The ``System of Chymists'' and the ``Newtonian dream'' in Greek-speaking Communities in the 17th-18th Centuries

NASA Astrophysics Data System (ADS)

Bokaris, Efthymios P.; Koutalis, Vangelis

2008-06-01

The acceptance of new chemical ideas, before the Chemical Revolution of Lavoisier, in Greek-speaking communities in the 17th and 18th centuries did not create a discourse of chemical philosophy, as it did in Europe, but rather a “philosophy” of chemistry as it was formed through the evolution of didactic traditions of Chemistry. This “philosophical” chemistry was not based on the existence of any academic institutions, it was focused on the ontology of principles and forces governing the analysis/synthesis of matter and formulated two didactic traditions. The one, named “the system of chymists”, close to the Boylean/Cartesian tradition, accepted, contrary to Aristotelianism, the five “chymical” principles and also the analytical ideal, but the “chymical” principles were not under a conceptual and experimental investigation, as they were in Europe. Also, a crucial issue for this tradition remained the “mechanical” principles which were under the influence of the metaphysical nature of the Aristotelian principles. The other, close to the Boylean/Newtonian tradition, was the integrated presentation of the Newtonian “dream”, which maintained a discursive attitude with reference to the “chemical attractions”-“chemical affinities” and actualised the mathematical atomism of Boscovich, according to which the elementary texture of matter could be causally explained within this complex architecture of mathematical “ punkta”. In this tradition also coexisted, in a discursive synthesis, the “chemical element” of Lavoisier and the arguments of the new theory and its opposition to the phlogiston theory, but the “chemical affinities” were under the realm of the “physical element” as “metaphysical point”.

A Call for Mathematics Education Colleagues and Stakeholders to Collaboratively Engage with NCTM: In Response to Martin's Commentary

ERIC Educational Resources Information Center

Briars, Diane J.; Larson, Matt; Strutchens, Marilyn E.; Barnes, David

2015-01-01

In his commentary "The Collective Black and 'Principles to Actions,'" Martin (2015) offers a thought-provoking critique of "Principles to Actions: Ensuring Mathematical Success for All" (National Council of Teachers of Mathematics [NCTM], 2014). Martin (2015) states that the mathematics education community, in general, and the…

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Hobbes on natural philosophy as "True Physics" and mixed mathematics.

PubMed

Adams, Marcus P

2016-04-01

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. Copyright © 2015 Elsevier Ltd. All rights reserved.

Natural hazard metaphors for financial crises

NASA Astrophysics Data System (ADS)

Woo, Gordon

2001-02-01

Linguistic metaphors drawn from natural hazards are commonly used at times of financial crisis. A brewing storm, a seismic shock, etc., evoke the abruptness and severity of a market collapse. If the language of windstorms, earthquakes and volcanic eruptions is helpful in illustrating a financial crisis, what about the mathematics of natural catastrophes? Already, earthquake prediction methods have been applied to economic recessions, and volcanic eruption forecasting techniques have been applied to market crashes. The purpose of this contribution is to survey broadly the mathematics of natural catastrophes, so as to convey the range of underlying principles, some of which may serve as mathematical metaphors for financial applications.

Dynamics of non-holonomic systems with stochastic transport

NASA Astrophysics Data System (ADS)

Holm, D. D.; Putkaradze, V.

2018-01-01

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

Bridging CAGD knowledge into CAD/CG applications: Mathematical theories as stepping stones of innovations

NASA Astrophysics Data System (ADS)

