory, causal path models are developed to test direct and indirect effects of gender, mentoring resources, and gender homophily on STEM faculty's career advancement. The research models were tested using structural equation modeling (SEM) with data collected from a national survey, funded by the National Science Foundation, completed in 2011 by tenured and tenure-track academic STEM faculty from higher education institutions in the United States. Findings suggest that there is no gender difference in career advancement controlling for mentoring resources and gender homophily in the mentoring dyads and other factors including research productivity and domestic caregiving responsibilities. Findings also show that the positive relationship between gender homophily in mentoring dyads and the reception of the mentoring resources, especially regarding providing help on career development and research collaboration, lead to enhanced early stage career advancement. Insights from the findings contribute both to theoretical understandings of the overall effects of gender, mentoring, and gender homophily in the mentoring dyads on female academic scientists' career advancement at early career stages and to provide evidence of positive effects of same-gender mentoring dyads to universities.

Business Model Evaluation for an Advanced Multimedia Service Portfolio

NASA Astrophysics Data System (ADS)

Pisciella, Paolo; Zoric, Josip; Gaivoronski, Alexei A.

In this paper we analyze quantitatively a business model for the collaborative provision of an advanced mobile data service portfolio composed of three multimedia services: Video on Demand, Internet Protocol Television and User Generated Content. We provide a description of the provision system considering the relation occurring between tecnical aspects and business aspects for each agent providing the basic multimedia service. Such a techno-business analysis is then projected into a mathematical model dealing with the problem of the definition of incentives between the different agents involved in a collaborative service provision. Through the implementation of this model we aim at shaping the behaviour of each of the contributing agents modifying the level of profitability that the Service Portfolio yields to each of them.

Incentivizing advanced mathematics study at upper secondary level: the case of bonus points in Ireland

NASA Astrophysics Data System (ADS)

Treacy, Páraic Thomas

2018-04-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant increase in the number of students studying upper secondary mathematics at Higher Level. However, thematic analysis of interviews with experienced upper secondary mathematics examiners and exploration of mathematics diagnostic test data outlined in this paper suggest that the difficulty of the Higher Level upper secondary mathematics final examination in Ireland has reduced since the introduction of the bonus points initiative. The sharp increase in students attempting this examination coupled with a policy of maintaining a consistent proportion of students achieving passing grades was identified as a key reason for this possible reduction in standards.

32 CFR 901.5 - Academic examination requirements.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Level 1 (Standard) Mathematics or Level II (Intensive) Mathematics. (Level 1 recommended for candidates without advanced high school mathematics.) (b) ACT. Candidates who elect to use the ACT tests must take the complete battery of tests: English, mathematics, social studies, and natural sciences. ...

Teacher Leaders: Advancing Mathematics Learning

ERIC Educational Resources Information Center

Kinzer, Cathy J.; Rincón, Mari; Ward, Jana; Rincón, Ricardo; Gomez, Lesli

2014-01-01

Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…

Indicators of Multiplicative Reasoning among Fourth Grade Students

ERIC Educational Resources Information Center

Carrier, James A.

2010-01-01

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

Integrative approaches for modeling regulation and function of the respiratory system.

PubMed

Ben-Tal, Alona; Tawhai, Merryn H

2013-01-01

Mathematical models have been central to understanding the interaction between neural control and breathing. Models of the entire respiratory system-which comprises the lungs and the neural circuitry that controls their ventilation-have been derived using simplifying assumptions to compartmentalize each component of the system and to define the interactions between components. These full system models often rely-through necessity-on empirically derived relationships or parameters, in addition to physiological values. In parallel with the development of whole respiratory system models are mathematical models that focus on furthering a detailed understanding of the neural control network, or of the several functions that contribute to gas exchange within the lung. These models are biophysically based, and rely on physiological parameters. They include single-unit models for a breathing lung or neural circuit, through to spatially distributed models of ventilation and perfusion, or multicircuit models for neural control. The challenge is to bring together these more recent advances in models of neural control with models of lung function, into a full simulation for the respiratory system that builds upon the more detailed models but remains computationally tractable. This requires first understanding the mathematical models that have been developed for the respiratory system at different levels, and which could be used to study how physiological levels of O2 and CO2 in the blood are maintained. Copyright © 2013 Wiley Periodicals, Inc.

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets — Part A: Mathematical Model and the Influence of Dimple Radius

NASA Astrophysics Data System (ADS)

Ming, Tingzhen; Cai, Cunjin; Yang, Wei; Shen, Wenqing; Gan, Ting

2018-06-01

With increasing heat fluxes caused by electronic components, dimples have attracted wide attention by researchers and have been applied to microchannel heat sink in modern advanced cooling technologies. In this work, the combination of dimples, impinging jets and microchannel heat sink was proposed to improve the heat transfer performance on a cooling surface with a constant heat flux 500 W/cm2. A mathematical model was advanced for numerically analyzing the fluid flow and heat transfer characteristics of a microchannel heat sink with impinging jets and dimples (MHSIJD), and the velocity distribution, pressure drop, and thermal performance of MHSIJD were analyzed by varying the radii of dimples. The results showed that the combination of dimples and MHSIJ can achieve excellent heat transfer performance; for the MHSIJD model in this work, the maximum and average temperatures can be as low as 320 K and 305 K, respectively when mass flow rate is 30 g/s; when dimple radius is larger than 0.195 mm, both the heat transfer coefficient and the overall performance h/ΔP of MHSIJD are higher than those of MHSIJ.

Clinical Assessment in Mathematics: Learning the Craft.

ERIC Educational Resources Information Center

Hunting, Robert P.; Doig, Brian A.

1997-01-01

Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…

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

PubMed Central

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

2016-01-01

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

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

PubMed

Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K; Gudmand-Hoeyer, Johanne; Ellervik, Christina; Skov, Vibe; Kjær, Lasse; Pallisgaard, Niels; Kruse, Torben A; Thomassen, Mads; Troelsen, Jesper; Hasselbalch, Hans Carl; Ottesen, Johnny T

2017-01-01

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

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

ERIC Educational Resources Information Center

Natour, Denise M.

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

TIMMS Advanced 2015 Assessment Frameworks

ERIC Educational Resources Information Center

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

It is critical for countries to ensure that capable secondary school students receive further preparation in advanced mathematics and science, so that they are ready to enter challenging university-level studies that prepare them for careers in science, technology, engineering, and mathematics (STEM) fields. This group of students will become the…

Advancing K-8 Teachers' STEM Education for Teaching Interdisciplinary Science and Mathematics with Technologies

ERIC Educational Resources Information Center

Niess, Margaret; Gillow-Wiles, Henry

2013-01-01

This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…

Explorations with 142857: Connecting the Elementary with the Advanced

ERIC Educational Resources Information Center

Flores, Alfinio

2008-01-01

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

Cookies and Pi

ERIC Educational Resources Information Center

Dempsey, Michael

2009-01-01

If students are in an advanced mathematics class, then at some point they enjoyed mathematics and looked forward to learning and practicing it. There is no reason that this passion and enjoyment should ever be lost because the subject becomes more difficult or rigorous. This author, who teaches advanced precalculus to high school juniors,…

Crypt dynamics and colorectal cancer: advances in mathematical modelling.

PubMed

van Leeuwen, I M M; Byrne, H M; Jensen, O E; King, J R

2006-06-01

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I.

PubMed

Afenya, Evans K; Ouifki, Rachid; Camara, Baba I; Mundle, Suneel D

2016-04-01

Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture. Copyright © 2016 Elsevier Inc. All rights reserved.

Advances in electrophoretic separations

NASA Technical Reports Server (NTRS)

Snyder, R. S.; Rhodes, P. H.

1984-01-01

Free fluid electrophoresis is described using laboratory and space experiments combined with extensive mathematical modeling. Buoyancy driven convective flows due to thermal and concentration gradients are absent in the reduced gravity environment of space. The elimination of convection in weightlessness offers possible improvements in electrophoresis and other separation methods which occur in fluid media. The mathematical modeling suggests new ways of doing electrophoresis in space and explains various phenomena observed during past experiments. The extent to which ground based separation techniques are limited by gravity induced convection is investigated and space experiments are designed to evaluate specific characteristics of the fluid/particle environment. A series of experiments are proposed that require weightlessness and apparatus is developed that can be used to carry out these experiments in the near future.

Exemplarity in Mathematics Education: from a Romanticist Viewpoint to a Modern Hermeneutical One

NASA Astrophysics Data System (ADS)

Patronis, Tasos; Spanos, Dimitris

2013-08-01

This paper proposes a setting of exemplarity different from the already known one, which is basically a Romanticist philosophical setting. Our general aim is to describe and explore the nature of some exemplary themes and interpretive models in advanced mathematics teaching and learning. In order to do so, we move from Romanticism towards the viewpoint of Modern Hermeneutics, by applying ideas appearing mainly in Gadamer and Ricoeur. We use this new setting as a philosophical framework, to interpret some results from two didactical research studies that have already appeared on infinitesimals.

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks.

PubMed

Deng, Zhimin; Tian, Tianhai

2014-07-29

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions. The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Teaching Undergraduate Mathematics in Interactive Groups: How Does It Fit with Students' Learning?

ERIC Educational Resources Information Center

Sheryn, Louise; Ell, Fiona

2014-01-01

Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in…

An Effort to Close Achievement Gaps at Scale through Self-Affirmation

ERIC Educational Resources Information Center

Borman, Geoffrey D.; Grigg, Jeffrey

2013-01-01

This study addresses closing the academic performance gaps between African American and Latino students and their White counterparts, and between girls and boys in mathematics. Of the various models and theories of these social inequalities that have been advanced in literature, one particularly compelling line of research concerns the idea of…

Note Launchers: Promoting Active Reading of Mathematics Textbooks

ERIC Educational Resources Information Center

Helms, Josh W.; Helms, Kimberly Turner

2010-01-01

Note launchers, an instructor-designed reading guide, model how to select, decide, and focus upon what textbook material is important to learn. Reading guides are specially-designed study aids that can steer students through difficult parts of assigned readings (Bean, 1996) while encouraging advance preparation. As an example of a reading guide,…

Role Models and Informal STEM-Related Activities Positively Impact Female Interest in STEM

ERIC Educational Resources Information Center

Weber, Katherine

2011-01-01

The United States' economy depends greatly on a citizenry that possesses scientific and technical skills within the fields of science, technology, engineering, and mathematics (STEM) for economic growth. In the past few decades, technological advancement has created a demand for a highly skilled workforce possessing scientific and mathematical…

DRS: Derivational Reasoning System

NASA Technical Reports Server (NTRS)

Bose, Bhaskar

1995-01-01

The high reliability requirements for airborne systems requires fault-tolerant architectures to address failures in the presence of physical faults, and the elimination of design flaws during the specification and validation phase of the design cycle. Although much progress has been made in developing methods to address physical faults, design flaws remain a serious problem. Formal methods provides a mathematical basis for removing design flaws from digital systems. DRS (Derivational Reasoning System) is a formal design tool based on advanced research in mathematical modeling and formal synthesis. The system implements a basic design algebra for synthesizing digital circuit descriptions from high level functional specifications. DRS incorporates an executable specification language, a set of correctness preserving transformations, verification interface, and a logic synthesis interface, making it a powerful tool for realizing hardware from abstract specifications. DRS integrates recent advances in transformational reasoning, automated theorem proving and high-level CAD synthesis systems in order to provide enhanced reliability in designs with reduced time and cost.

A visiting scientist program in atmospheric sciences for the Goddard Space Flight Center

NASA Technical Reports Server (NTRS)

Davis, M. H.

1989-01-01

A visiting scientist program was conducted in the atmospheric sciences and related areas at the Goddard Laboratory for Atmospheres. Research was performed in mathematical analysis as applied to computer modeling of the atmospheres; development of atmospheric modeling programs; analysis of remotely sensed atmospheric, surface, and oceanic data and its incorporation into atmospheric models; development of advanced remote sensing instrumentation; and related research areas. The specific research efforts are detailed by tasks.

Integrated Formulation of Beacon-Based Exception Analysis for Multimissions

NASA Technical Reports Server (NTRS)

Mackey, Ryan; James, Mark; Park, Han; Zak, Mickail

2003-01-01

Further work on beacon-based exception analysis for multimissions (BEAM), a method of real-time, automated diagnosis of a complex electromechanical systems, has greatly expanded its capability and suitability of application. This expanded formulation, which fully integrates physical models and symbolic analysis, is described. The new formulation of BEAM expands upon previous advanced techniques for analysis of signal data, utilizing mathematical modeling of the system physics, and expert-system reasoning,

Mathematical model for lift/cruise fan V/STOL aircraft simulator programming data

NASA Technical Reports Server (NTRS)

Bland, M. P.; Fajfar, B.; Konsewicz, R. K.

1976-01-01

Simulation data are reported for the purpose of programming the flight simulator for advanced aircraft for tests of the lift/cruise fan V/STOL Research Technology Aircraft. These simulation tests are to provide insight into problem areas which are encountered in operational use of the aircraft. A mathematical model is defined in sufficient detail to represent all the necessary pertinent aircraft and system characteristics. The model includes the capability to simulate two basic versions of an aircraft propulsion system: (1) the gas coupled configuration which uses insulated air ducts to transmit power between gas generators and fans in the form of high energy engine exhaust and (2) the mechanically coupled power system which uses shafts, clutches, and gearboxes for power transmittal. Both configurations are modeled such that the simulation can include vertical as well as rolling takeoff and landing, hover, powered lift flight, aerodynamic flight, and the transition between powered lift and aerodynamic flight.

Big data to smart data in Alzheimer's disease: Real-world examples of advanced modeling and simulation.

PubMed

Haas, Magali; Stephenson, Diane; Romero, Klaus; Gordon, Mark Forrest; Zach, Neta; Geerts, Hugo

2016-09-01

Many disease-modifying clinical development programs in Alzheimer's disease (AD) have failed to date, and development of new and advanced preclinical models that generate actionable knowledge is desperately needed. This review reports on computer-based modeling and simulation approach as a powerful tool in AD research. Statistical data-analysis techniques can identify associations between certain data and phenotypes, such as diagnosis or disease progression. Other approaches integrate domain expertise in a formalized mathematical way to understand how specific components of pathology integrate into complex brain networks. Private-public partnerships focused on data sharing, causal inference and pathway-based analysis, crowdsourcing, and mechanism-based quantitative systems modeling represent successful real-world modeling examples with substantial impact on CNS diseases. Similar to other disease indications, successful real-world examples of advanced simulation can generate actionable support of drug discovery and development in AD, illustrating the value that can be generated for different stakeholders. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Mathematics of gravitational lensing: multiple imaging and magnification

NASA Astrophysics Data System (ADS)

Petters, A. O.; Werner, M. C.

2010-09-01

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.

Aircraft geometry verification with enhanced computer generated displays

NASA Technical Reports Server (NTRS)

Cozzolongo, J. V.

1982-01-01

A method for visual verification of aerodynamic geometries using computer generated, color shaded images is described. The mathematical models representing aircraft geometries are created for use in theoretical aerodynamic analyses and in computer aided manufacturing. The aerodynamic shapes are defined using parametric bi-cubic splined patches. This mathematical representation is then used as input to an algorithm that generates a color shaded image of the geometry. A discussion of the techniques used in the mathematical representation of the geometry and in the rendering of the color shaded display is presented. The results include examples of color shaded displays, which are contrasted with wire frame type displays. The examples also show the use of mapped surface pressures in terms of color shaded images of V/STOL fighter/attack aircraft and advanced turboprop aircraft.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology.

PubMed

Koutinas, Michalis; Kiparissides, Alexandros; Pistikopoulos, Efstratios N; Mantalaris, Athanasios

2012-01-01

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology

PubMed Central

Koutinas, Michalis; Kiparissides, Alexandros; Pistikopoulos, Efstratios N.; Mantalaris, Athanasios

2013-01-01

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals. PMID:24688682

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

NASA Astrophysics Data System (ADS)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-10-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

An advanced model framework for solid electrolyte intercalation batteries.

PubMed

Landstorfer, Manuel; Funken, Stefan; Jacob, Timo

2011-07-28

Recent developments of solid electrolytes, especially lithium ion conductors, led to all solid state batteries for various applications. In addition, mathematical models sprout for different electrode materials and battery types, but are missing for solid electrolyte cells. We present a mathematical model for ion flux in solid electrolytes, based on non-equilibrium thermodynamics and functional derivatives. Intercalated ion diffusion within the electrodes is further considered, allowing the computation of the ion concentration at the electrode/electrolyte interface. A generalized Frumkin-Butler-Volmer equation describes the kinetics of (de-)intercalation reactions and is here extended to non-blocking electrodes. Using this approach, numerical simulations were carried out to investigate the space charge region at the interface. Finally, discharge simulations were performed to study different limitations of an all solid state battery cell. This journal is © the Owner Societies 2011

The Effectiveness of Technology Integration in a Metropolitan Elementary Mathematics Program: Mad Dog Math

ERIC Educational Resources Information Center

Cohen, Miriam

2012-01-01

The outcome of American students' performances during international comparisons consistently scoring inadequately in mathematics exposes the crisis of deficient mathematics achievement thus causing deep concerns. Learners who acquire a strong theoretical foundation in mathematics at the primary level thrived later in more advanced level…

Lessons from the Past Look to the Future.

ERIC Educational Resources Information Center

Howden, Hilde

2000-01-01

Technological advances and many other changes in society change how and what students learn. Indicates the need to learn lessons from the past in order to be more mathematically literate and broaden the mathematics curriculum to a mathematical sciences curriculum that incorporates 21st century mathematics. (Contains 14 references.) (ASK)

Enhancing Mathematical Problem Solving for Secondary Students with or at Risk of Learning Disabilities: A Literature Review

ERIC Educational Resources Information Center

Hwang, Jiwon; Riccomini, Paul J.

2016-01-01

Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…

Mathematics in Literature and Cinema: An Interdisciplinary Course

ERIC Educational Resources Information Center

Chabrán, H. Rafael; Kozek, Mark

2016-01-01

We describe our team-taught, interdisciplinary course "Numb3rs in Lett3rs & Fi1ms: Mathematics in Literature and Cinema," which explores mathematics in the context of modern literature and cinema. Our goal with this course is to advance collaborations between mathematics and the written/theatre-based creative arts.

Evidence of the Need to Prepare Prospective Teachers to Engage in Mathematics Consultations

ERIC Educational Resources Information Center

van Ingen, Sarah; Eskelson, Samuel L.; Allsopp, David

2016-01-01

The mathematics consultation represents a powerful opportunity for mathematics teachers to leverage the knowledge base of special education professionals to advance equity for students with special education needs. Yet, most teacher preparation programs do not specifically prepare prospective teachers to engage in mathematics-specific…

A Simulation Study Comparing Incineration and Composting in a Mars-Based Advanced Life Support System

NASA Technical Reports Server (NTRS)

Hogan, John; Kang, Sukwon; Cavazzoni, Jim; Levri, Julie; Finn, Cory; Luna, Bernadette (Technical Monitor)

2000-01-01

The objective of this study is to compare incineration and composting in a Mars-based advanced life support (ALS) system. The variables explored include waste pre-processing requirements, reactor sizing and buffer capacities. The study incorporates detailed mathematical models of biomass production and waste processing into an existing dynamic ALS system model. The ALS system and incineration models (written in MATLAB/SIMULINK(c)) were developed at the NASA Ames Research Center. The composting process is modeled using first order kinetics, with different degradation rates for individual waste components (carbohydrates, proteins, fats, cellulose and lignin). The biomass waste streams are generated using modified "Eneray Cascade" crop models, which use light- and dark-cycle temperatures, irradiance, photoperiod, [CO2], planting density, and relative humidity as model inputs. The study also includes an evaluation of equivalent system mass (ESM).