Gobithaasan, R. U.; Miura, Kenjiro T.; Hassan, Mohamad Nor

2014-07-01

Computer Aided Geometric Design (CAGD) which surpasses the underlying theories of Computer Aided Design (CAD) and Computer Graphics (CG) has been taught in a number of Malaysian universities under the umbrella of Mathematical Sciences' faculty/department. On the other hand, CAD/CG is taught either under the Engineering or Computer Science Faculty. Even though CAGD researchers/educators/students (denoted as contributors) have been enriching this field of study by means of article/journal publication, many fail to convert the idea into constructive innovation due to the gap that occurs between CAGD contributors and practitioners (engineers/product/designers/architects/artists). This paper addresses this issue by advocating a number of technologies that can be used to transform CAGD contributors into innovators where immediate impact in terms of practical application can be experienced by the CAD/CG practitioners. The underlying principle of solving this issue is twofold. First would be to expose the CAGD contributors on ways to turn mathematical ideas into plug-ins and second is to impart relevant CAGD theories to CAD/CG to practitioners. Both cases are discussed in detail and the final section shows examples to illustrate the importance of turning mathematical knowledge into innovations.

40 CFR 280.12 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... physical and chemical properties upon contact with one another for the design life of the tank system under... reason of thorough knowledge of the physical sciences and the principles of engineering and mathematics... UST systems located on the same property where the stored heating oil is used. Operational life refers...

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

Business Mathematics Curriculum Guide.

ERIC Educational Resources Information Center

Ebersole, Benjamin P., Comp.; And Others

This revised course in business mathematics emphasizes computations needed for problem solving, but greater attention is focused on mathematical principles that were developed in previous grades. In addition, the course aims to develop further an understanding of business principles and practices which can be used in gainful employment and in the…

A Protocol for Evaluating Contextual Design Principles

PubMed Central

Stamps, Arthur

2014-01-01

This paper explains how scientific data can be incorporated into urban design decisions, such as evaluating contextual design principles. The recommended protocols are based on the Cochrane Reviews that have been widely used in medical research. The major concepts of a Cochrane Review are explained, as well as the underlying mathematics. The underlying math is meta-analysis. Data are reported for three applications and seven contextual design policies. It is suggested that use of the Cochrane protocols will be of great assistance to planners by providing scientific data that can be used to evaluate the efficacies of contextual design policies prior to implementing those policies. PMID:25431448

Modeling Spatial and Temporal Aspects of Visual Backward Masking

ERIC Educational Resources Information Center

Hermens, Frouke; Luksys, Gediminas; Gerstner, Wulfram; Herzog, Michael H.; Ernst, Udo

2008-01-01

Visual backward masking is a versatile tool for understanding principles and limitations of visual information processing in the human brain. However, the mechanisms underlying masking are still poorly understood. In the current contribution, the authors show that a structurally simple mathematical model can explain many spatial and temporal…

Rational Number and Proportional Reasoning in Early Secondary School: Towards Principled Improvement in Mathematics

ERIC Educational Resources Information Center

Howe, Christine; Luthman, Stefanie; Ruthven, Kenneth; Mercer, Neil; Hofmann, Riikka; Ilie, Sonia; Guardia, Paula

2015-01-01

Reflecting concerns about student attainment and participation in mathematics and science, the Effecting Principled Improvement in STEM Education ("epiSTEMe") project attempted to support pedagogical advancement in these two disciplines. Using principles identified as effective in the research literature (and combining these in a novel…

The Collective Black and "Principles to Actions"

ERIC Educational Resources Information Center

Martin, Danny Bernard

2015-01-01

In this commentary, Danny Martin describes five key take-aways and two sets of questions that arose from his reading of "Principles to Actions: Ensuring Mathematics Success for All (National Council of Teachers of Mathematics [NCTM], 2014). Martin begins by noting that "Principles to Actions" is clearly a political document that…

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

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

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

Lamp control using the principles of mathematical logic

NASA Astrophysics Data System (ADS)

Yudianto, E.; Firmansyah, F. F.; Akbar, P. S. B. S.; Nisyak, R.; Maudi, F. A.; Saputri, A. N.

2018-03-01

Along with the rapid development of technology, there are so many innovations on tools that can facilitate human’s work, one of which is a remote lamp controller. This light controller can provide convenience and comfort for people in turning on or off lights, especially they are traveling. The way remote light controller is used applies the principle of mathematical logic, particularly biimplication. The principle of mathematical logic (biimplication) on this light controller is applied to GSM module (gprs) and SMS.