Switching moving boundary models for two-phase flow evaporators and condensers

NASA Astrophysics Data System (ADS)

Bonilla, Javier; Dormido, Sebastián; Cellier, François E.

2015-03-01

The moving boundary method is an appealing approach for the design, testing and validation of advanced control schemes for evaporators and condensers. When it comes to advanced control strategies, not only accurate but fast dynamic models are required. Moving boundary models are fast low-order dynamic models, and they can describe the dynamic behavior with high accuracy. This paper presents a mathematical formulation based on physical principles for two-phase flow moving boundary evaporator and condenser models which support dynamic switching between all possible flow configurations. The models were implemented in a library using the equation-based object-oriented Modelica language. Several integrity tests in steady-state and transient predictions together with stability tests verified the models. Experimental data from a direct steam generation parabolic-trough solar thermal power plant is used to validate and compare the developed moving boundary models against finite volume models.

Theoretical models for supercritical fluid extraction.

PubMed

Huang, Zhen; Shi, Xiao-Han; Jiang, Wei-Juan

2012-08-10

For the proper design of supercritical fluid extraction processes, it is essential to have a sound knowledge of the mass transfer mechanism of the extraction process and the appropriate mathematical representation. In this paper, the advances and applications of kinetic models for describing supercritical fluid extraction from various solid matrices have been presented. The theoretical models overviewed here include the hot ball diffusion, broken and intact cell, shrinking core and some relatively simple models. Mathematical representations of these models have been in detail interpreted as well as their assumptions, parameter identifications and application examples. Extraction process of the analyte solute from the solid matrix by means of supercritical fluid includes the dissolution of the analyte from the solid, the analyte diffusion in the matrix and its transport to the bulk supercritical fluid. Mechanisms involved in a mass transfer model are discussed in terms of external mass transfer resistance, internal mass transfer resistance, solute-solid interactions and axial dispersion. The correlations of the external mass transfer coefficient and axial dispersion coefficient with certain dimensionless numbers are also discussed. Among these models, the broken and intact cell model seems to be the most relevant mathematical model as it is able to provide realistic description of the plant material structure for better understanding the mass-transfer kinetics and thus it has been widely employed for modeling supercritical fluid extraction of natural matters. Copyright © 2012 Elsevier B.V. All rights reserved.

Career Advancement Outcomes in Academic Science, Technology, Engineering and Mathematics (STEM): Gender, Mentoring Resources, and Homophily

ERIC Educational Resources Information Center

Lee, Sang Eun

2017-01-01

This dissertation examines gender differences in career advancement outcomes among academic science, technology, engineering and mathematics (STEM) scientists. In particular, this research examines effects of gender, PhD advisors and postdoctoral supervisors mentoring resources and gender homophily in the mentoring dyads on the career advancement…

Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics: Three Large-Scale Studies

ERIC Educational Resources Information Center

Roschelle, Jeremy; Shechtman, Nicole; Tatar, Deborah; Hegedus, Stephen; Hopkins, Bill; Empson, Susan; Knudsen, Jennifer; Gallagher, Lawrence P.

2010-01-01

The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum,…

Strategic Alliance to Advanced Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level

ERIC Educational Resources Information Center

Scarborough, Jule Dee

2004-01-01

This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…

Advanced Mathematics 305--Optional Half Credit. Interim Guide.

ERIC Educational Resources Information Center

Manitoba Dept. of Education, Winnipeg.

This manual outlines an advanced mathematics course for secondary school students in Manitoba (Canada). Included are eight different topics for a total of ten modules, with each module accounting for 18 40-minute periods. Teachers, or teachers and students cooperatively, should select the equivalent of five modules from the eight topics covered.…

Science and Mathematics Advanced Placement Exams: Growth and Achievement over Time

ERIC Educational Resources Information Center

Judson, Eugene

2017-01-01

Rapid growth of Advanced Placement (AP) exams in the last 2 decades has been paralleled by national enthusiasm to promote availability and rigor of science, technology, engineering, and mathematics (STEM). Trends were examined in STEM AP to evaluate and compare growth and achievement. Analysis included individual STEM subjects and disaggregation…

The Equity Education. Fostering the Advancement of Women in the Sciences, Mathematics, and Engineering.

ERIC Educational Resources Information Center

Davis, Cinda-Sue; And Others

This volume includes 10 reports that present findings and recommendations for advancing women in science, mathematics and engineering. Critical issues facing women in these disciplines are addressed, including demographic myths and realities at various educational levels; the educational pipeline for girls and women; involvement in education and…

Fighting Cancer with Mathematics and Viruses.

PubMed

Santiago, Daniel N; Heidbuechel, Johannes P W; Kandell, Wendy M; Walker, Rachel; Djeu, Julie; Engeland, Christine E; Abate-Daga, Daniel; Enderling, Heiko

2017-08-23

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.

Fighting Cancer with Mathematics and Viruses

PubMed Central

Santiago, Daniel N.; Heidbuechel, Johannes P. W.; Kandell, Wendy M.; Walker, Rachel; Djeu, Julie; Abate-Daga, Daniel; Enderling, Heiko

2017-01-01

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments. PMID:28832539

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.

Lessons from sea louse and salmon epidemiology.

PubMed

Groner, Maya L; Rogers, Luke A; Bateman, Andrew W; Connors, Brendan M; Frazer, L Neil; Godwin, Sean C; Krkošek, Martin; Lewis, Mark A; Peacock, Stephanie J; Rees, Erin E; Revie, Crawford W; Schlägel, Ulrike E

2016-03-05

Effective disease management can benefit from mathematical models that identify drivers of epidemiological change and guide decision-making. This is well illustrated in the host-parasite system of sea lice and salmon, which has been modelled extensively due to the economic costs associated with sea louse infections on salmon farms and the conservation concerns associated with sea louse infections on wild salmon. Consequently, a rich modelling literature devoted to sea louse and salmon epidemiology has been developed. We provide a synthesis of the mathematical and statistical models that have been used to study the epidemiology of sea lice and salmon. These studies span both conceptual and tactical models to quantify the effects of infections on host populations and communities, describe and predict patterns of transmission and dispersal, and guide evidence-based management of wild and farmed salmon. As aquaculture production continues to increase, advances made in modelling sea louse and salmon epidemiology should inform the sustainable management of marine resources. © 2016 The Author(s).

Lessons from sea louse and salmon epidemiology

PubMed Central

Rogers, Luke A.; Bateman, Andrew W.; Connors, Brendan M.; Frazer, L. Neil; Godwin, Sean C.; Krkošek, Martin; Lewis, Mark A.; Peacock, Stephanie J.; Rees, Erin E.; Revie, Crawford W.; Schlägel, Ulrike E.

2016-01-01

Effective disease management can benefit from mathematical models that identify drivers of epidemiological change and guide decision-making. This is well illustrated in the host–parasite system of sea lice and salmon, which has been modelled extensively due to the economic costs associated with sea louse infections on salmon farms and the conservation concerns associated with sea louse infections on wild salmon. Consequently, a rich modelling literature devoted to sea louse and salmon epidemiology has been developed. We provide a synthesis of the mathematical and statistical models that have been used to study the epidemiology of sea lice and salmon. These studies span both conceptual and tactical models to quantify the effects of infections on host populations and communities, describe and predict patterns of transmission and dispersal, and guide evidence-based management of wild and farmed salmon. As aquaculture production continues to increase, advances made in modelling sea louse and salmon epidemiology should inform the sustainable management of marine resources. PMID:26880836

The Simulation of a Jumbo Jet Transport Aircraft. Volume 2: Modeling Data

NASA Technical Reports Server (NTRS)

Hanke, C. R.; Nordwall, D. R.

1970-01-01

The manned simulation of a large transport aircraft is described. Aircraft and systems data necessary to implement the mathematical model described in Volume I and a discussion of how these data are used in model are presented. The results of the real-time computations in the NASA Ames Research Center Flight Simulator for Advanced Aircraft are shown and compared to flight test data and to the results obtained in a training simulator known to be satisfactory.

Optimized planning methodologies of ASON implementation

NASA Astrophysics Data System (ADS)

Zhou, Michael M.; Tamil, Lakshman S.

2005-02-01

Advanced network planning concerns effective network-resource allocation for dynamic and open business environment. Planning methodologies of ASON implementation based on qualitative analysis and mathematical modeling are presented in this paper. The methodology includes method of rationalizing technology and architecture, building network and nodal models, and developing dynamic programming for multi-period deployment. The multi-layered nodal architecture proposed here can accommodate various nodal configurations for a multi-plane optical network and the network modeling presented here computes the required network elements for optimizing resource allocation.

Total Quality Management in the Classroom: Applications to University-Level Mathematics.

ERIC Educational Resources Information Center

Williams, Frank

1995-01-01

Describes a Total Quality Management-based system of instruction that is used in a variety of undergraduate mathematics courses. The courses that incorporate this approach include mathematics appreciation, introductory calculus, and advanced applied linear algebra. (DDR)

Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy Patrick; Newton, Charlene

2014-01-01

Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…

For the Technologically Challenged: Four Free Online Tools to Liven up a Mathematics Classroom

ERIC Educational Resources Information Center

Northcote, Maria

2015-01-01

Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students.…

University of Chicago School Mathematics Project 6-12 Curriculum. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2011

2011-01-01

The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world applications, and the use…

Pedagogical Applications from Real Analysis for Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas; Weber, Keith

2017-01-01

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

Learning Mathematics in English at Basic Schools in Ghana: A Benefit or Hindrance?

ERIC Educational Resources Information Center

Fredua-Kwarteng, Eric; Ahia, Francis

2015-01-01

Facilitating effective mathematics learning and higher mathematics achievement have long been recognized as a key to the scientific and technological advancement of the African continent. While the central role that language proficiency plays in mathematics teaching and learning has received an overwhelming research attention in the literature…

An Invitation to the Mathematics of Topological Quantum Computation

NASA Astrophysics Data System (ADS)

Rowell, E. C.

2016-03-01

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials.

Microstructure Engineering in Hot Strip Mills, Part 1 of 2: Integrated mathematical Model

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

J.K. Brimacombe; I.V. Samaraseker; E.B. Hawbolt

1998-09-30

This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evaluation and mechanical properties of steel strip in a hot-strip mill. This achievement results from a join research effort that is part of the American Iron and Steel Institute's (AISI) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American steel makers.

Gender and Course Selection in Upper Secondary Education: Effects of Academic Self-Concept and Intrinsic Value

ERIC Educational Resources Information Center

Nagy, Gabriel; Trautwein, Ulrich; Baumert, Jurgen; Koller, Olaf; Garrett, Jessica

2006-01-01

Predictions about processes linking gender to students' choices of advanced courses were derived from the internal/external frame of reference (I/E) model and expectancy value (EV) theory. The predictions were tested for the domains of mathematics and biology using data from 1,148 students attending academically oriented secondary schools in…

NASA Office of Aeronautics and Space Technology Summer Workshop. Volume 9: Entry technology panel

NASA Technical Reports Server (NTRS)

1975-01-01

An advanced space transportation system heavy lift orbiter, hypersonic atmospheric entry missions, development of an emergency astronaut life boat, and basic research in boundary layer transition are among the topics discussed. Emphasis is placed on the need for space testing and for better mathematical models describing the flow fields around complex structures.

Computational Toxicology as Implemented by the U.S. EPA: Providing High Throughput Decision Support Tools for Screening and Assessing Chemical Exposure, Hazard and Risk

EPA Science Inventory

Computational toxicology is the application of mathematical and computer models to help assess chemical hazards and risks to human health and the environment. Supported by advances in informatics, high-throughput screening (HTS) technologies, and systems biology, the U.S. Environ...

Who Succeeds in STEM Studies? An Analysis of Binghamton University Undergraduate Students

ERIC Educational Resources Information Center

Kokkelenberg, Edward C.; Sinha, Esha

2010-01-01

Using student level data, the characteristics of STEM and Non-STEM students are examined for attributes associated with academic success. We use fixed effects models to analyze the variables' role in attaining graduation and college GPA and find preparation and ability, as evidenced by Advanced Placement course work, mathematical ability, gender,…

Business Partnerships to Advance STEM Education: A Model of Success for the Nation

ERIC Educational Resources Information Center

Diaz-Rubio, Ivette

2013-01-01

In order to best prepare the U.S. workforce, schools need to focus on science, technology, engineering, and mathematics (STEM) education. However, given the current educational climate of reduced school funding, high teacher turnover, and increasing student diversity, the public school system simply cannot do this alone. This is where businesses…

Technologies That Facilitate the Study of Advanced Mathematics by Students Who Are Blind: Teachers' Perspectives

ERIC Educational Resources Information Center

DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.

2015-01-01

This research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advanced mathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of…

Technologies Used in the Study of Advanced Mathematics by Students Who Are Visually Impaired in Classrooms: Teachers' Perspectives

ERIC Educational Resources Information Center

DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.

2015-01-01

Introduction: This research examined the perspectives of teachers of students who are visually impaired regarding the use and effectiveness of high-tech assistive technology purported to assist visually impaired students in advanced mathematics. Methods: The data for this study were collected via a mixed-methods online survey distributed through…

An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

PubMed

Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

2017-04-01

Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Advanced high school biology in an era of rapid change: a summary of the biology panel report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools.

PubMed

Wood, William B

2002-01-01

A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors.

Advanced High School Biology in an Era of Rapid Change: A Summary of the Biology Panel Report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

PubMed Central

2002-01-01

A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors. PMID:12669097

A Standard Kinematic Model for Flight Simulation at NASA Ames

NASA Technical Reports Server (NTRS)

Mcfarland, R. E.

1975-01-01

A standard kinematic model for aircraft simulation exists at NASA-Ames on a variety of computer systems, one of which is used to control the flight simulator for advanced aircraft (FSAA). The derivation of the kinematic model is given and various mathematical relationships are presented as a guide. These include descriptions of standardized simulation subsystems such as the atmospheric turbulence model and the generalized six-degrees-of-freedom trim routine, as well as an introduction to the emulative batch-processing system which enables this facility to optimize its real-time environment.

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

PubMed

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

2014-01-01

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

Mathematical Discovery and "Affect": The "Effect" of Aha! Experiences on Undergraduate Mathematics Students

ERIC Educational Resources Information Center

Liljedahl, Peter G.

2005-01-01

The AHA! experience-the moment of illumination on the heels of lengthy, and seemingly fruitless, intentional effort-has long been the basis for lore in mathematics. Unfortunately, such lore is often restricted to the discussion of these phenomena in the context of great mathematicians and great mathematical advancement. But are such experiences…

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

ERIC Educational Resources Information Center

Garner, Mary L.; Watson, Virginia; Rogers, Beth; Head, Catherine

2017-01-01

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and…

Advancements in Research on Creativity and Giftedness in Mathematics Education: Introduction to the Special Issue

ERIC Educational Resources Information Center

Singer, Florence Mihaela; Sheffield, Linda Jensen; Leikin, Roza

2017-01-01

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and…

Using the Computer Algebra System "Maple" to Generate Research Questions for Pre-Service Teachers in a Capstone Course

ERIC Educational Resources Information Center

Farley, Rosemary Carroll

2013-01-01

At Manhattan College, secondary mathematics education students take a capstone course designed specifically for them. In this course, students revisit important topics in the high school curriculum from a mathematically advanced perspective; incorporating the mathematical knowledge they have attained in their college mathematics classes to an…

Mathematical Creativity: Psychology, Progress and Caveats

ERIC Educational Resources Information Center

Sriraman, Bharath

2017-01-01

The aim of this paper is to provide a concise survey of advances in the study of the psychology of creativity, with an emphasis on literature that is typically not cited in mathematics education. In spite of claims that mathematical creativity is an ill-defined area of inquiry in mathematics education, the literature from psychology can serve as…

Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

Engineering Undergraduates' Views of A-Level Mathematics and Further Mathematics as Preparation for Their Degree

ERIC Educational Resources Information Center

Darlington, Ellie; Bowyer, Jessica

2017-01-01

An ongoing reform programme of the post-16 Advanced "A"-level qualifications in England and Wales means that pre-university mathematics content and assessment will change from 2017. Undergraduate engineering is a subject that relies heavily on mathematics, and applicants to engineering degree programmes in the UK are required to have…

Mathematics in Finance and Economics: Importance of Teaching Higher Order Mathematical Thinking Skills in Finance

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand

2013-01-01

This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes.…

Integrated Modeling of Complex Optomechanical Systems

NASA Astrophysics Data System (ADS)

Andersen, Torben; Enmark, Anita

2011-09-01

Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.

A qualitative study of motivation in Alaska Native Science and Engineering Program (ANSEP) precollege students

NASA Astrophysics Data System (ADS)

Yatchmeneff, Michele

The dramatic underrepresentation of Alaska Natives in science, technology, engineering and mathematics (STEM) degrees and professions calls for rigorous research in how students access these fields. Research has shown that students who complete advanced mathematics and science courses while in high school are more academically prepared to pursue and succeed in STEM degree programs and professions. There is limited research on what motivates precollege students to become more academically prepared before they graduate from high school. In Alaska, Alaska Native precollege students regularly underperform on required State of Alaska mathematics and science exams when compared to non-Alaska Native students. Research also suggests that different things may motivate Alaska Native students than racial majority students. Therefore there is a need to better understand what motivates Alaska Native students to take and successfully complete advanced mathematics and science courses while in high school so that they are academically prepared to pursue and succeed in STEM degrees and professions. The Alaska Native Science & Engineering Program (ANSEP) is a longitudinal STEM educational enrichment program that works with Alaska Native students starting in middle school through doctoral degrees and further professional endeavors. Research suggests that Alaska Native students participating in ANSEP are completing STEM degrees at higher rates than before the program was available. ANSEP appears to be unique due to its longitudinal approach and the large numbers of Alaska Native precollege, university, and graduate students it supports. ANSEP provides precollege students with opportunities to take advanced high school and college-level mathematics and science courses and complete STEM related projects. Students work and live together on campus during the program components. Student outcome data suggests that ANSEP has been successful at motivating precollege participants to successfully complete advanced high school and college-level mathematics and science courses prior to high school graduation. This study was designed to examine the motivations of Alaska Native high school students who participated in the ANSEP Precollege components to take advanced mathematics and science courses in high school or before college. Participants were 30 high school or college students, 25 of whom were Alaska Native, who were currently attending or had attended Alaska Native Science & Engineering Program (ANSEP) Precollege components in high school. Self-determination theory was used as this study's theoretical framework to develop the semi-structured interview questions and also analyze the interviews. A thematic approach was used to analyze the interviews. The results of this study indicated that ANSEP helped the Alaska Native high school students gain a sense of autonomy, competence, and relatedness in order to be motivated to take advanced mathematics and science courses in high school or before college. In particular, Alaska Native high school students described that relatedness was an important element to them being motivated to take advanced mathematics and science courses. More specifically, participants reported that the Alaska Native community developed at the ANSEP Building and the relationships they developed with their Alaska Native high school peers and staff played an influential role in the motivation of these students. These findings are important because research suggests that autonomy and competence are more important elements than relatedness because they generate or maintain intrinsic motivation. Alaska Native high school students reported that ANSEP was more successful in helping them gain a sense of competence and relatedness than at helping them gain a sense of autonomy. More specifically, the reason the participants did not feel ANSEP developed their sense of autonomy was because ANSEP restricted their actions during the ANSEP Precollege study sessions. My study implies that Alaska Native students need to feel like they belong in order to be motivated to take and succeed at taking advanced mathematics and science courses. Educators and STEM program leaders should incorporate elements of belonging into the educational environments they develop for their Alaska Native students. Future research should be conducted to determine if other racial minority students need to feel like they belong in order to be motivated to take and succeed at taking advanced mathematics and science courses. My study also indicated that Alaska Native students were motivated to take advanced mathematics and science courses by knowing ANSEP would support them in future programming because of its longitudinal approach. Funding agencies of STEM programs should consider funding programs that provide a longitudinal approach to help Alaska Native students' sense of competence grow. Future research should include studying other STEM programs to determine if they are motivating their students to take and succeed in advanced mathematics and science courses.