On the Dirichlet's Box Principle

ERIC Educational Resources Information Center

Poon, Kin-Keung; Shiu, Wai-Chee

2008-01-01

In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…

Numerical simulation of dynamics of brushless dc motors for aerospace and other applications. Volume 1: Model development and applications, part A

NASA Technical Reports Server (NTRS)

Demerdash, N. A. O.; Nehl, T. W.

1979-01-01

The development, fabrication and evaluation of a prototype electromechanical actuator (EMA) is discussed. Application of the EMA as a motor for control surfaces in aerospace flight is examined. A mathematical model of the EMA is developed for design optimization. Nonlinearities which complicate the mathematical model are discussed. The dynamics of the EMA from the underlying physical principles are determined and a discussion of similating the control logic by means of equivalent boolean expressions is presented.

Phenomenological and mechanics aspects of nondestructive evaluation and characterization by sound and ultrasound of material and fracture properties

NASA Technical Reports Server (NTRS)

Fu, L. S. W.

1982-01-01

Developments in fracture mechanics and elastic wave theory enhance the understanding of many physical phenomena in a mathematical context. Available literature in the material, and fracture characterization by NDT, and the related mathematical methods in mechanics that provide fundamental underlying principles for its interpretation and evaluation are reviewed. Information on the energy release mechanism of defects and the interaction of microstructures within the material is basic in the formulation of the mechanics problems that supply guidance for nondestructive evaluation (NDE).

Slope across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah

2014-01-01

This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…

Math/Science/Technology Projects for the Technology Teacher. A Professional Monograph.

ERIC Educational Resources Information Center

Maley, Donald L., Ed.

The underlying development behind this monograph grew out of a series of 14 panels (20 inches by 28 inches) illustrating the basic linkages between existing industrial arts/technology education activities and mathematics or science principles or societal and environmental impacts. Specifically, each panel contained a full-color photograph of a…

Mathematical modelling of solar ultraviolet radiation induced optical degradation in anodized aluminum

NASA Technical Reports Server (NTRS)

Ruley, John D.

1986-01-01

In the design of spacecraft for proper thermal balance, accurate information on the long-term optical behavior of the spacecraft outer skin materials is necessary. A phenomenological model for such behavior is given. The underlying principles are explained and some examples are given of the model's fit to actual measurements under simulated Earth-orbit conditions. Comments are given on the applicability of the model to materials testing and thermal modelling.

Acceleration of neutrons in a scheme of a tautochronous mathematical pendulum (physical principles)

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

Rivlin, Lev A

We consider the physical principles of neutron acceleration through a multiple synchronous interaction with a gradient rf magnetic field in a scheme of a tautochronous mathematical pendulum. (laser applications and other aspects of quantum electronics)

[Fuzzy mathematic quantitative law of composing principle in the study of traditional Chinese medicine].

PubMed

Liu, Ming; Gao, Yue; Xiao, Rui; Zhang, Bo-li

2009-01-01

This study is to analyze microcosmic significance of Chinese medicine composing principle "principal, assistant, complement and mediating guide" and it's fuzzy mathematic quantitative law. According to molecular biology and maximal membership principle, fuzzy subset and membership functions were proposed. Using in vivo experiment on the effects of SiWu Decoction and its ingredients on mice with radiation-induced blood deficiency, it is concluded that DiHuang and DangGui belonged to the principal and assistant subset, BaiShao belonged to the contrary complement subset, ChuanXiong belonged to the mediating guide subset by maximal membership principle. It is discussed that traditional Chinese medicine will be consummate medical science when its theory can be described by mathematic language.

Mathematical Analysis for Non-reciprocal-interaction-based Model of Collective Behavior

NASA Astrophysics Data System (ADS)

Kano, Takeshi; Osuka, Koichi; Kawakatsu, Toshihiro; Ishiguro, Akio

2017-12-01

In many natural and social systems, collective behaviors emerge as a consequence of non-reciprocal interaction between their constituents. As a first step towards understanding the core principle that underlies these phenomena, we previously proposed a minimal model of collective behavior based on non-reciprocal interactions by drawing inspiration from friendship formation in human society, and demonstrated via simulations that various non-trivial patterns emerge by changing parameters. In this study, a mathematical analysis of the proposed model wherein the system size is small is performed. Through the analysis, the mechanism of the transition between several patterns is elucidated.