The Role of Teachers' Knowledge of Functions in Their Teaching: A Conceptual Approach with Illustrations from Two Cases

ERIC Educational Resources Information Center

Watson, Anne; Harel, Guershon

2013-01-01

We investigate whether and how personal mathematical knowledge at an advanced level impacts on teaching at a lower school level. We study this in the context of functions because understanding them permeates secondary and advanced mathematics. Textbook treatment of these can be patchy, implying a need for knowledgeable teachers to rectify…

Smooth Transition for Advancement to Graduate Education (STAGE) for Underrepresented Groups in the Mathematical Sciences Pilot Project: Broadening Participation through Mentoring

ERIC Educational Resources Information Center

Eubanks-Turner, Christina; Beaulieu, Patricia; Pal, Nabendu

2018-01-01

The Smooth Transition for Advancement to Graduate Education (STAGE) project was a three-year pilot project designed to mentor undergraduate students primarily from under-represented groups in the mathematical sciences. The STAGE pilot project focused on mentoring students as they transitioned from undergraduate education to either graduate school…

PREFACE: Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013)

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Landolfi, G.; Martina, L.; Vitolo, R.

2014-03-01

Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF. Conference photograph

Mathematical modeling provides kinetic details of the human immune response to vaccination

PubMed Central

Le, Dustin; Miller, Joseph D.; Ganusov, Vitaly V.

2015-01-01

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data. PMID:25621280

Mathematical modeling provides kinetic details of the human immune response to vaccination.

PubMed

Le, Dustin; Miller, Joseph D; Ganusov, Vitaly V

2014-01-01

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data.

Theoretical Explanations in Mathematical Physics

NASA Astrophysics Data System (ADS)

Rivadulla, Andrés

Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.

Emerging Engineers Design a Paper Table

ERIC Educational Resources Information Center

Enderson, Mary C.; Grant, Melva R.

2013-01-01

With the advancement of specialized middle schools and high schools focusing on the arts, communication, engineering, mathematics, and science, many students who attend traditional schools miss out on valuable learning opportunities--in particular, when it comes to learning mathematics. Mathematics classrooms can be filled with real-world…

Predicting Mathematical Aptitude for Higher Education

ERIC Educational Resources Information Center

McDonald, Betty

2008-01-01

This present study seeks to predict mathematical aptitude for higher education by examining the relationship between mathematics results from the Caribbean Examinations Council (CXC) general proficiency examination and the results from the General Certificate of Education (GCE) advanced level examination. This present study arose from a more…

A Case against Computer Symbolic Manipulation in School Mathematics Today.

ERIC Educational Resources Information Center

Waits, Bert K.; Demana, Franklin

1992-01-01

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

Enhancing School Mathematics Culturally: A Path of Reconciliation

ERIC Educational Resources Information Center

Aikenhead, Glen S.

2017-01-01

Culturally responsive or place-based school mathematics that focuses on Indigenous students has an established presence in the research literature. This culture-based innovation represents a historical shift from conventional approaches to mathematics education. Moreover, it has demonstratively advanced the academic achievement for both Indigenous…

Mathematics Content Coverage and Student Learning in Kindergarten

ERIC Educational Resources Information Center

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2016-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998-1999 and…

Advanced Mathematics Communication beyond Modality of Sight

ERIC Educational Resources Information Center

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…

An empirical investigation of differences between mathematics specialists and non-specialists at the high school level in Cyprus: A Logistic regression Approach

NASA Astrophysics Data System (ADS)

Papanastasiou, Elena C.; Zembylas, Michalinos

2006-12-01

AN EMPIRICAL INVESTIGATION OF DIFFERENCES BETWEEN MATHEMATICS SPECIALISTS AND NON-SPECIALISTS AT THE HIGH-SCHOOL LEVEL in Cyprus - The data obtained from high-school seniors for the Third International Mathematics and Science Study (TIMSS) for the country of Cyprus appear to be contradictory. Although Cypriot students did not perform well in mathematics in elementary school, middle school, and in the non-advanced sectors of high school, students in advanced mathematics courses in high school managed to perform exceptionally well. In seeking to account for this apparent disparity, the present study examines the differences between mathematics specialists and non-specialists at the high-school level and discusses the implications that these have for teaching practice. It shows how students educated in an environment that might not be optimal for producing high-achieving students in mathematics and science in elementary and middle school (according to the TIMSS) might nonetheless manage to excel in these fields at the end of their schooling. In conclusion, the authors address the implications of their study for similar educational systems in other developing countries.

Pore space analysis of NAPL distribution in sand-clay media

USGS Publications Warehouse

Matmon, D.; Hayden, N.J.

2003-01-01

This paper introduces a conceptual model of clays and non-aqueous phase liquids (NAPLs) at the pore scale that has been developed from a mathematical unit cell model, and direct micromodel observation and measurement of clay-containing porous media. The mathematical model uses a unit cell concept with uniform spherical grains for simulating the sand in the sand-clay matrix (???10% clay). Micromodels made with glass slides and including different clay-containing porous media were used to investigate the two clays (kaolinite and montmorillonite) and NAPL distribution within the pore space. The results were used to understand the distribution of NAPL advancing into initially saturated sand and sand-clay media, and provided a detailed analysis of the pore-scale geometry, pore size distribution, NAPL entry pressures, and the effect of clay on this geometry. Interesting NAPL saturation profiles were observed as a result of the complexity of the pore space geometry with the different packing angles and the presence of clays. The unit cell approach has applications for enhancing the mechanistic understanding and conceptualization, both visually and mathematically, of pore-scale processes such as NAPL and clay distribution. ?? 2003 Elsevier Science Ltd. All rights reserved.

Beyond theories of plant invasions: Lessons from natural landscapes

USGS Publications Warehouse

Stohlgren, Thomas J.

2002-01-01

There are a growing number of contrasting theories about plant invasions, but most are only weakly supported by small-scale field experiments, observational studies, and mathematical models. Among the most contentious theories is that species-rich habitats should be less vulnerable to plant invasion than species-poor sites, stemming from earlier theories that competition is a major force in structuring plant communities. Early ecologists such as Charles Darwin (1859) and Charles Elton (1958) suggested that a lack of intense interspecific competition on islands made these low-diversity habitats vulnerable to invasion. Small-scale field experiments have supported and contradicted this theory, as have various mathematical models. In contrast, many large-scale observational studies and detailed vegetation surveys in continental areas often report that species-rich areas are more heavily invaded than species-poor areas, but there are exceptions here as well. In this article, I show how these seemingly contrasting patterns converge once appropriate spatial and temporal scales are considered in complex natural environments. I suggest ways in which small-scale experiments, mathematical models, and large- scale observational studies can be improved and better integrated to advance a theoretically based understanding of plant invasions.

Concurrent processing simulation of the space station

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Building Model NASA Satellites: Elementary Students Studying Science Using a NASA-Themed Transmedia Book Featuring Digital Fabrication Activities

ERIC Educational Resources Information Center

Tillman, Daniel; An, Song; Boren, Rachel; Slykhuis, David

2014-01-01

This study assessed the impact of nine lessons incorporating a NASA-themed transmedia book featuring digital fabrication activities on 5th-grade students (n = 29) recognized as advanced in mathematics based on their academic record. Data collected included a pretest and posttest of science content questions taken from released Virginia Standards…

Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

When Traditional Won't Do: Experiences from a "Lower-Level" Mathematics Classroom

ERIC Educational Resources Information Center

Hill, Crystal

2010-01-01

As the last bell rings, students scurry to their respective classrooms, doors begin to close, and the class period begins. Imagine that you are in the hallway of the school and you look into an advanced mathematics class, into an Algebra I, Part I, mathematics class (a course designed for students who have not found success in mathematics). What…

Characteristics and Impact of the Further Mathematics Knowledge Networks: Analysis of an English Professional Development Initiative on the Teaching of Advanced Mathematics

ERIC Educational Resources Information Center

Ruthven, Kenneth

2014-01-01

Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…

Hua Loo-Keng and the Movement of Popularizing Mathematics in the People's Republic of China

ERIC Educational Resources Information Center

Richard, Jean W.

2010-01-01

This paper examines the mathematical and teaching practices of the renowned self-taught Chinese mathematician Hua Loo-keng in the movement of popularizing mathematics in the People's Republic of China. In this movement, Hua Loo-keng taught industrial workers and peasants with a low level of education how to use fairly advanced mathematical methods…

A network model for characterizing brine channels in sea ice

NASA Astrophysics Data System (ADS)

Lieblappen, Ross M.; Kumar, Deip D.; Pauls, Scott D.; Obbard, Rachel W.

2018-03-01

The brine pore space in sea ice can form complex connected structures whose geometry is critical in the governance of important physical transport processes between the ocean, sea ice, and surface. Recent advances in three-dimensional imaging using X-ray micro-computed tomography have enabled the visualization and quantification of the brine network morphology and variability. Using imaging of first-year sea ice samples at in situ temperatures, we create a new mathematical network model to characterize the topology and connectivity of the brine channels. This model provides a statistical framework where we can characterize the pore networks via two parameters, depth and temperature, for use in dynamical sea ice models. Our approach advances the quantification of brine connectivity in sea ice, which can help investigations of bulk physical properties, such as fluid permeability, that are key in both global and regional sea ice models.

Systems biology of yeast: enabling technology for development of cell factories for production of advanced biofuels.

PubMed

de Jong, Bouke; Siewers, Verena; Nielsen, Jens

2012-08-01

Transportation fuels will gradually shift from oil based fuels towards alternative fuel resources like biofuels. Current bioethanol and biodiesel can, however, not cover the increasing demand for biofuels and there is therefore a need for advanced biofuels with superior fuel properties. Novel cell factories will provide a production platform for advanced biofuels. However, deep cellular understanding is required for improvement of current biofuel cell factories. Fast screening and analysis (-omics) methods and metabolome-wide mathematical models are promising techniques. An integrated systems approach of these techniques drives diversity and quantity of several new biofuel compounds. This review will cover the recent technological developments that support improvement of the advanced biofuels 1-butanol, biodiesels and jetfuels. Copyright © 2011 Elsevier Ltd. All rights reserved.

Test Platforms for Model-Based Flight Research

NASA Astrophysics Data System (ADS)

Dorobantu, Andrei

Demonstrating the reliability of flight control algorithms is critical to integrating unmanned aircraft systems into the civilian airspace. For many potential applications, design and certification of these algorithms will rely heavily on mathematical models of the aircraft dynamics. Therefore, the aerospace community must develop flight test platforms to support the advancement of model-based techniques. The University of Minnesota has developed a test platform dedicated to model-based flight research for unmanned aircraft systems. This thesis provides an overview of the test platform and its research activities in the areas of system identification, model validation, and closed-loop control for small unmanned aircraft.

Quantitative analysis of transverse bacterial migration induced by chemotaxis in a packed column with structured physical heterogeneity.

PubMed

Wang, Meng; Ford, Roseanne M

2010-01-15

A two-dimensional mathematical model was developed to simulate transport phenomena of chemotactic bacteria in a sand-packed column designed with structured physical heterogeneity in the presence of a localized chemical source. In contrast to mathematical models in previous research work, in which bacteria were typically treated as immobile colloids, this model incorporated a convective-like chemotaxis term to represent chemotactic migration. Consistency between experimental observation and model prediction supported the assertions that (1) dispersion-induced microbial transfer between adjacent conductive zones occurred at the interface and had little influence on bacterial transport in the bulk flow of the permeable layers and (2) the enhanced transverse bacterial migration in chemotactic experiments relative to nonchemotactic controls was mainly due to directed migration toward the chemical source zone. On the basis of parameter sensitivity analysis, chemotactic parameters determined in bulk aqueous fluid were adequate to predict the microbial transport in our intermediate-scale porous media system. Additionally, the analysis of adsorption coefficient values supported the observation of a previous study that microbial deposition to the surface of porous media might be decreased under the effect of chemoattractant gradients. By quantitatively describing bacterial transport and distribution in a heterogeneous system, this mathematical model serves to advance our understanding of chemotaxis and motility effects in granular media systems and provides insights for modeling microbial transport in in situ microbial processes.

Connecting the Dots: Rediscovering Continuity

ERIC Educational Resources Information Center

Camenga, Kristin A.; Yates, Rebekah B. Johnson

2014-01-01

The topic of continuity is typically not introduced until calculus and then reexamined in real analysis. Recognizing the connections between secondary school mathematics and the advanced mathematics studied at the college level allows teachers to better identify mathematical concepts in student ideas, motivate students by piquing their curiosity,…

Examining spectral properties of Landsat 8 OLI for predicting above-ground carbon of Labanan Forest, Berau

NASA Astrophysics Data System (ADS)

Suhardiman, A.; Tampubolon, B. A.; Sumaryono, M.

2018-04-01

Many studies revealed significant correlation between satellite image properties and forest data attributes such as stand volume, biomass or carbon stock. However, further study is still relevant due to advancement of remote sensing technology as well as improvement on methods of data analysis. In this study, the properties of three vegetation indices derived from Landsat 8 OLI were tested upon above-ground carbon stock data from 50 circular sample plots (30-meter radius) from ground survey in PT. Inhutani I forest concession in Labanan, Berau, East Kalimantan. Correlation analysis using Pearson method exhibited a promising results when the coefficient of correlation (r-value) was higher than 0.5. Further regression analysis was carried out to develop mathematical model describing the correlation between sample plots data and vegetation index image using various mathematical models.Power and exponential model were demonstrated a good result for all vegetation indices. In order to choose the most adequate mathematical model for predicting Above-ground Carbon (AGC), the Bayesian Information Criterion (BIC) was applied. The lowest BIC value (i.e. -376.41) shown by Transformed Vegetation Index (TVI) indicates this formula, AGC = 9.608*TVI21.54, is the best predictor of AGC of study area.

Applying Mathematical Tools to Accelerate Vaccine Development: Modeling Shigella Immune Dynamics

PubMed Central

Davis, Courtney L.; Wahid, Rezwanul; Toapanta, Franklin R.; Simon, Jakub K.

2013-01-01

We establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella’s outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine design. PMID:23589755

Applying mathematical tools to accelerate vaccine development: modeling Shigella immune dynamics.

PubMed

Davis, Courtney L; Wahid, Rezwanul; Toapanta, Franklin R; Simon, Jakub K; Sztein, Marcelo B; Levy, Doron

2013-01-01

We establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella's outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine design.

Opportunities and constraints of presently used thermal manikins for thermo-physiological simulation of the human body.

PubMed

Psikuta, Agnes; Kuklane, Kalev; Bogdan, Anna; Havenith, George; Annaheim, Simon; Rossi, René M

2016-03-01

Combining the strengths of an advanced mathematical model of human physiology and a thermal manikin is a new paradigm for simulating thermal behaviour of humans. However, the forerunners of such adaptive manikins showed some substantial limitations. This project aimed to determine the opportunities and constraints of the existing thermal manikins when dynamically controlled by a mathematical model of human thermal physiology. Four thermal manikins were selected and evaluated for their heat flux measurement uncertainty including lateral heat flows between manikin body parts and the response of each sector to the frequent change of the set-point temperature typical when using a physiological model for control. In general, all evaluated manikins are suitable for coupling with a physiological model with some recommendations for further improvement of manikin dynamic performance. The proposed methodology is useful to improve the performance of the adaptive manikins and help to provide a reliable and versatile tool for the broad research and development domain of clothing, automotive and building engineering.

A review of heat transfer in human tooth--experimental characterization and mathematical modeling.

PubMed

Lin, Min; Xu, Feng; Lu, Tian Jian; Bai, Bo Feng

2010-06-01

With rapid advances in modern dentistry, high-energy output instruments (e.g., dental lasers and light polymerizing units) are increasingly employed in dental surgery for applications such as laser assisted tooth ablation, bleaching, hypersensitivity treatment and polymerization of dental restorative materials. Extreme high temperature occurs within the tooth during these treatments, which may induce tooth thermal pain (TTP) sensation. Despite the wide application of these dental treatments, the underlying mechanisms are far from clear. Therefore, there is an urgent need to better understand heat transfer (HT) process in tooth, thermally induced damage of tooth, and the corresponding TTP. This will enhance the design and optimization of clinical treatment strategies. This paper presents the state-of-the-art of the current understanding on HT in tooth, with both experimental study and mathematical modeling reviewed. Limitations of the current experimental and mathematical methodologies are discussed and potential solutions are suggested. Interpretation of TTP in terms of thermally stimulated dentinal fluid flow is also discussed. Copyright (c) 2010 Academy of Dental Materials. All rights reserved.

Physical and mathematical cochlear models

NASA Astrophysics Data System (ADS)

Lim, Kian-Meng

2000-10-01

The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity, and non-linear effects such as compression of response with stimulus level, two-tone suppression and the generation of harmonic and distortion products.

Modeling Tumor Clonal Evolution for Drug Combinations Design.

PubMed

Zhao, Boyang; Hemann, Michael T; Lauffenburger, Douglas A

2016-03-01

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

Predictive models of forest dynamics.

PubMed

Purves, Drew; Pacala, Stephen

2008-06-13

Dynamic global vegetation models (DGVMs) have shown that forest dynamics could dramatically alter the response of the global climate system to increased atmospheric carbon dioxide over the next century. But there is little agreement between different DGVMs, making forest dynamics one of the greatest sources of uncertainty in predicting future climate. DGVM predictions could be strengthened by integrating the ecological realities of biodiversity and height-structured competition for light, facilitated by recent advances in the mathematics of forest modeling, ecological understanding of diverse forest communities, and the availability of forest inventory data.

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression.

PubMed

Saitou, Takashi; Imamura, Takeshi

2016-01-01

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation. © 2015 Japanese Society of Developmental Biologists.

Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Rodríguez, Nancy

2015-03-01

The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].

The Chess and Mathematics Connection: More than Just a Game

ERIC Educational Resources Information Center

Berkman, Robert M.

2004-01-01

This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to…

34 CFR 200.13 - Adequate yearly progress in general.

Code of Federal Regulations, 2011 CFR

2011-07-01

...) Measures progress separately for reading/language arts and for mathematics; (6) Is the same for all public... mathematics; and (ii) The proficient and advanced scores of students with disabilities based on the modified... assessed in reading/language arts and in mathematics. (3) A State's or LEA's number of proficient and...

34 CFR 200.13 - Adequate yearly progress in general.

Code of Federal Regulations, 2012 CFR

2012-07-01

...) Measures progress separately for reading/language arts and for mathematics; (6) Is the same for all public... mathematics; and (ii) The proficient and advanced scores of students with disabilities based on the modified... assessed in reading/language arts and in mathematics. (3) A State's or LEA's number of proficient and...

34 CFR 200.13 - Adequate yearly progress in general.

Code of Federal Regulations, 2013 CFR

2013-07-01

...) Measures progress separately for reading/language arts and for mathematics; (6) Is the same for all public... mathematics; and (ii) The proficient and advanced scores of students with disabilities based on the modified... assessed in reading/language arts and in mathematics. (3) A State's or LEA's number of proficient and...

34 CFR 200.13 - Adequate yearly progress in general.

Code of Federal Regulations, 2014 CFR

2014-07-01

...) Measures progress separately for reading/language arts and for mathematics; (6) Is the same for all public... mathematics; and (ii) The proficient and advanced scores of students with disabilities based on the modified... assessed in reading/language arts and in mathematics. (3) A State's or LEA's number of proficient and...

Math Problem

ERIC Educational Resources Information Center

Oguntoyinbo, Lekan

2012-01-01

Many experts give the nation's schools a poor grade for their approach to teaching mathematics and for their preparation of mathematics teachers. While many policymakers make much of data that suggest children in the United States lag behind many other advanced countries in math, many experts call for a change in mathematics education,…

Profiling Student Use of Calculators in the Learning of High School Mathematics

ERIC Educational Resources Information Center

Crowe, Cheryll E.; Ma, Xin

2010-01-01

Using data from the 2005 National Assessment of Educational Progress, students' use of calculators in the learning of high school mathematics was profiled based on their family background, curriculum background, and advanced mathematics coursework. A statistical method new to educational research--classification and regression trees--was applied…

Effects of Virtual Manipulatives with Different Approaches on Students' Knowledge of Slope

ERIC Educational Resources Information Center

Demir, Mustafa

2018-01-01

Virtual Manipulatives (VMs) are computer-based, dynamic, and visual representations of mathematical concepts, provide interactive learning environments to advance mathematics instruction (Moyer et al., 2002). Despite their broad use, few research explored the integration of VMs into mathematics instruction (Moyer-Packenham & Westenskow, 2013).…

34 CFR 200.13 - Adequate yearly progress in general.

Code of Federal Regulations, 2010 CFR

2010-07-01

...) Measures progress separately for reading/language arts and for mathematics; (6) Is the same for all public... mathematics; and (ii) The proficient and advanced scores of students with disabilities based on the modified... assessed in reading/language arts and in mathematics. (3) A State's or LEA's number of proficient and...

Developing Culturally Responsive Mathematics Teachers: Secondary Teachers' Evolving Conceptions of Knowing Students

ERIC Educational Resources Information Center

Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.

2017-01-01

Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…

Technology in K-12 Mathematics Classrooms

ERIC Educational Resources Information Center

Ozel, Serkan; Yetkiner, Zeynep Ebrar; Capraro, Robert M.

2008-01-01

Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…

Students' Exploratory Thinking about a Nonroutine Calculus Task

ERIC Educational Resources Information Center

Nabb, Keith

2013-01-01

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

Terminology, concepts, and models in genetic epidemiology.

PubMed

Teare, M Dawn; Koref, Mauro F Santibàñez

2011-01-01

Genetic epidemiology brings together approaches and techniques developed in mathematical genetics and statistics, medical genetics, quantitative genetics, and epidemiology. In the 1980s, the focus was on the mapping and identification of genes where defects had large effects at the individual level. More recently, statistical and experimental advances have made possible to identify and characterise genes associated with small effects at the individual level. In this chapter, we provide a brief outline of the models, concepts, and terminology used in genetic epidemiology.

Shuttle cryogenics supply system optimization study. Volume 5, B-3, part 2: Appendix to programmers manual for math model

NASA Technical Reports Server (NTRS)

1973-01-01

A computer programmer's manual for a digital computer which will permit rapid and accurate parametric analysis of current and advanced attitude control propulsion systems is presented. The concept is for a cold helium pressurized, subcritical cryogen fluid supplied, bipropellant gas-fed attitude control propulsion system. The cryogen fluids are stored as liquids under low pressure and temperature conditions. The mathematical model provides a generalized form for the procedural technique employed in setting up the analysis program.

The Logic of Concepts: Case Studies in Engineering and Law

DTIC Science & Technology

1981-01-01

oscillation for virtually all feedback systems, this means that tending to maintain the controlled variable is not a notion that is any clearer or more...makes your work a bit easier is not to say that you ought to do it. Virtually any idealization of an actual thing simplifies the mathematical model de...was still being invoked in justification of judgments, it was virtually impossible to use the Parke model in advance of a deci- sion to predict what

Proceedings of the Advanced Seminar on one-dimensional, open-channel Flow and transport modeling

USGS Publications Warehouse

Schaffranek, Raymond W.

1989-01-01

In view of the increased use of mathematical/numerical simulation models, of the diversity of both model investigations and informational project objectives, and of the technical demands of complex model applications by U.S. Geological Survey personnel, an advanced seminar on one-dimensional open-channel flow and transport modeling was organized and held on June 15-18, 1987, at the National Space Technology Laboratory, Bay St. Louis, Mississippi. Principal emphasis in the Seminar was on one-dimensional flow and transport model-implementation techniques, operational practices, and application considerations. The purposes of the Seminar were to provide a forum for the exchange of information, knowledge, and experience among model users, as well as to identify immediate and future needs with respect to model development and enhancement, user support, training requirements, and technology transfer. The Seminar program consisted of a mix of topical and project presentations by Geological Survey personnel. This report is a compilation of short papers that summarize the presentations made at the Seminar.

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

PubMed

Vandervert, Larry

2017-01-01

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

AMOVA ["Accumulative Manifold Validation Analysis"]: An Advanced Statistical Methodology Designed to Measure and Test the Validity, Reliability, and Overall Efficacy of Inquiry-Based Psychometric Instruments

ERIC Educational Resources Information Center

Osler, James Edward, II

2015-01-01

This monograph provides an epistemological rational for the Accumulative Manifold Validation Analysis [also referred by the acronym "AMOVA"] statistical methodology designed to test psychometric instruments. This form of inquiry is a form of mathematical optimization in the discipline of linear stochastic modelling. AMOVA is an in-depth…

Modeling the Combined Terrorist-Narcotics Trafficker Threat to National Security

DTIC Science & Technology

2012-05-01

views expressed in this article are those of the authors and do not reflect the official policy or position of the National Defense University...Mason University. Dr. Woodcock was Chief Scientist , Vice President, and Director of the Advanced Mathematics Program, BAE SYSTEMS-Portal Solutions...this relationship. In some cases, both organizations need the same facilitators: improve financial gains, expand geographical domains, provide common

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

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

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

2012-07-01

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

Fundamental studies of structure borne noise for advanced turboprop applications

NASA Technical Reports Server (NTRS)

Eversman, W.; Koval, L. R.

1985-01-01

The transmission of sound generated by wing-mounted, advanced turboprop engines into the cabin interior via structural paths is considered. The structural model employed is a beam representation of the wing box carried into the fuselage via a representative frame type of carry through structure. The structure for the cabin cavity is a stiffened shell of rectangular or cylindrical geometry. The structure is modelled using a finite element formulation and the acoustic cavity is modelled using an analytical representation appropriate for the geometry. The structural and acoustic models are coupled by the use of hard wall cavity modes for the interior and vacuum structural modes for the shell. The coupling is accomplished using a combination of analytical and finite element models. The advantage is the substantial reduction in dimensionality achieved by modelling the interior analytically. The mathematical model for the interior noise problem is demonstrated with a simple plate/cavity system which has all of the features of the fuselage interior noise problem.

The Dependence on Mathematical Theory in TIMSS, PISA and TIMSS Advanced Test Items and Its Relation to Student Achievement

ERIC Educational Resources Information Center

Hole, Arne; Grønmo, Liv Sissel; Onstad, Torgeir

2018-01-01

Background: This paper discusses a framework for analyzing the dependence on mathematical theory in test items, that is, a framework for discussing to what extent knowledge of mathematical theory is helpful for the student in solving the item. The framework can be applied to any test in which some knowledge of mathematical theory may be useful,…

Do Advanced Mathematics Skills Predict Success in Biology and Chemistry Degrees?

ERIC Educational Resources Information Center

Adkins, Michael; Noyes, Andrew

2018-01-01

The mathematical preparedness of science undergraduates has been a subject of debate for some time. This paper investigates the relationship between school mathematics attainment and degree outcomes in biology and chemistry across England, a much larger scale of analysis than has hitherto been reported in the literature. A unique dataset which…

How Young Children View Mathematical Representations: A Study Using Eye-Tracking Technology

ERIC Educational Resources Information Center

Bolden, David; Barmby, Patrick; Raine, Stephanie; Gardner, Matthew

2015-01-01

Background: It has been shown that mathematical representations can aid children's understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children's focus of attention and…

Widening and Increasing Post-16 Mathematics Participation: Pathways, Pedagogies and Politics

ERIC Educational Resources Information Center

Noyes, Andrew; Wake, Geoff; Drake, Pat

2011-01-01

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway--"Use of Mathematics"--sits in parallel with long-established,…

Undergraduate Mathematics Majors' Writing Performance Producing Proofs and Counterexamples about Continuous Functions

ERIC Educational Resources Information Center

Ko, Yi-Yin; Knuth, Eric

2009-01-01

In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies…

Blended Learning, E-Learning and Mobile Learning in Mathematics Education

ERIC Educational Resources Information Center

Borba, Marcelo C.; Askar, Petek; Engelbrecht, Johann; Gadanidis, George; Llinares, Salvador; Aguilar, Mario Sánchez

2016-01-01

In this literature survey we focus on identifying recent advances in research on digital technology in the field of mathematics education. To conduct the survey we have used internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals, including the ones in…

Demonstration Lessons in Mathematics Education: Teachers' Observation Foci and Intended Changes in Practice

ERIC Educational Resources Information Center

Clarke, Doug; Roche, Anne; Wilkie, Karina; Wright, Vince; Brown, Jill; Downton, Ann; Horne, Marj; Knight, Rose; McDonough, Andrea; Sexton, Matthew; Worrall, Chris

2013-01-01

As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the…

A Phenomenological Exploration of Mathematical Engagement: Approaching an Old Metaphor Anew.

ERIC Educational Resources Information Center

Handa, Yuichi

2003-01-01

Investigates the heart of the experience of mathematical engagement and the meaning derived from such activities. Analyzes dialogue between five people, two of whom are professional mathematicians, another two who are graduate students in either engineering or education, and one who lacks advanced mathematical training but maintains a positive…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

ERIC Educational Resources Information Center

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

A Framework for Mathematical Thinking: The Case of Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

Fifty Years of A-Level Mathematics: Have Standards Changed?

ERIC Educational Resources Information Center

Jones, Ian; Wheadon, Chris; Humphries, Sara; Inglis, Matthew

2016-01-01

Advanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the…

Zimbabwean Female Participation in Physics: The Influence of Identity Formation on Perception and Participation

ERIC Educational Resources Information Center

Gudyanga, Anna; Kurup, Raj

2017-01-01

The study investigated the influence of identity formation on the perceptions and participation of Zimbabwean Advanced Level (A' Level) female adolescent students in physics. Nine female adolescent students eighteen years and above: three doing mathematics and physics, one doing physics without mathematics and five doing mathematics without…

Fostering Teacher Learning of Conjecturing, Generalising and Justifying through Mathematics Studio

ERIC Educational Resources Information Center

Lesseig, Kristin

2016-01-01

Calls to advance students' ability to engage in mathematical reasoning practices including conjecturing, generalising and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote…

"Can You Tell Me More?" Student Journaling and Reasoning

ERIC Educational Resources Information Center

Yow, Jan A.

2015-01-01

Journals provide a history of each student's thinking over time and allow this history to be easy to review. Journaling in mathematics has been found to be a valuable tool both for students and for teachers. Students benefit from journaling because it advances their mathematical understanding and ability to communicate in mathematics; teachers…

Mathematical Rigor in the Common Core

ERIC Educational Resources Information Center

Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin

2013-01-01

A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…

Advanced Mathematical Study and the Development of Conditional Reasoning Skills

PubMed Central

Attridge, Nina; Inglis, Matthew

2013-01-01

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought. PMID:23869241

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Nanoparticle-mediated drug delivery to treat infections in the female reproductive tract: evaluation of experimental systems and the potential for mathematical modeling.

PubMed

Sims, Lee B; Frieboes, Hermann B; Steinbach-Rankins, Jill M

2018-01-01

A variety of drug-delivery platforms have been employed to deliver therapeutic agents across cervicovaginal mucus (CVM) and the vaginal mucosa, offering the capability to increase the longevity and retention of active agents to treat infections of the female reproductive tract (FRT). Nanoparticles (NPs) have been shown to improve retention, diffusion, and cell-specific targeting via specific surface modifications, relative to other delivery platforms. In particular, polymeric NPs represent a promising option that has shown improved distribution through the CVM. These NPs are typically fabricated from nontoxic, non-inflammatory, US Food and Drug Administration-approved polymers that improve biocompatibility. This review summarizes recent experimental studies that have evaluated NP transport in the FRT, and highlights research areas that more thoroughly and efficiently inform polymeric NP design, including mathematical modeling. An overview of the in vitro, ex vivo, and in vivo NP studies conducted to date - whereby transport parameters are determined, extrapolated, and validated - is presented first. The impact of different NP design features on transport through the FRT is summarized, and gaps that exist due to the limitations of iterative experimentation alone are identified. The potential of mathematical modeling to complement the characterization and evaluation of diffusion and transport of delivery vehicles and active agents through the CVM and mucosa is discussed. Lastly, potential advancements combining experimental and mathematical knowledge are suggested to inform next-generation NP designs, such that infections in the FRT may be more effectively treated.

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

PubMed

Konstorum, Anna; Vella, Anthony T; Adler, Adam J; Laubenbacher, Reinhard C

2017-06-01

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development. © 2017 The Author(s).

Chemical kinetic mechanistic models to investigate cancer biology and impact cancer medicine.

PubMed

Stites, Edward C

2013-04-01

Traditional experimental biology has provided a mechanistic understanding of cancer in which the malignancy develops through the acquisition of mutations that disrupt cellular processes. Several drugs developed to target such mutations have now demonstrated clinical value. These advances are unequivocal testaments to the value of traditional cellular and molecular biology. However, several features of cancer may limit the pace of progress that can be made with established experimental approaches alone. The mutated genes (and resultant mutant proteins) function within large biochemical networks. Biochemical networks typically have a large number of component molecules and are characterized by a large number of quantitative properties. Responses to a stimulus or perturbation are typically nonlinear and can display qualitative changes that depend upon the specific values of variable system properties. Features such as these can complicate the interpretation of experimental data and the formulation of logical hypotheses that drive further research. Mathematical models based upon the molecular reactions that define these networks combined with computational studies have the potential to deal with these obstacles and to enable currently available information to be more completely utilized. Many of the pressing problems in cancer biology and cancer medicine may benefit from a mathematical treatment. As work in this area advances, one can envision a future where such models may meaningfully contribute to the clinical management of cancer patients.

Mathematical modeling and simulation in animal health. Part I: Moving beyond pharmacokinetics.

PubMed

Riviere, J E; Gabrielsson, J; Fink, M; Mochel, J

2016-06-01

The application of mathematical modeling to problems in animal health has a rich history in the form of pharmacokinetic modeling applied to problems in veterinary medicine. Advances in modeling and simulation beyond pharmacokinetics have the potential to streamline and speed-up drug research and development programs. To foster these goals, a series of manuscripts will be published with the following goals: (i) expand the application of modeling and simulation to issues in veterinary pharmacology; (ii) bridge the gap between the level of modeling and simulation practiced in human and veterinary pharmacology; (iii) explore how modeling and simulation concepts can be used to improve our understanding of common issues not readily addressed in human pharmacology (e.g. breed differences, tissue residue depletion, vast weight ranges among adults within a single species, interspecies differences, small animal species research where data collection is limited to sparse sampling, availability of different sampling matrices); and (iv) describe how quantitative pharmacology approaches could help understanding key pharmacokinetic and pharmacodynamic characteristics of a drug candidate, with the goal of providing explicit, reproducible, and predictive evidence for optimizing drug development plans, enabling critical decision making, and eventually bringing safe and effective medicines to patients. This study introduces these concepts and introduces new approaches to modeling and simulation as well as clearly articulate basic assumptions and good practices. The driving force behind these activities is to create predictive models that are based on solid physiological and pharmacological principles as well as adhering to the limitations that are fundamental to applying mathematical and statistical models to biological systems. © 2015 John Wiley & Sons Ltd.

PREFACE: International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications

NASA Astrophysics Data System (ADS)

Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin

2013-04-01

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.

Demystifying the cytokine network: Mathematical models point the way.

PubMed

Morel, Penelope A; Lee, Robin E C; Faeder, James R

2017-10-01

Cytokines provide the means by which immune cells communicate with each other and with parenchymal cells. There are over one hundred cytokines and many exist in families that share receptor components and signal transduction pathways, creating complex networks. Reductionist approaches to understanding the role of specific cytokines, through the use of gene-targeted mice, have revealed further complexity in the form of redundancy and pleiotropy in cytokine function. Creating an understanding of the complex interactions between cytokines and their target cells is challenging experimentally. Mathematical and computational modeling provides a robust set of tools by which complex interactions between cytokines can be studied and analyzed, in the process creating novel insights that can be further tested experimentally. This review will discuss and provide examples of the different modeling approaches that have been used to increase our understanding of cytokine networks. This includes discussion of knowledge-based and data-driven modeling approaches and the recent advance in single-cell analysis. The use of modeling to optimize cytokine-based therapies will also be discussed. Copyright © 2016 Elsevier Ltd. All rights reserved.

Construction of a model demonstrating neural pathways and reflex arcs.

PubMed

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

1996-12-01

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

Conceptual metaphors and mathematical practice: on cognitive studies of historical developments in mathematics.

PubMed

Schlimm, Dirk

2013-04-01

This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of historical developments of mathematics has been primarily on the former, even if they claim to be about the latter. Copyright © 2013 Cognitive Science Society, Inc.

Advances in Cross-Cutting Ideas for Computational Climate Science

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

Ng, Esmond; Evans, Katherine J.; Caldwell, Peter

This report presents results from the DOE-sponsored workshop titled, ``Advancing X-Cutting Ideas for Computational Climate Science Workshop,'' known as AXICCS, held on September 12--13, 2016 in Rockville, MD. The workshop brought together experts in climate science, computational climate science, computer science, and mathematics to discuss interesting but unsolved science questions regarding climate modeling and simulation, promoted collaboration among the diverse scientists in attendance, and brainstormed about possible tools and capabilities that could be developed to help address them. Emerged from discussions at the workshop were several research opportunities that the group felt could advance climate science significantly. These include (1)more » process-resolving models to provide insight into important processes and features of interest and inform the development of advanced physical parameterizations, (2) a community effort to develop and provide integrated model credibility, (3) including, organizing, and managing increasingly connected model components that increase model fidelity yet complexity, and (4) treating Earth system models as one interconnected organism without numerical or data based boundaries that limit interactions. The group also identified several cross-cutting advances in mathematics, computer science, and computational science that would be needed to enable one or more of these big ideas. It is critical to address the need for organized, verified, and optimized software, which enables the models to grow and continue to provide solutions in which the community can have confidence. Effectively utilizing the newest computer hardware enables simulation efficiency and the ability to handle output from increasingly complex and detailed models. This will be accomplished through hierarchical multiscale algorithms in tandem with new strategies for data handling, analysis, and storage. These big ideas and cross-cutting technologies for enabling breakthrough climate simulation advancements also need the "glue" of outreach and learning across the scientific domains to be successful. The workshop identified several strategies to allow productive, continuous engagement across those who have a broad knowledge of the various angles of the problem. Specific ideas to foster education and tools to make material progress were discussed. Examples include follow-on cross-cutting meetings that enable unstructured discussions of the types this workshop fostered. A concerted effort to recruit undergraduate and graduate students from all relevant domains and provide them experience, training, and networking across their immediate expertise is needed. This will broaden and expand their exposure to the future needs and solutions, and provide a pipeline of scientists with a diversity of knowledge and know-how. Providing real-world experience with subject matter experts from multiple angles may also motivate the students to attack these problems and even come up with the missing solutions.« less

Advances in Cross-Cutting Ideas for Computational Climate Science

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

Ng, E.; Evans, K.; Caldwell, P.