Applied Mathematics Should Be Taught Mixed.

ERIC Educational Resources Information Center

Brown, Gary I.

1994-01-01

Discusses the differences between applied and pure mathematics and provides extensive history of mixed mathematics. Argues that applied mathematics should be taught allowing for speculative mathematics, which involves breaking down a given problem into simpler parts until one arrives at first principles. (ASK)

Facilitating Mathematical Practices through Visual Representations

ERIC Educational Resources Information Center

Murata, Aki; Stewart, Chana

2017-01-01

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

Mirror, Mirror

ERIC Educational Resources Information Center

Fuentes, Sarah Quebec

2015-01-01

NCTM's "Principles to Actions: Ensuring Mathematical Success for All" (2014), outlines eight teaching practices for effective teaching and learning mathematics. One of them, facilitate meaningful mathematical discourse, states, "Effective teaching of mathematics facilitates discourse among students to build shared understanding of…

Middle-School Mathematics Teachers' Beliefs in NCTM's Vision

ERIC Educational Resources Information Center

Perrin, John Robert

2012-01-01

This study examined the extent to which seventh- and eighth-grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in…

Essential Concepts and Underlying Theories from Physics, Chemistry, and Mathematics for "Biochemistry and Molecular Biology" Majors

ERIC Educational Resources Information Center

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A.; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry,…

Science and Math Activities and Resources for Teaching Home Economics (S.M.A.R.T.).

ERIC Educational Resources Information Center

Levine, Marjorie C.

This guide was written to aid home economics teachers in developing a greater understanding and use of basic skills in the home economics curriculum. The objectives of this guide are (1) to expand the awareness of underlying mathematics and science principles in the consumer and vocational home economics curriculum and (2) to provide a bank of…

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

PubMed

Williams, Howard; McOwan, Peter W

2014-01-01

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

Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia.

PubMed

Wilson, Anna J; Dehaene, Stanislas; Pinel, Philippe; Revkin, Susannah K; Cohen, Laurent; Cohen, David

2006-05-30

Adaptive game software has been successful in remediation of dyslexia. Here we describe the cognitive and algorithmic principles underlying the development of similar software for dyscalculia. Our software is based on current understanding of the cerebral representation of number and the hypotheses that dyscalculia is due to a "core deficit" in number sense or in the link between number sense and symbolic number representations. "The Number Race" software trains children on an entertaining numerical comparison task, by presenting problems adapted to the performance level of the individual child. We report full mathematical specifications of the algorithm used, which relies on an internal model of the child's knowledge in a multidimensional "learning space" consisting of three difficulty dimensions: numerical distance, response deadline, and conceptual complexity (from non-symbolic numerosity processing to increasingly complex symbolic operations). The performance of the software was evaluated both by mathematical simulations and by five weeks of use by nine children with mathematical learning difficulties. The results indicate that the software adapts well to varying levels of initial knowledge and learning speeds. Feedback from children, parents and teachers was positive. A companion article describes the evolution of number sense and arithmetic scores before and after training. The software, open-source and freely available online, is designed for learning disabled children aged 5-8, and may also be useful for general instruction of normal preschool children. The learning algorithm reported is highly general, and may be applied in other domains.

Applying Cognitive Psychology Based Instructional Design Principles in Mathematics Teaching and Learning: Introduction

ERIC Educational Resources Information Center

Verschaffel, Lieven; Van Dooren, W.; Star, J.

2017-01-01

This special issue comprises contributions that address the breadth of current lines of recent research from cognitive psychology that appear promising for positively impacting students' learning of mathematics. More specifically, we included contributions (a) that refer to cognitive psychology based principles and techniques, such as explanatory…

Digital Games for Learning Mathematics: Possibilities and Limitations

ERIC Educational Resources Information Center

Jorgensen, Robyn; Lowrie, Tom

2012-01-01

Drawing from Gee's learning principles developed from the digital games environment, we provide a critical analysis of the difference between using these principles in a literacy environment as opposed to a mathematical environment. Using stimulated recall, primary school-aged students played with a number of contemporary digital games. Feedback…

Rockets: An Educator's Guide with Activities in Science, Mathematics, and Technology.

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Washington, DC.

This educational guide discusses rockets and includes activities in science, mathematics, and technology. It begins with background information on the history of rocketry, scientific principles, and practical rocketry. The sections on scientific principles and practical rocketry focus on Sir Isaac Newton's Three Laws of Motion. These laws explain…

Implementing the Common Core: Applying Shifts to Instruction

ERIC Educational Resources Information Center

Gaddy, Angeline K.; Harmon, Shannon E.; Barlow, Angela T.; Milligan, Charles D.; Huang, Rongjin

2014-01-01

With such publications as "Curriculum and Evaluation Standards" (1989) and "Principles and Standards for School Mathematic" (2000), NCTM has played a significant role in defining a vision for school mathematics. In particular, the Curriculum Principle (NCTM 2000, pp. 14-16) described the need for students to learn important…

Avoiding reification. Heuristic effectiveness of mathematics and the prediction of the Ω- particle

NASA Astrophysics Data System (ADS)

Ginammi, Michele

2016-02-01

According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne'eman's prediction of the Ω- particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on the employment of a highly controversial principle-what he calls the "reification principle". Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any "reificatory" role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science.

Underlying Principles of Natural Selection in Network Evolution: Systems Biology Approach

PubMed Central

Chen, Bor-Sen; Wu, Wei-Sheng

2007-01-01

Systems biology is a rapidly expanding field that integrates diverse areas of science such as physics, engineering, computer science, mathematics, and biology toward the goal of elucidating the underlying principles of hierarchical metabolic and regulatory systems in the cell, and ultimately leading to predictive understanding of cellular response to perturbations. Because post-genomics research is taking place throughout the tree of life, comparative approaches offer a way for combining data from many organisms to shed light on the evolution and function of biological networks from the gene to the organismal level. Therefore, systems biology can build on decades of theoretical work in evolutionary biology, and at the same time evolutionary biology can use the systems biology approach to go in new uncharted directions. In this study, we present a review of how the post-genomics era is adopting comparative approaches and dynamic system methods to understand the underlying design principles of network evolution and to shape the nascent field of evolutionary systems biology. Finally, the application of evolutionary systems biology to robust biological network designs is also discussed from the synthetic biology perspective. PMID:19468310

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

NASA Astrophysics Data System (ADS)

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

Communication and Representation as Elements in Mathematical Literacy

ERIC Educational Resources Information Center

Thompson, Denisse R.; Chappell, Michaele F.

2007-01-01

The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…

Structure Shapes Dynamics and Directionality in Diverse Brain Networks: Mathematical Principles and Empirical Confirmation in Three Species

NASA Astrophysics Data System (ADS)

Moon, Joon-Young; Kim, Junhyeok; Ko, Tae-Wook; Kim, Minkyung; Iturria-Medina, Yasser; Choi, Jee-Hyun; Lee, Joseph; Mashour, George A.; Lee, Uncheol

2017-04-01

Identifying how spatially distributed information becomes integrated in the brain is essential to understanding higher cognitive functions. Previous computational and empirical studies suggest a significant influence of brain network structure on brain network function. However, there have been few analytical approaches to explain the role of network structure in shaping regional activities and directionality patterns. In this study, analytical methods are applied to a coupled oscillator model implemented in inhomogeneous networks. We first derive a mathematical principle that explains the emergence of directionality from the underlying brain network structure. We then apply the analytical methods to the anatomical brain networks of human, macaque, and mouse, successfully predicting simulation and empirical electroencephalographic data. The results demonstrate that the global directionality patterns in resting state brain networks can be predicted solely by their unique network structures. This study forms a foundation for a more comprehensive understanding of how neural information is directed and integrated in complex brain networks.