This report presents results from the DOE-sponsored workshop titled, Advancing X-Cutting Ideas for Computational Climate Science Workshop,'' known as AXICCS, held on September 12--13, 2016 in Rockville, MD. The workshop brought together experts in climate science, computational climate science, computer science, and mathematics to discuss interesting but unsolved science questions regarding climate modeling and simulation, promoted collaboration among the diverse scientists in attendance, and brainstormed about possible tools and capabilities that could be developed to help address them. Emerged from discussions at the workshop were several research opportunities that the group felt could advance climate science significantly. These include (1)more » process-resolving models to provide insight into important processes and features of interest and inform the development of advanced physical parameterizations, (2) a community effort to develop and provide integrated model credibility, (3) including, organizing, and managing increasingly connected model components that increase model fidelity yet complexity, and (4) treating Earth system models as one interconnected organism without numerical or data based boundaries that limit interactions. The group also identified several cross-cutting advances in mathematics, computer science, and computational science that would be needed to enable one or more of these big ideas. It is critical to address the need for organized, verified, and optimized software, which enables the models to grow and continue to provide solutions in which the community can have confidence. Effectively utilizing the newest computer hardware enables simulation efficiency and the ability to handle output from increasingly complex and detailed models. This will be accomplished through hierarchical multiscale algorithms in tandem with new strategies for data handling, analysis, and storage. These big ideas and cross-cutting technologies for enabling breakthrough climate simulation advancements also need the "glue" of outreach and learning across the scientific domains to be successful. The workshop identified several strategies to allow productive, continuous engagement across those who have a broad knowledge of the various angles of the problem. Specific ideas to foster education and tools to make material progress were discussed. Examples include follow-on cross-cutting meetings that enable unstructured discussions of the types this workshop fostered. A concerted effort to recruit undergraduate and graduate students from all relevant domains and provide them experience, training, and networking across their immediate expertise is needed. This will broaden and expand their exposure to the future needs and solutions, and provide a pipeline of scientists with a diversity of knowledge and know-how. Providing real-world experience with subject matter experts from multiple angles may also motivate the students to attack these problems and even come up with the missing solutions.« less

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

Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Travelling wave ultrasonic motors, Part I: Working principle and mathematical modelling of the stator

NASA Astrophysics Data System (ADS)

Hagedorn, P.; Wallaschek, J.

1992-05-01

Travelling wave ultrasonic motors have recently been attracting considerable attention: they may possibly soon replace—at least in certain areas—small electromagnetic motors. This development has been made possible by recent advances in power electronics, material research and digital control, which allow utilization of the piezoelectric effect for low power motors. In these motors the mechanical energy is generated with frequencies of the order of 40 kHz via piezo-elements producing bending waves in a stator, which has approximately the form of a circular plate. The rotor is then driven by the stator via contact forces, and with an extremely simple mechanism frequency reductions of 1:40 000 and more are obtained between the stator vibration and the rotor motion. As a consequence, one can work in the 40 kHz range on the electrical side, while a low frequency rotation is obtained on the mechanical side, as is desirable for many applications. In the present paper, which is the first of a series, the working principle of travelling wave ultrasonic motors is reviewed, and the main phenomena are mathematically modelled. In further papers a detailed mathematical description of the stator vibration and a first model of the contact problem will be given.

Implications of Eighth Grade Algebra I on High School Mathematics Achievement

ERIC Educational Resources Information Center

Bayard, Robert

2012-01-01

As of 2008, approximately 40% of eighth grade students in the United States enroll in Algebra I (National Council of Teachers of Mathematics, 2008). Although research has shown that students have more opportunities to take advanced mathematics courses by taking eighth grade Algebra I, in the United States, approximately only one-third to one-half…

TEACHING OF ADVANCED MATHEMATICAL CONCEPTS TO CULTURALLY DISADVANTAGED ELEMENTARY SCHOOL CHILDREN.

ERIC Educational Resources Information Center

RUPLEY, WILLIAM H.

THE SUCCESS OF DISCOVERY MATHEMATICS TEACHING IN THE ELEMENTARY SCHOOL WAS TESTED OVER A 1-YEAR PERIOD. THE PROJECT WAS INTENDED TO SEE IF A TRAINED MATHEMATICIAN WORKING AT AN ELEMENTARY SCHOOL WITH DISADVANTAGED CHILDREN COULD (1) MOTIVATE THE CHILDREN TO BE INTERESTED IN SCHOOL WORK BY INTERESTING THEM IN MATHEMATICS AND (2) COMMUNICATE WITH…

Mathematical Literacy Teachers' Engagement with Contextual Tasks Based on Personal Finance

ERIC Educational Resources Information Center

Bansilal, Sarah; Mkhwanazi, Thokozani; Mahlabela, Patisizwe

2012-01-01

This article reports on a study carried out with a group of 108 practising Mathematical Literacy (ML) teachers who participated in an Advanced Certificate in Education (ACE) programme. The purpose of the qualitative study was to identify and describe the teachers' varying levels of engagement with mathematics tools and resources. The teachers were…

Does Knowing More Advanced Mathematics Ensure Effectiveness of Working towards Demonstrating Specialised Mathematical Content Knowledge of Second-Year Pre-Service Teachers?

ERIC Educational Resources Information Center

Livy, Sharyn

2012-01-01

The theoretical understanding that underpins a teacher's foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics' teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have specialised content knowledge (SCK) demonstrate a unique kind of content knowledge which is more than knowing the…

The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2016-01-01

The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without…

Students in Rural Schools Have Limited Access to Advanced Mathematics Courses. Issue Brief No. 7

ERIC Educational Resources Information Center

Graham, Suzanne E.

2009-01-01

This Carsey brief reveals that students in rural areas and small towns have less access to higher-level mathematics courses than students in urban settings, which results in serious educational consequences, including lower scores on assessment tests and fewer qualified students entering science, technology, engineering, and mathematics (STEM) job…

Mathematics: Report of the Project 2061 Phase I Mathematics Panel.

ERIC Educational Resources Information Center

Blackwell, David; Henkin, Leon

This is one of five panel reports that have been prepared as part of the first phase of Project 2061, a long-term multipurpose undertaking of the American Association for the Advancement of Science designed to help reform science, mathematics, and technology education in the United States. Major sections included are: (1) "Introduction";…

The Association between Secondary Mathematics and First Year University Performance in Health Sciences

ERIC Educational Resources Information Center

Joyce, Christopher; Hine, Gregory; Anderton, Ryan

2017-01-01

In recent years, there has been a significant decline in the rate of participation in secondary school mathematics courses within Australia, particularly in advanced or higher level mathematics. The aim of this study was to investigate how grade point average (GPA) differed between five health science degrees at an Australian university. The…

A Comparison Study of Student Performance and Study Habits in College Algebra at a Hispanic Serving College

ERIC Educational Resources Information Center

Salinas, Lelia

2011-01-01

Large numbers of students arrive at colleges and universities unprepared, specifically in the area of mathematics. In Texas, approximately 47% of entering freshman students enroll in developmental mathematics. Mathematics is cited in the literature as cornerstone for success in science, and advanced technology. In this study, the extent to which…

Do Screencasts Help to Revise Prerequisite Mathematics? An Investigation of Student Performance and Perception

ERIC Educational Resources Information Center

Loch, Birgit; Jordan, Camilla R.; Lowe, Tim W.; Mestel, Ben D.

2014-01-01

Basic calculus skills that are prerequisites for advanced mathematical studies continue to be a problem for a significant proportion of higher education students. While there are many types of revision material that could be offered to students, in this paper we investigate whether short, narrated video recordings of mathematical explanations…

The Use of Software in Academic Stream High School Mathematics Teaching

ERIC Educational Resources Information Center

Clay, Simon; Fotou, Nikolaos; Monaghan, John

2017-01-01

This paper reports on classroom observations of senior high school mathematics lessons with a focus on the use of digital technology. The observations were of teachers enrolled in an in-service course, Teaching Advanced Mathematics. The paper reports selected results and comments on: software that was observed to have been used; the use (or not)…

All Students Need Advanced Mathematics. Math Works

ERIC Educational Resources Information Center

Achieve, Inc., 2013

2013-01-01

This fact sheet explains that to thrive in today's world, all students will need to graduate with very strong math skills. That can only mean one thing: advanced math courses are now essential math courses. Highlights of this paper include: (1) Advanced math equals college success; (2) Advanced math equals career opportunity; and (3) Advanced math…

Theoretical studies of the physics of the solar atmosphere

NASA Technical Reports Server (NTRS)

Hollweg, Joseph V.

1992-01-01

Significant advances in our theoretical basis for understanding several physical processes related to dynamical phenomena on the sun were achieved. We have advanced a new model for spicules and fibrils. We have provided a simple physical view of resonance absorption of MHD surface waves; this allowed an approximate mathematical procedure for obtaining a wealth of new analytical results which we applied to coronal heating and p-mode absorption at magnetic regions. We provided the first comprehensive models for the heating and acceleration of the transition region, corona, and solar wind. We provided a new view of viscosity under coronal conditions. We provided new insights into Alfven wave propagation in the solar atmosphere. And recently we have begun work in a new direction: parametric instabilities of Alfven waves.

Considerations in miniaturizing simplified agro-ecosystems for advanced life support

NASA Technical Reports Server (NTRS)

Volk, T.

1996-01-01

Miniaturizing the Earth's biogeochemical cycles to support human life during future space missions is the goal of the NASA research and engineering program in advanced life support. Mission requirements to reduce mass, volume, and power have focused efforts on (1) a maximally simplified agro-ecosystem of humans, food crops, and microbes; and, (2) a design for optimized productivity of food crops with high light levels over long days, with hydroponics, with elevated carbon dioxide and other controlled environmental factors, as well as with genetic selection for desirable crop properties. Mathematical modeling contributes to the goals by establishing trade-offs, by analyzing the growth and development of experimental crops, and by pointing to the possibilities of directed phasic control using modified field crop models to increase the harvest index.

Considerations in miniaturizing simplified agro-ecosystems for advanced life support.

PubMed

Volk, T

1996-01-01

Miniaturizing the Earth's biogeochemical cycles to support human life during future space missions is the goal of the NASA research and engineering program in advanced life support. Mission requirements to reduce mass, volume, and power have focused efforts on (1) a maximally simplified agro-ecosystem of humans, food crops, and microbes; and, (2) a design for optimized productivity of food crops with high light levels over long days, with hydroponics, with elevated carbon dioxide and other controlled environmental factors, as well as with genetic selection for desirable crop properties. Mathematical modeling contributes to the goals by establishing trade-offs, by analyzing the growth and development of experimental crops, and by pointing to the possibilities of directed phasic control using modified field crop models to increase the harvest index.

Dynamic Analysis of Sounding Rocket Pneumatic System Revision

NASA Technical Reports Server (NTRS)

Armen, Jerald

2010-01-01

The recent fusion of decades of advancements in mathematical models, numerical algorithms and curve fitting techniques marked the beginning of a new era in the science of simulation. It is becoming indispensable to the study of rockets and aerospace analysis. In pneumatic system, which is the main focus of this paper, particular emphasis will be placed on the efforts of compressible flow in Attitude Control System of sounding rocket.

OPERATIONS RESEARCH IN THE DESIGN OF MANAGEMENT INFORMATION SYSTEMS

DTIC Science & Technology

management information systems is concerned with the identification and detailed specification of the information and data processing...of advanced data processing techniques in management information systems today, the close coordination of operations research and data systems activities has become a practical necessity for the modern business firm.... information systems in which mathematical models are employed as the basis for analysis and systems design. Operations research provides a

Electronic and mechanical improvement of the receiving terminal of a free-space microwave power transmission system

NASA Technical Reports Server (NTRS)

Brown, W. C.

1977-01-01

Significant advancements were made in a number of areas: improved efficiency of basic receiving element at low power density levels, improved resolution and confidence in efficiency measurements mathematical modelling and computer simulation of the receiving element and the design, construction, and testing of an environmentally protected two-plane construction suitable for low cost, highly automated construction of large receiving arrays.

FNAS/summer faculty fellowship research continuation program. Task 6: Integrated model development for liquid fueled rocket propulsion systems. Task 9: Aspects of model-based rocket engine condition monitoring and control

NASA Technical Reports Server (NTRS)

Santi, L. Michael; Helmicki, Arthur J.

1993-01-01

The objective of Phase I of this research effort was to develop an advanced mathematical-empirical model of SSME steady-state performance. Task 6 of Phase I is to develop component specific modification strategy for baseline case influence coefficient matrices. This report describes the background of SSME performance characteristics and provides a description of the control variable basis of three different gains models. The procedure used to establish influence coefficients for each of these three models is also described. Gains model analysis results are compared to Rocketdyne's power balance model (PBM).

On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure.

PubMed

Torfs, Elena; Balemans, Sophie; Locatelli, Florent; Diehl, Stefan; Bürger, Raimund; Laurent, Julien; François, Pierre; Nopens, Ingmar

2017-03-01

Advanced 1-D models for Secondary Settling Tanks (SSTs) explicitly account for several phenomena that influence the settling process (such as hindered settling and compression settling). For each of these phenomena a valid mathematical expression needs to be selected and its parameters calibrated to obtain a model that can be used for operation and control. This is, however, a challenging task as these phenomena may occur simultaneously. Therefore, the presented work evaluates several available expressions for hindered settling based on long-term batch settling data. Specific attention is paid to the behaviour of these hindered settling functions in the compression region in order to evaluate how the modelling of sludge compression is influenced by the choice of a certain hindered settling function. The analysis shows that the exponential hindered settling forms, which are most commonly used in traditional SST models, not only account for hindered settling but partly lump other phenomena (compression) as well. This makes them unsuitable for advanced 1-D models that explicitly include each phenomenon in a modular way. A power-law function is shown to be more appropriate to describe the hindered settling velocity in advanced 1-D SST models. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling Tumor Clonal Evolution for Drug Combinations Design

PubMed Central

Zhao, Boyang; Hemann, Michael T.; Lauffenburger, Douglas A.

2016-01-01

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs. PMID:28435907

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.

Challenges for Complex Microbial Ecosystems: Combination of Experimental Approaches with Mathematical Modeling

PubMed Central

Haruta, Shin; Yoshida, Takehito; Aoi, Yoshiteru; Kaneko, Kunihiko; Futamata, Hiroyuki

2013-01-01

In the past couple of decades, molecular ecological techniques have been developed to elucidate microbial diversity and distribution in microbial ecosystems. Currently, modern techniques, represented by meta-omics and single cell observations, are revealing the incredible complexity of microbial ecosystems and the large degree of phenotypic variation. These studies propound that microbiological techniques are insufficient to untangle the complex microbial network. This minireview introduces the application of advanced mathematical approaches in combination with microbiological experiments to microbial ecological studies. These combinational approaches have successfully elucidated novel microbial behaviors that had not been recognized previously. Furthermore, the theoretical perspective also provides an understanding of the plasticity, robustness and stability of complex microbial ecosystems in nature. PMID:23995424

Uncertainty assessment of a model for biological nitrogen and phosphorus removal: Application to a large wastewater treatment plant

NASA Astrophysics Data System (ADS)

Mannina, Giorgio; Cosenza, Alida; Viviani, Gaspare

In the last few years, the use of mathematical models in WasteWater Treatment Plant (WWTP) processes has become a common way to predict WWTP behaviour. However, mathematical models generally demand advanced input for their implementation that must be evaluated by an extensive data-gathering campaign, which cannot always be carried out. This fact, together with the intrinsic complexity of the model structure, leads to model results that may be very uncertain. Quantification of the uncertainty is imperative. However, despite the importance of uncertainty quantification, only few studies have been carried out in the wastewater treatment field, and those studies only included a few of the sources of model uncertainty. Seeking the development of the area, the paper presents the uncertainty assessment of a mathematical model simulating biological nitrogen and phosphorus removal. The uncertainty assessment was conducted according to the Generalised Likelihood Uncertainty Estimation (GLUE) methodology that has been scarcely applied in wastewater field. The model was based on activated-sludge models 1 (ASM) and 2 (ASM2). Different approaches can be used for uncertainty analysis. The GLUE methodology requires a large number of Monte Carlo simulations in which a random sampling of individual parameters drawn from probability distributions is used to determine a set of parameter values. Using this approach, model reliability was evaluated based on its capacity to globally limit the uncertainty. The method was applied to a large full-scale WWTP for which quantity and quality data was gathered. The analysis enabled to gain useful insights for WWTP modelling identifying the crucial aspects where higher uncertainty rely and where therefore, more efforts should be provided in terms of both data gathering and modelling practises.

Identifying potential disaster zones around the Verkhnekamskoye potash deposit (Russia) using advanced information technology (IT)

NASA Astrophysics Data System (ADS)

Royer, J. J.; Filippov, L. O.

2017-07-01

This work aims at improving the exploitation of the K, Mg, salts ore of the Verkhnekamskoye deposit using advanced information technology (IT) such as 3D geostatistical modeling techniques together with high performance flotation. It is expected to provide a more profitable exploitation of the actual deposit avoiding the formation of dramatic sinkholes by a better knowledge of the deposit. The GeoChron modelling method for sedimentary formations (Mallet, 2014) was used to improve the knowledge of the Verkhnekamskoye potash deposit, Perm region, Russia. After a short introduction on the modern theory of mathematical modelling applied to mineral resources exploitation and geology, new results are presented on the sedimentary architecture of the ore deposit. They enlighten the structural geology and the fault orientations, a key point for avoiding catastrophic water inflows recharging zone during exploitation. These results are important for avoiding catastrophic sinkholes during exploitation.

Systems Biology-Driven Hypotheses Tested In Vivo: The Need to Advancing Molecular Imaging Tools.

PubMed

Verma, Garima; Palombo, Alessandro; Grigioni, Mauro; La Monaca, Morena; D'Avenio, Giuseppe

2018-01-01

Processing and interpretation of biological images may provide invaluable insights on complex, living systems because images capture the overall dynamics as a "whole." Therefore, "extraction" of key, quantitative morphological parameters could be, at least in principle, helpful in building a reliable systems biology approach in understanding living objects. Molecular imaging tools for system biology models have attained widespread usage in modern experimental laboratories. Here, we provide an overview on advances in the computational technology and different instrumentations focused on molecular image processing and analysis. Quantitative data analysis through various open source software and algorithmic protocols will provide a novel approach for modeling the experimental research program. Besides this, we also highlight the predictable future trends regarding methods for automatically analyzing biological data. Such tools will be very useful to understand the detailed biological and mathematical expressions under in-silico system biology processes with modeling properties.

Active disturbance rejection controller for chemical reactor

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

Both, Roxana; Dulf, Eva H.; Muresan, Cristina I., E-mail: roxana.both@aut.utcluj.ro

2015-03-10

In the petrochemical industry, the synthesis of 2 ethyl-hexanol-oxo-alcohols (plasticizers alcohol) is of high importance, being achieved through hydrogenation of 2 ethyl-hexenal inside catalytic trickle bed three-phase reactors. For this type of processes the use of advanced control strategies is suitable due to their nonlinear behavior and extreme sensitivity to load changes and other disturbances. Due to the complexity of the mathematical model an approach was to use a simple linear model of the process in combination with an advanced control algorithm which takes into account the model uncertainties, the disturbances and command signal limitations like robust control. However themore » resulting controller is complex, involving cost effective hardware. This paper proposes a simple integer-order control scheme using a linear model of the process, based on active disturbance rejection method. By treating the model dynamics as a common disturbance and actively rejecting it, active disturbance rejection control (ADRC) can achieve the desired response. Simulation results are provided to demonstrate the effectiveness of the proposed method.« less

Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

NASA Astrophysics Data System (ADS)

Huang, Lingxiao; Liu, Libo; Sun, Xuehong; Zheng, Lanxiang; Jing, Hefang; Zhang, Xuande; Li, Chunguang

2018-01-01

This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

[Organization of anesthesia management and advanced life support at military medical evacuation levels].