Listening Responsively

ERIC Educational Resources Information Center

Callahan, Kadian M.

2011-01-01

Standards documents, such as the Common Core State Standards for Mathematics and "Principles and Standards for School Mathematics", expect teachers to foster mathematics learning by engaging students in meaningful mathematical discourse to expose students to different ways of thinking about and solving problems and positively influence their…

Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs

ERIC Educational Resources Information Center

Ollerton, Richard L.

2013-01-01

Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…

A Historical Analysis of Primary Mathematics Curricula in Terms of Teaching Principles

ERIC Educational Resources Information Center

Ozmantar, Mehmet Fatih

2017-01-01

This study carries out a comparative analysis of primary mathematics curricula put into practice during Turkish Republican period. The data for this study are composed of official curricula documents which are examined in terms of teaching principles. The study adopts a qualitative approach and employs document analysis method. The official…

Principles and Guidelines for Equitable Mathematics Teaching Practices and Materials for English Language Learners

ERIC Educational Resources Information Center

Moschkovich, Judit

2013-01-01

In this essay, the author describes principles for equitable mathematics teaching practices for English Language Learners (ELLs) and outlines guidelines for materials to support such practices. Although research cannot provide a recipe for equitable teaching practices for ELLs, teachers, educators, and administrators can use this set of…

Examining the Design Features of a Communication-Rich, Problem-Centred Mathematics Professional Development

ERIC Educational Resources Information Center

de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik

2018-01-01

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The…

Mathematical foundations of biomechanics.

PubMed

Niederer, Peter F

2010-01-01

The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

Learning to Assess and Assessing to Learn: A Descriptive Study of a District-Wide Mathematics Assessment Implementation

ERIC Educational Resources Information Center

Ringer, Catharina W.

2013-01-01

In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…

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

NASA Technical Reports Server (NTRS)

1974-01-01

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

STEM Gives Meaning to Mathematics

ERIC Educational Resources Information Center

Hefty, Lukas J.

2015-01-01

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

Making the Most of Mathematical Discussions

ERIC Educational Resources Information Center

Staples, Megan; Colonis, Melissa M.

2007-01-01

The importance of mathematical discourse and its connection to developing conceptual understanding, communication, and reasoning is well documented throughout the National Council of Teachers of Mathematics (NCTM's) "Principles and Standards for School Mathematics" (2000). This article highlights the differences between two kinds of discussions:…

Design Principles for Creating Locally-Rooted National Science and Mathematics Curricula in Timor-Leste

ERIC Educational Resources Information Center

Gabrielson, Curtis A.; Hsi, Sherry

2012-01-01

This paper articulates and illustrates design principles that guided the development of a set of hands-on teaching activities for the national science and mathematics curricula at junior-high and high-school level education in Timor-Leste, a small, low-income nation in Southeast Asia. A partnership between a university, an international science…

Magic in the machine: a computational magician's assistant

PubMed Central

Williams, Howard; McOwan, Peter W.

2014-01-01

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

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles.

PubMed

Wheeler, Richard John

2015-11-05

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point "snapshot" of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes--cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)--as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. © 2015 Wheeler. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia

PubMed Central

Wilson, Anna J; Dehaene, Stanislas; Pinel, Philippe; Revkin, Susannah K; Cohen, Laurent; Cohen, David