PubMed

Shchegolev, A V; Petrakov, V A; Savchenko, I F

2014-07-01

Anesthesia management and advanced life support for the severely wounded personnel at military medical evacuation levels in armed conflict (local war) is time-consuming and resource-requiring task. One of the mathematical modeling methods was used to evaluate capabilities of anesthesia and intensive care units at tactical level. Obtained result allows us to tell that there is a need to make several system changes of the existing system of anesthesia management and advanced life support for the severely wounded personnel at military medical evacuation levels. In addition to increasing number of staff of anesthesiology-critical care during the given period of time another solution should be the creation of an early evacuation to a specialized medical care level by special means while conducting intensive monitoring and treatment.

Revisiting Bevacizumab + Cytotoxics Scheduling Using Mathematical Modeling: Proof of Concept Study in Experimental Non-Small Cell Lung Carcinoma.

PubMed

Imbs, Diane-Charlotte; El Cheikh, Raouf; Boyer, Arnaud; Ciccolini, Joseph; Mascaux, Céline; Lacarelle, Bruno; Barlesi, Fabrice; Barbolosi, Dominique; Benzekry, Sébastien

2018-01-01

Concomitant administration of bevacizumab and pemetrexed-cisplatin is a common treatment for advanced nonsquamous non-small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC-bearing mice. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.

Mathematical modeling and experimental testing of three bioreactor configurations based on windkessel models

PubMed Central

Ruel, Jean; Lachance, Geneviève

2010-01-01

This paper presents an experimental study of three bioreactor configurations. The bioreactor is intended to be used for the development of tissue-engineered heart valve substitutes. Therefore it must be able to reproduce physiological flow and pressure waveforms accurately. A detailed analysis of three bioreactor arrangements is presented using mathematical models based on the windkessel (WK) approach. First, a review of the many applications of this approach in medical studies enhances its fundamental nature and its usefulness. Then the models are developed with reference to the actual components of the bioreactor. This study emphasizes different conflicting issues arising in the design process of a bioreactor for biomedical purposes, where an optimization process is essential to reach a compromise satisfying all conditions. Two important aspects are the need for a simple system providing ease of use and long-term sterility, opposed to the need for an advanced (thus more complex) architecture capable of a more accurate reproduction of the physiological environment. Three classic WK architectures are analyzed, and experimental results enhance the advantages and limitations of each one. PMID:21977286

Recent advances in the analysis of behavioural organization and interpretation as indicators of animal welfare

PubMed Central

Asher, Lucy; Collins, Lisa M.; Ortiz-Pelaez, Angel; Drewe, Julian A.; Nicol, Christine J.; Pfeiffer, Dirk U.

2009-01-01

While the incorporation of mathematical and engineering methods has greatly advanced in other areas of the life sciences, they have been under-utilized in the field of animal welfare. Exceptions are beginning to emerge and share a common motivation to quantify ‘hidden’ aspects in the structure of the behaviour of an individual, or group of animals. Such analyses have the potential to quantify behavioural markers of pain and stress and quantify abnormal behaviour objectively. This review seeks to explore the scope of such analytical methods as behavioural indicators of welfare. We outline four classes of analyses that can be used to quantify aspects of behavioural organization. The underlying principles, possible applications and limitations are described for: fractal analysis, temporal methods, social network analysis, and agent-based modelling and simulation. We hope to encourage further application of analyses of behavioural organization by highlighting potential applications in the assessment of animal welfare, and increasing awareness of the scope for the development of new mathematical methods in this area. PMID:19740922

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

Morales, George J.; Maggs, James E.

The project expanded and developed mathematical descriptions, and corresponding numerical modeling, of non-diffusive transport to incorporate new perspectives derived from basic transport experiments performed in the LAPD device at UCLA, and at fusion devices throughout the world. By non-diffusive it is meant that the transport of fundamental macroscopic parameters of a system, such as temperature and density, does not follow the standard diffusive behavior predicted by a classical Fokker-Planck equation. The appearance of non-diffusive behavior is often related to underlying microscopic processes that cause the value of a system parameter, at one spatial position, to be linked to distant events,more » i.e., non-locality. In the LAPD experiments the underlying process was traced to large amplitude, coherent drift-waves that give rise to chaotic trajectories. Significant advances were made in this project. The results have lead to a new perspective about the fundamentals of edge transport in magnetically confined plasmas; the insight has important consequences for worldwide studies in fusion devices. Progress was also made in advancing the mathematical techniques used to describe fractional diffusion.« less

The Impact of Motivation on Student's Academic Achievement and Learning Outcomes in Mathematics among Secondary School Students in Nigeria

ERIC Educational Resources Information Center

Tella, Adedeji

2007-01-01

In our match towards scientific and technological advancement, we need nothing short of good performance in mathematics at all levels of schooling. In an effort to achieve this, this study investigated the impact of motivation on students' school academic achievement in mathematics in secondary schools using motivation for academic preference…

Comparing Differences in Math Achievement and Attitudes toward Math in a Sixth Grade Mathematics Enrichment Pilot Program

ERIC Educational Resources Information Center

Tow, Tamara

2011-01-01

High-stakes assessments have encouraged educators to ignore the needs of the top performers. Therefore, the Oakwood School District decided to implement a mathematics pilot enrichment program in order to meet the needs of the advanced mathematics students. As a result, this study used quantitative data to determine if there was a significant…

Teacher Knowledge That Supports Student Processes in Learning Mathematics: A Study at All-Female Middle Schools in Saudi Arabia

ERIC Educational Resources Information Center

Alsaeed, Maha Saad

2012-01-01

Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they promote…

Avoiding Misinterpretations of Piaget and Vygotsky: Mathematical Teaching without Learning, Learning without Teaching, or Helpful Learning-Path Teaching?

ERIC Educational Resources Information Center

Fuson, Karen C.

2009-01-01

This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be…

What Is Happening in the Use of ICT Mathematics to Support Young Adolescent Learners? A New Zealand Experience

ERIC Educational Resources Information Center

Nicholas, Karen; Fletcher, Jo

2017-01-01

Advances in learning approaches can enhance deeper levels of mathematical thinking and engagement through the use of new digital environments and technologies. The growing utilisation of portable digital devices in schools has meant there are enhanced tools to support mathematical learning and understandings. This article focused on those who work…

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

ERIC Educational Resources Information Center

Satsangi, Rajiv; Bouck, Emily C.

2015-01-01

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

Uncertainty and variability in computational and mathematical models of cardiac physiology.

PubMed

Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

2016-12-01

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs. © 2016 The Authors. The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

PubMed Central

Lowengrub, J S; Frieboes, H B; Jin, F; Chuang, Y-L; Li, X; Macklin, P; Wise, S M; Cristini, V

2010-01-01

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis. PMID:20808719

Nonlinear modelling of cancer: bridging the gap between cells and tumours

NASA Astrophysics Data System (ADS)

Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y.-L.; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V.

2010-01-01

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

PubMed Central

Zenker, Sven; Rubin, Jonathan; Clermont, Gilles

2007-01-01

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

Modeling Flow in Porous Media with Double Porosity/Permeability.

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Multiscale Mathematical Modeling in Dental Tissue Engineering: Toward Computer-Aided Design of a Regenerative System Based on Hydroxyapatite Granules, Focussing on Early and Mid-Term Stiffness Recovery

PubMed Central

Scheiner, Stefan; Komlev, Vladimir S.; Gurin, Alexey N.; Hellmich, Christian

2016-01-01

We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall conglomerate-type scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions. In this context, the question arises how the compound stiffness is driven by the key design parameters of the tissue engineering system: macroporosity, crack density, as well as scaffold resorption/bone formation rates. We here tackle this question by combining the latest state-of-the-art mathematical modeling techniques in the field of multiscale micromechanics, into an unprecedented suite of highly efficient, semi-analytically defined computation steps resolving several levels of hierarchical organization, from the millimeter- down to the nanometer-scale. This includes several types of homogenization schemes, namely such for porous polycrystals with elongated solid elements, for cracked matrix-inclusion composites, as well as for assemblies of coated spherical compounds. Together with the experimentally known stiffnesses of hydroxyapatite crystals and mandibular bone tissue, the new mathematical model suggests that early stiffness recovery (i.e., within several weeks) requires total avoidance of microcracks in the hydroxyapatite scaffolds, while mid-term stiffness recovery (i.e., within several months) is additionally promoted by provision of small granule sizes, in combination with high bone formation and low scaffold resorption rates. PMID:27708584

Mathematical Approaches to Understanding and Imaging Atrial Fibrillation: Significance for Mechanisms and Management

PubMed Central

Trayanova, Natalia A

2014-01-01

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This articles aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention. PMID:24763468

Towards a model-based cognitive neuroscience of stopping - a neuroimaging perspective.

PubMed

Sebastian, Alexandra; Forstmann, Birte U; Matzke, Dora

2018-07-01

Our understanding of the neural correlates of response inhibition has greatly advanced over the last decade. Nevertheless the specific function of regions within this stopping network remains controversial. The traditional neuroimaging approach cannot capture many processes affecting stopping performance. Despite the shortcomings of the traditional neuroimaging approach and a great progress in mathematical and computational models of stopping, model-based cognitive neuroscience approaches in human neuroimaging studies are largely lacking. To foster model-based approaches to ultimately gain a deeper understanding of the neural signature of stopping, we outline the most prominent models of response inhibition and recent advances in the field. We highlight how a model-based approach in clinical samples has improved our understanding of altered cognitive functions in these disorders. Moreover, we show how linking evidence-accumulation models and neuroimaging data improves the identification of neural pathways involved in the stopping process and helps to delineate these from neural networks of related but distinct functions. In conclusion, adopting a model-based approach is indispensable to identifying the actual neural processes underlying stopping. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

Physics Doctorates: Skills Used & Satisfaction with Employment. Data from the Degree Recipient Follow-Up Survey for the Classes of 2013 and 2014. Focus On

ERIC Educational Resources Information Center

Pold, Jack; Mulvey, Patrick

2016-01-01

By the time people earn physics PhDs, they have learned a great deal about physics and how research is conducted. However, physics PhDs also develop skills and knowledge in a number of related areas, such as advanced mathematics, programming, modeling, and technical writing. Physics PhDs draw upon an arsenal of skills and knowledge in their…

On the role of visual experience in mathematical development: Evidence from blind mathematicians.

PubMed

Amalric, Marie; Denghien, Isabelle; Dehaene, Stanislas

2018-04-01

Advanced mathematical reasoning, regardless of domain or difficulty, activates a reproducible set of bilateral brain areas including intraparietal, inferior temporal and dorsal prefrontal cortex. The respective roles of genetics, experience and education in the development of this math-responsive network, however, remain unresolved. Here, we investigate the role of visual experience by studying the exceptional case of three professional mathematicians who were blind from birth (n=1) or became blind during childhood (n=2). Subjects were scanned with fMRI while they judged the truth value of spoken mathematical and nonmathematical statements. Blind mathematicians activated the classical network of math-related areas during mathematical reflection, similar to that found in a group of sighted professional mathematicians. Thus, brain networks for advanced mathematical reasoning can develop in the absence of visual experience. Additional activations were found in occipital cortex, even in individuals who became blind during childhood, suggesting that either mental imagery or a more radical repurposing of visual cortex may occur in blind mathematicians. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Software development: Stratosphere modeling

NASA Technical Reports Server (NTRS)

Chen, H. C.

1977-01-01

A more comprehensive model for stratospheric chemistry and transport theory was developed for the purpose of aiding predictions of changes in the stratospheric ozone content as a consequence of natural and anthropogenic processes. This new and more advanced stratospheric model is time dependent and the dependent variables are zonal means of the relevant meteorological quantities which are functions of latitude and height. The model was constructed by the best mathematical approach on a large IBM S360 in American National Standard FORTRAN. It will be both a scientific tool and an assessment device used to evaluate other models. The interactions of dynamics, photochemistry and radiation in the stratosphere can be governed by a set of fundamental dynamical equations.

Geometry and Integrability

NASA Astrophysics Data System (ADS)

Mason, Lionel; Nutku, Yavuz

2003-12-01

Based on courses held at the Feza GÜrsey Institute, this collection of survey articles introduces advanced graduate students to an exciting area on the border of mathematics and mathematical physics. Including articles by key names such as Calogero, Donagi and Mason, it features the algebro-geometric material from Donagi as well as the twistor space methods in Woodhouse's contribution, forming a bridge between the pure mathematics and the more physical approaches.

Trends in Mathematics and Science Performance in 18 Countries: Multiple Regression Analysis of the Cohort Effects of TIMSS 1995-2007

ERIC Educational Resources Information Center

Hong, Hee Kyung

2012-01-01

The purpose of this study was to simultaneously examine relationships between teacher quality and instructional time and mathematics and science achievement of 8th grade cohorts in 18 advanced and developing economies. In addition, the study examined changes in mathematics and science performance across the two groups of economies over time using…

Accomplishment in Science, Technology, Engineering, and Mathematics (STEM) and Its Relation to STEM Educational Dose: A 25-Year Longitudinal Study

ERIC Educational Resources Information Center

Wai, Jonathan; Lubinski, David; Benbow, Camilla P.; Steiger, James H.

2010-01-01

Two studies examined the relationship between precollegiate advanced/enriched educational experiences and adult accomplishments in science, technology, engineering, and mathematics (STEM). In Study 1, 1,467 13-year-olds were identified as mathematically talented on the basis of scores [greater than or equal to] 500 (top 0.5%) on the math section…

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent advances in the analytical and numerical treatment of physical and engineering problems are discussed in reviews and reports. Topics addressed include fluid mechanics, numerical methods for differential equations, FEM approaches, and boundary-element methods. Consideration is given to optimization, decision theory, stochastics, actuarial mathematics, applied mathematics and mathematical physics, and numerical analysis.

RT-18: Value of Flexibility. Phase 1

DTIC Science & Technology

2010-09-25

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

Support with Caveats: Advocates' Views of the Theory of Formal Discipline as a Reason for the Study of Advanced Mathematics

ERIC Educational Resources Information Center

Wainwright, Elaine; Attridge, Nina; Wainwright, David; Alcock, Lara; Inglis, Matthew

2017-01-01

The Theory of Formal Discipline (TFD) suggests that studying mathematics improves general thinking skills. Empirical evidence for the TFD is sparse, yet it is cited in policy reports as a justification for the importance of mathematics in school curricula. The study reported in this article investigated the extent to which influential UK advocates…

Effect of membranes on oxygen transfer rate and consumption within a newly developed three-compartment bioartificial liver device: Advanced experimental and theoretical studies.

PubMed

Hilal-Alnaqbi, Ali; Mourad, Abdel-Hamid I; Yousef, Basem F

2014-01-01

A mathematical model is developed to predict oxygen transfer in the fiber-in-fiber (FIF) bioartificial liver device. The model parameters are taken from the constructed and tested FIF modules. We extended the Krogh cylinder model by including one more zone for oxygen transfer. Cellular oxygen uptake was based on Michaelis-Menten kinetics. The effect of varying a number of important model parameters is investigated, including (1) oxygen partial pressure at the inlet, (2) the hydraulic permeability of compartment B (cell region), (3) the hydraulic permeability of the inner membrane, and (4) the oxygen diffusivity of the outer membrane. The mathematical model is validated by comparing its output against the experimentally acquired values of an oxygen transfer rate and the hydrostatic pressure drop. Three governing simultaneous linear differential equations are derived to predict and validate the experimental measurements, e.g., the flow rate and the hydrostatic pressure drop. The model output simulated the experimental measurements to a high degree of accuracy. The model predictions show that the cells in the annulus can be oxygenated well even at high cell density or at a low level of gas phase PG if the value of the oxygen diffusion coefficient Dm is 16 × 10(-5) . The mathematical model also shows that the performance of the FIF improves by increasing the permeability of polypropylene membrane (inner fiber). Moreover, the model predicted that 60% of plasma has access to the cells in the annulus within the first 10% of the FIF bioreactor axial length for a specific polypropylene membrane permeability and can reach 95% within the first 30% of its axial length. © 2013 International Union of Biochemistry and Molecular Biology, Inc.

Quantifying Astronaut Tasks: Robotic Technology and Future Space Suit Design

NASA Technical Reports Server (NTRS)

Newman, Dava

2003-01-01

The primary aim of this research effort was to advance the current understanding of astronauts' capabilities and limitations in space-suited EVA by developing models of the constitutive and compatibility relations of a space suit, based on experimental data gained from human test subjects as well as a 12 degree-of-freedom human-sized robot, and utilizing these fundamental relations to estimate a human factors performance metric for space suited EVA work. The three specific objectives are to: 1) Compile a detailed database of torques required to bend the joints of a space suit, using realistic, multi- joint human motions. 2) Develop a mathematical model of the constitutive relations between space suit joint torques and joint angular positions, based on experimental data and compare other investigators' physics-based models to experimental data. 3) Estimate the work envelope of a space suited astronaut, using the constitutive and compatibility relations of the space suit. The body of work that makes up this report includes experimentation, empirical and physics-based modeling, and model applications. A detailed space suit joint torque-angle database was compiled with a novel experimental approach that used space-suited human test subjects to generate realistic, multi-joint motions and an instrumented robot to measure the torques required to accomplish these motions in a space suit. Based on the experimental data, a mathematical model is developed to predict joint torque from the joint angle history. Two physics-based models of pressurized fabric cylinder bending are compared to experimental data, yielding design insights. The mathematical model is applied to EVA operations in an inverse kinematic analysis coupled to the space suit model to calculate the volume in which space-suited astronauts can work with their hands, demonstrating that operational human factors metrics can be predicted from fundamental space suit information.

Advanced semi-active engine and transmission mounts: tools for modelling, analysis, design, and tuning

NASA Astrophysics Data System (ADS)

Farjoud, Alireza; Taylor, Russell; Schumann, Eric; Schlangen, Timothy

2014-02-01

This paper is focused on modelling, design, and testing of semi-active magneto-rheological (MR) engine and transmission mounts used in the automotive industry. The purpose is to develop a complete analysis, synthesis, design, and tuning tool that reduces the need for expensive and time-consuming laboratory and field tests. A detailed mathematical model of such devices is developed using multi-physics modelling techniques for physical systems with various energy domains. The model includes all major features of an MR mount including fluid dynamics, fluid track, elastic components, decoupler, rate-dip, gas-charged chamber, MR fluid rheology, magnetic circuit, electronic driver, and control algorithm. Conventional passive hydraulic mounts can also be studied using the same mathematical model. The model is validated using standard experimental procedures. It is used for design and parametric study of mounts; effects of various geometric and material parameters on dynamic response of mounts can be studied. Additionally, this model can be used to test various control strategies to obtain best vibration isolation performance by tuning control parameters. Another benefit of this work is that nonlinear interactions between sub-components of the mount can be observed and investigated. This is not possible by using simplified linear models currently available.

Image-Based Predictive Modeling of Heart Mechanics.

PubMed

Wang, V Y; Nielsen, P M F; Nash, M P

2015-01-01

Personalized biophysical modeling of the heart is a useful approach for noninvasively analyzing and predicting in vivo cardiac mechanics. Three main developments support this style of analysis: state-of-the-art cardiac imaging technologies, modern computational infrastructure, and advanced mathematical modeling techniques. In vivo measurements of cardiac structure and function can be integrated using sophisticated computational methods to investigate mechanisms of myocardial function and dysfunction, and can aid in clinical diagnosis and developing personalized treatment. In this article, we review the state-of-the-art in cardiac imaging modalities, model-based interpretation of 3D images of cardiac structure and function, and recent advances in modeling that allow personalized predictions of heart mechanics. We discuss how using such image-based modeling frameworks can increase the understanding of the fundamental biophysics behind cardiac mechanics, and assist with diagnosis, surgical guidance, and treatment planning. Addressing the challenges in this field will require a coordinated effort from both the clinical-imaging and modeling communities. We also discuss future directions that can be taken to bridge the gap between basic science and clinical translation.

Chances of success in and engagement with mathematics for students who enter university with a weak mathematics background

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2010-12-01

An increasing number of Australian students elect not to undertake studies in mathematical methods in the final years of their secondary schooling. Some higher education providers now offer pathways for these students to pursue mathematics studies up to a major specialization within the bachelor of science programme. This article analyses the performance in and engagement with mathematics of the students who elect to take up this option. Findings indicate that these are not very different when compared to students who enter university with an intermediate mathematics preparation. The biggest contrast in performance and engagement is with those students who have studied mathematics in senior secondary school to an advanced level.

Modeling Reality - How Computers Mirror Life

NASA Astrophysics Data System (ADS)

Bialynicki-Birula, Iwo; Bialynicka-Birula, Iwona

2005-01-01

The bookModeling Reality covers a wide range of fascinating subjects, accessible to anyone who wants to learn about the use of computer modeling to solve a diverse range of problems, but who does not possess a specialized training in mathematics or computer science. The material presented is pitched at the level of high-school graduates, even though it covers some advanced topics (cellular automata, Shannon's measure of information, deterministic chaos, fractals, game theory, neural networks, genetic algorithms, and Turing machines). These advanced topics are explained in terms of well known simple concepts: Cellular automata - Game of Life, Shannon's formula - Game of twenty questions, Game theory - Television quiz, etc. The book is unique in explaining in a straightforward, yet complete, fashion many important ideas, related to various models of reality and their applications. Twenty-five programs, written especially for this book, are provided on an accompanying CD. They greatly enhance its pedagogical value and make learning of even the more complex topics an enjoyable pleasure.

Calculated Parameters of Thyroid Homeostasis: Emerging Tools for Differential Diagnosis and Clinical Research

PubMed Central

Dietrich, Johannes W.; Landgrafe-Mende, Gabi; Wiora, Evelin; Chatzitomaris, Apostolos; Klein, Harald H.; Midgley, John E. M.; Hoermann, Rudolf

2016-01-01

Although technical problems of thyroid testing have largely been resolved by modern assay technology, biological variation remains a challenge. This applies to subclinical thyroid disease, non-thyroidal illness syndrome, and those 10% of hypothyroid patients, who report impaired quality of life, despite normal thyrotropin (TSH) concentrations under levothyroxine (L-T4) replacement. Among multiple explanations for this condition, inadequate treatment dosage and monotherapy with L-T4 in subjects with impaired deiodination have received major attention. Translation to clinical practice is difficult, however, since univariate reference ranges for TSH and thyroid hormones fail to deliver robust decision algorithms for therapeutic interventions in patients with more subtle thyroid dysfunctions. Advances in mathematical and simulative modeling of pituitary–thyroid feedback control have improved our understanding of physiological mechanisms governing the homeostatic behavior. From multiple cybernetic models developed since 1956, four examples have also been translated to applications in medical decision-making and clinical trials. Structure parameters representing fundamental properties of the processing structure include the calculated secretory capacity of the thyroid gland (SPINA-GT), sum activity of peripheral deiodinases (SPINA-GD) and Jostel’s TSH index for assessment of thyrotropic pituitary function, supplemented by a recently published algorithm for reconstructing the personal set point of thyroid homeostasis. In addition, a family of integrated models (University of California-Los Angeles platform) provides advanced methods for bioequivalence studies. This perspective article delivers an overview of current clinical research on the basis of mathematical thyroid models. In addition to a summary of large clinical trials, it provides previously unpublished results of validation studies based on simulation and clinical samples. PMID:27375554

Active and Passive Hydrologic Tomographic Surveys:A Revolution in Hydrology (Invited)

NASA Astrophysics Data System (ADS)

Yeh, T. J.

2013-12-01

Mathematical forward or inverse problems of flow through geological media always have unique solutions if necessary conditions are givens. Unique mathematical solutions to forward or inverse modeling of field problems are however always uncertain (an infinite number of possibilities) due to many reasons. They include non-representativeness of the governing equations, inaccurate necessary conditions, multi-scale heterogeneity, scale discrepancies between observation and model, noise and others. Conditional stochastic approaches, which derives the unbiased solution and quantifies the solution uncertainty, are therefore most appropriate for forward and inverse modeling of hydrological processes. Conditioning using non-redundant data sets reduces uncertainty. In this presentation, we explain non-redundant data sets in cross-hole aquifer tests, and demonstrate that active hydraulic tomographic survey (using man-made excitations) is a cost-effective approach to collect the same type but non-redundant data sets for reducing uncertainty in the inverse modeling. We subsequently show that including flux measurements (a piece of non-redundant data set) collected in the same well setup as in hydraulic tomography improves the estimated hydraulic conductivity field. We finally conclude with examples and propositions regarding how to collect and analyze data intelligently by exploiting natural recurrent events (river stage fluctuations, earthquakes, lightning, etc.) as energy sources for basin-scale passive tomographic surveys. The development of information fusion technologies that integrate traditional point measurements and active/passive hydrogeophysical tomographic surveys, as well as advances in sensor, computing, and information technologies may ultimately advance our capability of characterizing groundwater basins to achieve resolution far beyond the feat of current science and technology.

Calculated Parameters of Thyroid Homeostasis: Emerging Tools for Differential Diagnosis and Clinical Research.

PubMed

Dietrich, Johannes W; Landgrafe-Mende, Gabi; Wiora, Evelin; Chatzitomaris, Apostolos; Klein, Harald H; Midgley, John E M; Hoermann, Rudolf

2016-01-01

Although technical problems of thyroid testing have largely been resolved by modern assay technology, biological variation remains a challenge. This applies to subclinical thyroid disease, non-thyroidal illness syndrome, and those 10% of hypothyroid patients, who report impaired quality of life, despite normal thyrotropin (TSH) concentrations under levothyroxine (L-T4) replacement. Among multiple explanations for this condition, inadequate treatment dosage and monotherapy with L-T4 in subjects with impaired deiodination have received major attention. Translation to clinical practice is difficult, however, since univariate reference ranges for TSH and thyroid hormones fail to deliver robust decision algorithms for therapeutic interventions in patients with more subtle thyroid dysfunctions. Advances in mathematical and simulative modeling of pituitary-thyroid feedback control have improved our understanding of physiological mechanisms governing the homeostatic behavior. From multiple cybernetic models developed since 1956, four examples have also been translated to applications in medical decision-making and clinical trials. Structure parameters representing fundamental properties of the processing structure include the calculated secretory capacity of the thyroid gland (SPINA-GT), sum activity of peripheral deiodinases (SPINA-GD) and Jostel's TSH index for assessment of thyrotropic pituitary function, supplemented by a recently published algorithm for reconstructing the personal set point of thyroid homeostasis. In addition, a family of integrated models (University of California-Los Angeles platform) provides advanced methods for bioequivalence studies. This perspective article delivers an overview of current clinical research on the basis of mathematical thyroid models. In addition to a summary of large clinical trials, it provides previously unpublished results of validation studies based on simulation and clinical samples.

Advanced statistical energy analysis

NASA Astrophysics Data System (ADS)

Heron, K. H.

1994-09-01

A high-frequency theory (advanced statistical energy analysis (ASEA)) is developed which takes account of the mechanism of tunnelling and uses a ray theory approach to track the power flowing around a plate or a beam network and then uses statistical energy analysis (SEA) to take care of any residual power. ASEA divides the energy of each sub-system into energy that is freely available for transfer to other sub-systems and energy that is fixed within the sub-systems that are physically separate and can be interpreted as a series of mathematical models, the first of which is identical to standard SEA and subsequent higher order models are convergent on an accurate prediction. Using a structural assembly of six rods as an example, ASEA is shown to converge onto the exact results while SEA is shown to overpredict by up to 60 dB.

Simulation of dental collisions and occlusal dynamics in the virtual environment.

PubMed

Stavness, I K; Hannam, A G; Tobias, D L; Zhang, X

2016-04-01

Semi-adjustable articulators have often been used to simulate occlusal dynamics, but advances in intra-oral scanning and computer software now enable dynamics to be modelled mathematically. Computer simulation of occlusal dynamics requires accurate virtual casts, records to register them and methods to handle mesh collisions during movement. Here, physical casts in a semi-adjustable articulator were scanned with a conventional clinical intra-oral scanner. A coordinate measuring machine was used to index their positions in intercuspation, protrusion, right and left laterotrusion, and to model features of the articulator. Penetrations between the indexed meshes were identified and resolved using restitution forces, and the final registrations were verified by distance measurements between dental landmarks at multiple sites. These sites were confirmed as closely approximating via measurements made from homologous transilluminated vinylpolysiloxane interocclusal impressions in the mounted casts. Movements between the indexed positions were simulated with two models in a custom biomechanical software platform. In model DENTAL, 6 degree-of-freedom movements were made to minimise deviation from a straight line path and also shaped by dynamic mesh collisions detected and resolved mathematically. In model ARTIC, the paths were further constrained by surfaces matching the control settings of the articulator. Despite these differences, the lower mid-incisor point paths were very similar in both models. The study suggests that mathematical simulation utilising interocclusal 'bite' registrations can closely replicate the primary movements of casts mounted in a semi-adjustable articulator. Additional indexing positions and appropriate software could, in some situations, replace the need for mechanical semi-adjustable articulation and/or its virtual representation. © 2015 John Wiley & Sons Ltd.

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

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.; Houck, Jacob A.

1990-01-01

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

Advanced Reactors-Intermediate Heat Exchanger (IHX) Coupling: Theoretical Modeling and Experimental Validation

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

Utgikar, Vivek; Sun, Xiaodong; Christensen, Richard

2016-12-29

The overall goal of the research project was to model the behavior of the advanced reactorintermediate heat exchange system and to develop advanced control techniques for off-normal conditions. The specific objectives defined for the project were: 1. To develop the steady-state thermal hydraulic design of the intermediate heat exchanger (IHX); 2. To develop mathematical models to describe the advanced nuclear reactor-IHX-chemical process/power generation coupling during normal and off-normal operations, and to simulate models using multiphysics software; 3. To develop control strategies using genetic algorithm or neural network techniques and couple these techniques with the multiphysics software; 4. To validate themore » models experimentally The project objectives were accomplished by defining and executing four different tasks corresponding to these specific objectives. The first task involved selection of IHX candidates and developing steady state designs for those. The second task involved modeling of the transient and offnormal operation of the reactor-IHX system. The subsequent task dealt with the development of control strategies and involved algorithm development and simulation. The last task involved experimental validation of the thermal hydraulic performances of the two prototype heat exchangers designed and fabricated for the project at steady state and transient conditions to simulate the coupling of the reactor- IHX-process plant system. The experimental work utilized the two test facilities at The Ohio State University (OSU) including one existing High-Temperature Helium Test Facility (HTHF) and the newly developed high-temperature molten salt facility.« less

Learning from the Unknown Student

ERIC Educational Resources Information Center

Barlow, Angela T.; Gerstenschlager, Natasha E.; Harmon, Shannon E.

2016-01-01

In this article, three instructional situations demonstrate the value of using an "unknown" student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others: (1) introducing alternative solution strategies; (2) critiquing inaccuracies…

Undergraduate Training for Industrial Careers.

ERIC Educational Resources Information Center

Stehney, Ann K.

1983-01-01

Forty-eight mathematicians in industry, business, and government replied to a questionnaire on the relative merits of the traditional undergraduate curriculum, advanced topics in pure mathematics, computer programing, additional computer science, and specialized or applied topics. They favored programing and applied mathematics, along with a…

Mathematics Readiness of First-Year University Students

ERIC Educational Resources Information Center

Atuahene, Francis; Russell, Tammy A.

2016-01-01

The majority of high school students, particularly underrepresented minorities (URMs) from low socioeconomic backgrounds are graduating from high school less prepared academically for advanced-level college mathematics. Using 2009 and 2010 course enrollment data, several statistical analyses (multiple linear regression, Cochran Mantel Haenszel…

Space structures insulating material's thermophysical and radiation properties estimation

NASA Astrophysics Data System (ADS)

Nenarokomov, A. V.; Alifanov, O. M.; Titov, D. M.

2007-11-01

In many practical situations in aerospace technology it is impossible to measure directly such properties of analyzed materials (for example, composites) as thermal and radiation characteristics. The only way that can often be used to overcome these difficulties is indirect measurements. This type of measurement is usually formulated as the solution of inverse heat transfer problems. Such problems are ill-posed in mathematical sense and their main feature shows itself in the solution instabilities. That is why special regularizing methods are needed to solve them. The experimental methods of identification of the mathematical models of heat transfer based on solving the inverse problems are one of the modern effective solving manners. The objective of this paper is to estimate thermal and radiation properties of advanced materials using the approach based on inverse methods.

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

PubMed

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

2013-05-30

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

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.

How can mathematical models advance tuberculosis control in high HIV prevalence settings?

PubMed

Houben, R M G J; Dowdy, D W; Vassall, A; Cohen, T; Nicol, M P; Granich, R M; Shea, J E; Eckhoff, P; Dye, C; Kimerling, M E; White, R G

2014-05-01

Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly.

A mathematical model of vowel identification by users of cochlear implants

PubMed Central

Sagi, Elad; Meyer, Ted A.; Kaiser, Adam R.; Teoh, Su Wooi; Svirsky, Mario A.

2010-01-01

A simple mathematical model is presented that predicts vowel identification by cochlear implant users based on these listeners’ resolving power for the mean locations of first, second, and∕or third formant energies along the implanted electrode array. This psychophysically based model provides hypotheses about the mechanism cochlear implant users employ to encode and process the input auditory signal to extract information relevant for identifying steady-state vowels. Using one free parameter, the model predicts most of the patterns of vowel confusions made by users of different cochlear implant devices and stimulation strategies, and who show widely different levels of speech perception (from near chance to near perfect). Furthermore, the model can predict results from the literature, such as Skinner, et al. [(1995). Ann. Otol. Rhinol. Laryngol. 104, 307–311] frequency mapping study, and the general trend in the vowel results of Zeng and Galvin’s [(1999). Ear Hear. 20, 60–74] studies of output electrical dynamic range reduction. The implementation of the model presented here is specific to vowel identification by cochlear implant users, but the framework of the model is more general. Computational models such as the one presented here can be useful for advancing knowledge about speech perception in hearing impaired populations, and for providing a guide for clinical research and clinical practice. PMID:20136228

Mathematical Perspectives

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

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometrymore » and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.« less

Development of Serum Marker Models to Increase Diagnostic Accuracy of Advanced Fibrosis in Nonalcoholic Fatty Liver Disease: The New LINKI Algorithm Compared with Established Algorithms.

PubMed

Lykiardopoulos, Byron; Hagström, Hannes; Fredrikson, Mats; Ignatova, Simone; Stål, Per; Hultcrantz, Rolf; Ekstedt, Mattias; Kechagias, Stergios

2016-01-01

Detection of advanced fibrosis (F3-F4) in nonalcoholic fatty liver disease (NAFLD) is important for ascertaining prognosis. Serum markers have been proposed as alternatives to biopsy. We attempted to develop a novel algorithm for detection of advanced fibrosis based on a more efficient combination of serological markers and to compare this with established algorithms. We included 158 patients with biopsy-proven NAFLD. Of these, 38 had advanced fibrosis. The following fibrosis algorithms were calculated: NAFLD fibrosis score, BARD, NIKEI, NASH-CRN regression score, APRI, FIB-4, King´s score, GUCI, Lok index, Forns score, and ELF. Study population was randomly divided in a training and a validation group. A multiple logistic regression analysis using bootstrapping methods was applied to the training group. Among many variables analyzed age, fasting glucose, hyaluronic acid and AST were included, and a model (LINKI-1) for predicting advanced fibrosis was created. Moreover, these variables were combined with platelet count in a mathematical way exaggerating the opposing effects, and alternative models (LINKI-2) were also created. Models were compared using area under the receiver operator characteristic curves (AUROC). Of established algorithms FIB-4 and King´s score had the best diagnostic accuracy with AUROCs 0.84 and 0.83, respectively. Higher accuracy was achieved with the novel LINKI algorithms. AUROCs in the total cohort for LINKI-1 was 0.91 and for LINKI-2 models 0.89. The LINKI algorithms for detection of advanced fibrosis in NAFLD showed better accuracy than established algorithms and should be validated in further studies including larger cohorts.

Advances in mechanistic understanding of release rate control mechanisms of extended-release hydrophilic matrix tablets.

PubMed

Timmins, Peter; Desai, Divyakant; Chen, Wei; Wray, Patrick; Brown, Jonathan; Hanley, Sarah

2016-08-01

Approaches to characterizing and developing understanding around the mechanisms that control the release of drugs from hydrophilic matrix tablets are reviewed. While historical context is provided and direct physical characterization methods are described, recent advances including the role of percolation thresholds, the application on magnetic resonance and other spectroscopic imaging techniques are considered. The influence of polymer and dosage form characteristics are reviewed. The utility of mathematical modeling is described. Finally, how all the information derived from applying the developed mechanistic understanding from all of these tools can be brought together to develop a robust and reliable hydrophilic matrix extended-release tablet formulation is proposed.

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…

Experimental advances and preliminary mathematical modeling of the Swiss-roll mixed-reactant direct borohydride fuel cell

NASA Astrophysics Data System (ADS)

Aziznia, Amin; Oloman, Colin W.; Gyenge, Előd L.

2014-11-01

The Swiss-roll single-cell mixed reactant (SR-MRFC) borohydride - oxygen fuel cell equipped with Pt/carbon cloth 3D anode and either MnO2 or Ag gas-diffusion cathodes is investigated by a combination of experimental studies and preliminary mathematical modeling of the polarization curve. We investigate the effects of four variables: cathode side metallic mesh fluid distributor, separator type (Nafion 112® vs. Viledon®), cathode catalyst (MnO2 vs. Ag), and the hydrophilic pore volume fraction of the gas-diffusion cathode. Using a two-phase feed of alkaline borohydride solution (1 M NaBH4 - 2 M NaOH) and O2 gas in an SR-MRFC equipped with Pt/C 3D anode, MnO2 gas diffusion cathode, Viledon® porous diaphragm, expanded mesh cathode-side fluid distributor, the maximum superficial power density is 2230 W m-2 at 323 K and 105 kPa(abs). The latter superficial power density is almost 3.5 times higher than our previously reported superficial power density for the same catalyst combinations. Furthermore, with a Pt anode and Ag cathode catalyst combination, a superficial power density of 2500 W m-2 is achieved with superior performance durability compared to the MnO2 cathode. The fuel cell results are substantiated by impedance spectroscopy analysis and preliminary mathematical model predictions based on mixed potential theory.

A review on data mining and continuous optimization applications in computational biology and medicine.

PubMed

Weber, Gerhard-Wilhelm; Ozöğür-Akyüz, Süreyya; Kropat, Erik

2009-06-01

An emerging research area in computational biology and biotechnology is devoted to mathematical modeling and prediction of gene-expression patterns; it nowadays requests mathematics to deeply understand its foundations. This article surveys data mining and machine learning methods for an analysis of complex systems in computational biology. It mathematically deepens recent advances in modeling and prediction by rigorously introducing the environment and aspects of errors and uncertainty into the genetic context within the framework of matrix and interval arithmetics. Given the data from DNA microarray experiments and environmental measurements, we extract nonlinear ordinary differential equations which contain parameters that are to be determined. This is done by a generalized Chebychev approximation and generalized semi-infinite optimization. Then, time-discretized dynamical systems are studied. By a combinatorial algorithm which constructs and follows polyhedra sequences, the region of parametric stability is detected. In addition, we analyze the topological landscape of gene-environment networks in terms of structural stability. As a second strategy, we will review recent model selection and kernel learning methods for binary classification which can be used to classify microarray data for cancerous cells or for discrimination of other kind of diseases. This review is practically motivated and theoretically elaborated; it is devoted to a contribution to better health care, progress in medicine, a better education, and more healthy living conditions.

A Diverse Community To Study Communities: Integration of Experiments and Mathematical Models To Study Microbial Consortia.

PubMed

Succurro, Antonella; Moejes, Fiona Wanjiku; Ebenhöh, Oliver

2017-08-01

The last few years have seen the advancement of high-throughput experimental techniques that have produced an extraordinary amount of data. Bioinformatics and statistical analyses have become instrumental to interpreting the information coming from, e.g., sequencing data and often motivate further targeted experiments. The broad discipline of "computational biology" extends far beyond the well-established field of bioinformatics, but it is our impression that more theoretical methods such as the use of mathematical models are not yet as well integrated into the research studying microbial interactions. The empirical complexity of microbial communities presents challenges that are difficult to address with in vivo / in vitro approaches alone, and with microbiology developing from a qualitative to a quantitative science, we see stronger opportunities arising for interdisciplinary projects integrating theoretical approaches with experiments. Indeed, the addition of in silico experiments, i.e., computational simulations, has a discovery potential that is, unfortunately, still largely underutilized and unrecognized by the scientific community. This minireview provides an overview of mathematical models of natural ecosystems and emphasizes that one critical point in the development of a theoretical description of a microbial community is the choice of problem scale. Since this choice is mostly dictated by the biological question to be addressed, in order to employ theoretical models fully and successfully it is vital to implement an interdisciplinary view at the conceptual stages of the experimental design. Copyright © 2017 Succurro et al.

Center for Center for Technology for Advanced Scientific Component Software (TASCS)

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

Kostadin, Damevski

A resounding success of the Scientific Discovery through Advanced Computing (SciDAC) program is that high-performance computational science is now universally recognized as a critical aspect of scientific discovery [71], complementing both theoretical and experimental research. As scientific communities prepare to exploit unprecedented computing capabilities of emerging leadership-class machines for multi-model simulations at the extreme scale [72], it is more important than ever to address the technical and social challenges of geographically distributed teams that combine expertise in domain science, applied mathematics, and computer science to build robust and flexible codes that can incorporate changes over time. The Center for Technologymore » for Advanced Scientific Component Software (TASCS)1 tackles these these issues by exploiting component-based software development to facilitate collaborative high-performance scientific computing.« less

The Role of STEM High Schools in Reducing Gaps in Science and Mathematics Coursetaking: Evidence from North Carolina. Research Report. RTI Press Publication RR-0025-1603

ERIC Educational Resources Information Center

Glennie, Elizabeth; Mason, Marcinda; Dalton, Ben

2016-01-01

Some states have created science, technology, engineering, and mathematics (STEM) schools to encourage student interest and enhance student proficiency in STEM subjects. We examined a set of STEM schools serving disadvantaged students to see whether these students were more likely to take and pass advanced science and mathematics classes than…

Teaching undergraduate mathematics in interactive groups: how does it fit with students' learning?

NASA Astrophysics Data System (ADS)

Sheryn, Louise; Ell, Fiona

2014-08-01

Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in combinatorics, taught using a non-traditional, formal group work approach, the 10 students shared their views about how such an approach fitted in with their experience of learning mathematics. A descriptive thematic analysis of the students' responses revealed that despite being very comfortable with the traditional approach to learning new mathematics, most students were open to a formal group work approach and could see benefits from it after their participation. The students' prior conceptions of the goal of undergraduate mathematics learning and their view of themselves as 'mathematicians' framed their experience of learning mathematics in a non-traditional class.

Determination of Material Constitutive Laws for Inconel 718 Superalloy Under Different Strain Rates and Working Temperatures

NASA Astrophysics Data System (ADS)

Grzesik, W.; Niesłony, P.; Laskowski, P.

2017-12-01

In this paper, a special procedure for the prediction of parameters of the Johnson-Cook constitutive material models is proposed based on the experimental data and specially developed MATLAB scripts which allow advanced modeling of complex 3D response surfaces. Experimental investigations concern two various strain rates of 10-3 and 101 1/s and the testing temperature ranging from the ambient up to 700 °C. As a result, a set of mathematical equations which fit the experimental data is determined. The applicability of the experimentally derived constitutive models to the FEM modeling of real machining processes of Inconel 718 alloy is verified.

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…

Mathematical Heroes--No Longer Unsung

ERIC Educational Resources Information Center

Chin, Cynthia E.

2007-01-01

The history of Fermat's Last Theorem, recounted in the theatrical piece "Fermat's Last Tango," is a useful vehicle for introducing students to the variety of personalities, processes, and products involved in advanced mathematical investigation. The musical's accessible, informative, and positive portrayal of mathematicians and their work is…

A Worked Example for Creating Worked Examples

ERIC Educational Resources Information Center

McGinn, Kelly M.; Lange, Karin E.; Booth, Julie L.

2015-01-01

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Increasing Interest of Young Women in Engineering

ERIC Educational Resources Information Center

Hinterlong, Diane; Lawrence, Branson; DeVol, Purva

2014-01-01

The internationally recognized Illinois Mathematics and Science Academy (IMSA) develops creative, ethical leaders in science, technology, engineering and mathematics. As a teaching and learning laboratory created by the State of Illinois, IMSA enrolls academically talented Illinois students in grades 10 through 12 in its advanced, residential…

New Technologies in Mathematics.

ERIC Educational Resources Information Center

Sarmiento, Jorge

An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…

This Rock 'n' Roll Video Teaches Math

ERIC Educational Resources Information Center

Niess, Margaret L.; Walker, Janet M.

2009-01-01

Mathematics is a discipline that has significantly advanced through the use of digital technologies with improved computational, graphical, and symbolic capabilities. Digital videos can be used to present challenging mathematical questions for students. Video clips offer instructional possibilities for moving students from a passive mode of…

Nurturing Young Student Mathematicians

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.

2013-01-01

Developing mathematical talent in our students should be of primary consideration in education today as nations respond to the challenges of economic crises and ever-changing technological advances. This paper describes two U.S. federally funded curriculum projects, Project M[superscript 3], Mentoring Mathematical Minds, and Project M[superscript…

Recreating History with Archimedes and Pi

ERIC Educational Resources Information Center

Santucci, Lora C.

2011-01-01

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

Recent Physics Doctorates: Skills Used & Satisfaction with Employment. Data from the Degree Recipient Follow-Up Survey for the Classes of 2009 and 2010. Focus On

ERIC Educational Resources Information Center

Anderson, Garrett; Mulvey, Patrick

2013-01-01

By the time people earn physics PhDs, they have learned a great deal about physics and how research is conducted. However, physics PhDs also develop skills and knowledge in a number of related areas, such as advanced mathematics, programming, modeling, and technical writing. New physics PhDs draw upon an arsenal of skills and knowledge in their…

The 1981 NASA/ASEE Summer Faculty Fellowship Program: Research reports

NASA Technical Reports Server (NTRS)

Karr, G. R.; Dozier, J. B.; Kent, M. I.; Barfield, B. F.

1982-01-01

Research reports related to spacecraft industry technological advances, requirements, and applications were considered. Some of the topic areas addressed were: (1) Fabrication, evaluation, and use of high performance composites and ceramics, (2) antenna designs, (3) electronics and microcomputer applications and mathematical modeling and programming techniques, (4) design, fabrication, and failure detection methods for structural materials, components, and total systems, and (5) chemical studies of bindary organic mixtures and polymer synthesis. Space environment parameters were also discussed.

Throw Away Your Mathematical Handbook! Undergraduate Physics with Wolfram|Alpha, a FREE(!) Internet-Based Mathematical Engine

NASA Astrophysics Data System (ADS)

Looney, Craig W.

2009-10-01

Wolfram|Alpha (http://www.wolframalpha.com/), a free internet-based mathematical engine released earlier this year, represents an orders-of magnitude advance in mathematical power freely available - without money, passwords, or downloads - on the web. Wolfram|Alpha is based on Mathematica, so it can plot functions, take derivatives, solve systems of equations, perform symbolic and numerical integration, and more. These capabilities (especially plotting and integration) will be explored in the context of topics covered in upper level undergraduate physics courses.

Agent-Centric Approach for Cybersecurity Decision-Support with Partial Observability

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

Tipireddy, Ramakrishna; Chatterjee, Samrat; Paulson, Patrick R.

Generating automated cyber resilience policies for real-world settings is a challenging research problem that must account for uncertainties in system state over time and dynamics between attackers and defenders. In addition to understanding attacker and defender motives and tools, and identifying “relevant” system and attack data, it is also critical to develop rigorous mathematical formulations representing the defender’s decision-support problem under uncertainty. Game-theoretic approaches involving cyber resource allocation optimization with Markov decision processes (MDP) have been previously proposed in the literature. Moreover, advancements in reinforcement learning approaches have motivated the development of partially observable stochastic games (POSGs) in various multi-agentmore » problem domains with partial information. Recent advances in cyber-system state space modeling have also generated interest in potential applicability of POSGs for cybersecurity. However, as is the case in strategic card games such as poker, research challenges using game-theoretic approaches for practical cyber defense applications include: 1) solving for equilibrium and designing efficient algorithms for large-scale, general problems; 2) establishing mathematical guarantees that equilibrium exists; 3) handling possible existence of multiple equilibria; and 4) exploitation of opponent weaknesses. Inspired by advances in solving strategic card games while acknowledging practical challenges associated with the use of game-theoretic approaches in cyber settings, this paper proposes an agent-centric approach for cybersecurity decision-support with partial system state observability.« less

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

A Mathematical Framework for the Complex System Approach to Group Dynamics: The Case of Recovery House Social Integration.

PubMed

Light, John M; Jason, Leonard A; Stevens, Edward B; Callahan, Sarah; Stone, Ariel

2016-03-01

The complex system conception of group social dynamics often involves not only changing individual characteristics, but also changing within-group relationships. Recent advances in stochastic dynamic network modeling allow these interdependencies to be modeled from data. This methodology is discussed within a context of other mathematical and statistical approaches that have been or could be applied to study the temporal evolution of relationships and behaviors within small- to medium-sized groups. An example model is presented, based on a pilot study of five Oxford House recovery homes, sober living environments for individuals following release from acute substance abuse treatment. This model demonstrates how dynamic network modeling can be applied to such systems, examines and discusses several options for pooling, and shows how results are interpreted in line with complex system concepts. Results suggest that this approach (a) is a credible modeling framework for studying group dynamics even with limited data, (b) improves upon the most common alternatives, and (c) is especially well-suited to complex system conceptions. Continuing improvements in stochastic models and associated software may finally lead to mainstream use of these techniques for the study of group dynamics, a shift already occurring in related fields of behavioral science.

Promise of new imaging technologies for assessing ovarian function.

PubMed

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

2003-10-15

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

Manuel Stein's Five Decades of Structural Mechanics Contributions (1944-1988)

NASA Technical Reports Server (NTRS)

Mikulas, Martin M.; Card, Michael F.; Peterson, Jim P.; Starnes, James H., Jr.

1998-01-01

Manuel Stein went to work for NACA (National Advisory Committee for Aeronautics) in 1944 and left in 1988. His research contributions spanned five decades of extremely defining times for the aerospace industry. Problems arising from the analysis and design of efficient thin plate and shell aerospace structures have stimulated research over the past half century. The primary structural technology drivers during Dr. Stein's career included 1940's aluminum aircraft, 1950's jet aircraft, 1960's launch vehicles and advanced spacecraft, 1970's reusable launch vehicles and commercial aircraft, and 1980's composite aircraft. Dr. Stein's research was driven by these areas and he made lasting contributions for each. Dr. Stein's research can be characterized by a judicious mixture of physical insight into the problem, understanding of the basic mechanisms, mathematical modeling of the observed phenomena, and extraordinary analytical and numerical solution methodologies of the resulting mathematical models. This paper summarizes Dr. Stein's life and his contributions to the technical community.

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.

Simultaneous Sensor and Process Fault Diagnostics for Propellant Feed System

NASA Technical Reports Server (NTRS)

Cao, J.; Kwan, C.; Figueroa, F.; Xu, R.

2006-01-01

The main objective of this research is to extract fault features from sensor faults and process faults by using advanced fault detection and isolation (FDI) algorithms. A tank system that has some common characteristics to a NASA testbed at Stennis Space Center was used to verify our proposed algorithms. First, a generic tank system was modeled. Second, a mathematical model suitable for FDI has been derived for the tank system. Third, a new and general FDI procedure has been designed to distinguish process faults and sensor faults. Extensive simulations clearly demonstrated the advantages of the new design.

Technological Education for the Rural Community (TERC) Project: Technical Mathematics for the Advanced Manufacturing Technician

ERIC Educational Resources Information Center

McCormack, Sherry L.; Zieman, Stuart

2017-01-01

Hopkinsville Community College's Technological Education for the Rural Community (TERC) project is funded through the National Science Foundation Advanced Technological Education (NSF ATE) division. It is advancing innovative educational pathways for technological education promoted at the community college level serving rural communities to fill…

Mathematical Visualization

ERIC Educational Resources Information Center

Rogness, Jonathan

2011-01-01

Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

Accelerating Mathematics Achievement Using Heterogeneous Grouping

ERIC Educational Resources Information Center

Burris, Carol Corbett; Heubert, Jay P.; Levin, Henry M.

2006-01-01

This longitudinal study examined the effects of providing an accelerated mathematics curriculum in heterogeneously grouped middle school classes in a diverse suburban school district. A quasi-experimental cohort design was used to evaluate subsequent completion of advanced high school math courses as well as academic achievement. Results showed…

Workplace Math. EPIC Workplace Learning Project, 1996.

ERIC Educational Resources Information Center

King, Catherine; Cyr, Anne Reis; Gross, Mary; Armstrong, Ray

Designed as a reference for teaching mathematics in the workplace, this manual presents teaching strategies and activities for beginning, intermediate, and advanced learners in four mathematics-related topics. Following an overview of the manual's purpose, definitions are provided of the three skill levels targeted by the activities. Strategies…

Collegiate Mathematics Teaching: An Unexamined Practice

ERIC Educational Resources Information Center

Speer, Natasha M.; Smith, John P., III; Horvath, Aladar

2010-01-01

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

Theorizing the Nexus of STEAM Practice

ERIC Educational Resources Information Center

Peppler, Kylie; Wohlwend, Karen

2018-01-01

Recent advances in arts education policy, as outlined in the latest National Core Arts Standards, advocate for bringing digital media into the arts education classroom. The promise of such Science, Technology, Engineering, Arts, and Mathematics (STEAM)-based approaches is that, by coupling Science, Technology, Engineering, and Mathematics (STEM)…

Just do it: flipped lecture, determinants and debate

NASA Astrophysics Data System (ADS)

Kensington-Miller, Barbara; Novak, Julia; Evans, Tanya

2016-08-01

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills, such as debate, argument and disagreement. The students were told in advance to use the online material to prepare, which had a short handout on matrix determinants posted, as the lesson would be interactive and would rely on them having studied this. At the beginning of the lesson, the two mathematicians worked together to model the skill of professional disagreement, one arguing for the cofactor expansion method and the other for the row reduction method. After voting for their preferred method, the students worked in small groups on examples to defend their choice. Each group elected a spokesperson and a political style debate followed as the students argued the pros and cons of each technique. Although one lecture does not establish whether the flipped lecture model is preferable for student instruction, the paper presents a case study for pursuing this approach and for further research on incorporating this style of teaching in Science, Technology, Engineering and Mathematics subjects.

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…

Handwritten mathematical symbols dataset.

PubMed

Chajri, Yassine; Bouikhalene, Belaid

2016-06-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc.

Hydrodynamic evaluation of a full-scale facultative pond by computational fluid dynamics (CFD) and field measurements.

PubMed

Passos, Ricardo Gomes; von Sperling, Marcos; Ribeiro, Thiago Bressani

2014-01-01

Knowledge of the hydraulic behaviour is very important in the characterization of a stabilization pond, since pond hydrodynamics plays a fundamental role in treatment efficiency. An advanced hydrodynamics characterization may be achieved by carrying out measurements with tracers, dyes and drogues or using mathematical simulation employing computational fluid dynamics (CFD). The current study involved experimental determinations and mathematical simulations of a full-scale facultative pond in Brazil. A 3D CFD model showed major flow lines, degree of dispersion, dead zones and short circuit regions in the pond. Drogue tracking, wind measurements and dye dispersion were also used in order to obtain information about the actual flow in the pond and as a means of assessing the performance of the CFD model. The drogue, designed and built as part of this research, and which included a geographical positioning system (GPS), presented very satisfactory results. The CFD modelling has proven to be very useful in the evaluation of the hydrodynamic conditions of the facultative pond. A virtual tracer test allowed an estimation of the real mean hydraulic retention time and mixing conditions in the pond. The computational model in CFD corresponded well to what was verified in the field.

Surface Properties of PEMFC Gas Diffusion Layers

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

WoodIII, David L; Rulison, Christopher; Borup, Rodney

2010-01-01

The wetting properties of PEMFC Gas Diffusion Layers (GDLs) were quantified by surface characterization measurements and modeling of material properties. Single-fiber contact-angle and surface energy (both Zisman and Owens-Wendt) data of a wide spectrum of GDL types is presented to delineate the effects of hydrophobic post-processing treatments. Modeling of the basic sessile-drop contact angle demonstrates that this value only gives a fraction of the total picture of interfacial wetting physics. Polar forces are shown to contribute 10-20 less than dispersive forces to the composite wetting of GDLs. Internal water contact angles obtained from Owens-Wendt analysis were measured at 13-19 highermore » than their single-fiber counterparts. An inverse relationship was found between internal contact angle and both Owens-Wendt surface energy and % polarity of the GDL. The most sophisticated PEMFC mathematical models use either experimentally measured capillary pressures or the standard Young-Laplace capillary-pressure equation. Based on the results of the Owens-Wendt analysis, an advancement to the Young-Laplace equation is proposed for use in these mathematical models, which utilizes only solid surface energies and fractional surface coverage of fluoropolymer. Capillary constants for the spectrum of analyzed GDLs are presented for the same purpose.« less

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…

Performance analysis and optimization of an advanced pharmaceutical wastewater treatment plant through a visual basic software tool (PWWT.VB).

PubMed

Pal, Parimal; Thakura, Ritwik; Chakrabortty, Sankha

2016-05-01

A user-friendly, menu-driven simulation software tool has been developed for the first time to optimize and analyze the system performance of an advanced continuous membrane-integrated pharmaceutical wastewater treatment plant. The software allows pre-analysis and manipulation of input data which helps in optimization and shows the software performance visually on a graphical platform. Moreover, the software helps the user to "visualize" the effects of the operating parameters through its model-predicted output profiles. The software is based on a dynamic mathematical model, developed for a systematically integrated forward osmosis-nanofiltration process for removal of toxic organic compounds from pharmaceutical wastewater. The model-predicted values have been observed to corroborate well with the extensive experimental investigations which were found to be consistent under varying operating conditions like operating pressure, operating flow rate, and draw solute concentration. Low values of the relative error (RE = 0.09) and high values of Willmott-d-index (d will = 0.981) reflected a high degree of accuracy and reliability of the software. This software is likely to be a very efficient tool for system design or simulation of an advanced membrane-integrated treatment plant for hazardous wastewater.

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…

Listening to and Learning from Student Thinking

ERIC Educational Resources Information Center

Kazemi, Elham; Gibbons, Lynsey K.; Lomax, Kendra; Franke, Megan L.

2016-01-01

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

Cognitive Technologies for Mathematics Education. Technical Report No. 37.

ERIC Educational Resources Information Center

Pea, Roy D.

This paper provides an historical perspective on the possible roles of cognitive technologies in thinking as "reorganizers" of the mind. It suggests that by understanding the transformational roles of advanced technologies for mathematical thinking, positive contributions can be made to research and practice on the use of computers in…