2006-01-01

Background Adaptive game software has been successful in remediation of dyslexia. Here we describe the cognitive and algorithmic principles underlying the development of similar software for dyscalculia. Our software is based on current understanding of the cerebral representation of number and the hypotheses that dyscalculia is due to a "core deficit" in number sense or in the link between number sense and symbolic number representations. Methods "The Number Race" software trains children on an entertaining numerical comparison task, by presenting problems adapted to the performance level of the individual child. We report full mathematical specifications of the algorithm used, which relies on an internal model of the child's knowledge in a multidimensional "learning space" consisting of three difficulty dimensions: numerical distance, response deadline, and conceptual complexity (from non-symbolic numerosity processing to increasingly complex symbolic operations). Results The performance of the software was evaluated both by mathematical simulations and by five weeks of use by nine children with mathematical learning difficulties. The results indicate that the software adapts well to varying levels of initial knowledge and learning speeds. Feedback from children, parents and teachers was positive. A companion article [1] describes the evolution of number sense and arithmetic scores before and after training. Conclusion The software, open-source and freely available online, is designed for learning disabled children aged 5–8, and may also be useful for general instruction of normal preschool children. The learning algorithm reported is highly general, and may be applied in other domains. PMID:16734905

Elementary School Teachers' Interpretation and Promotion of Creativity in the Learning of Mathematics: A Grounded Theory Study

ERIC Educational Resources Information Center

Shen, Yinjing

2014-01-01

Creativity is important for young children learning mathematics. Comparing the investment theory of creativity and national standards and principles for early mathematics shows that doing mathematics is more than applying rules and procedures; rather, learning mathematics takes a lot of creativity. However, much literature claimed that creativity…

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Coping with the Bounds: Speculations on Nonlinearity in Military Affairs

DTIC Science & Technology

2003-08-01

organizing criticality, cellular automata, solitons, and so on–because they all globally share this property . Nonlinearity reflects the science of the...Why does it matter? One rea- son for emphasizing nonlinearity is that it constitutes the well-established mathematical property underlying and making...have some hints as to what those principles might be.3 Complex adaptive systems, or cas, contain seven basic attributes. These consist of four properties

Preservice and Inservice Mathematics Teachers' Perspectives of High-Quality Mathematics Instruction

ERIC Educational Resources Information Center

Clooney, Sarah; Cunningham, Robert F.

2017-01-01

This study examined the perspectives of what high-quality mathematics instruction looks like. Written responses from preservice (n = 20) and inservice (n = 16) mathematics teachers were collected and categorized according to the Ten Principles developed by Anthony & Walshaw (2009). The responses of preservice teachers more often than inservice…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

Leadership in Mathematics Education: Roles and Responsibilities

ERIC Educational Resources Information Center

Posamentier, Alfred S.

2013-01-01

This article partitions leadership in mathematics education into two categories: leadership in defining and maintaining important principles in teaching mathematics, and leadership in informing the public about the importance of mathematics today and in the future. Examples of both types of leadership are given in the article. Teacher leaders in…

Harry Potter and the Coding of Secrets

ERIC Educational Resources Information Center

Chua, Boon Liang

2008-01-01

When students learn mathematics, they tend to understand and remember the mathematical processes that they find practical and relevant. It is not surprising then that "Principles and Standards for School Mathematics" (NCTM 2000) encourages teachers to help students discover the relevance of mathematics in their daily lives. To help young people…

Teaching Gifted Children Mathematics in Grades Four Through Six.

ERIC Educational Resources Information Center

Gensley, Juliana T.

Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed…

Principles to Actions: Mathematics Programs as the Core for Student Learning

ERIC Educational Resources Information Center

Brahier, Daniel; Leinwand, Steve; Huniker, DeAnn

2014-01-01

The National Council of Teachers of Mathematics (NCTM) launched the "standards-based" education movement in North America in 1989 with the release of "Curriculum and Evaluation Standards for School Mathematics," an unprecedented action to promote systemic improvement in mathematics education. Now, twenty-five years later, the…

Supporting Mathematics Teachers' Development through Higher Education

ERIC Educational Resources Information Center

Prendergast, Mark; Roche, Joseph

2017-01-01

Mathematics education, both nationally and internationally, is facing a number of challenges with significant on-going shifts in the structure, content, and core principles of mathematics curricula in countries around the world. For example, in Ireland there was an ambitious reform of the post-primary mathematics curricula in 2010 with further…

On Fences, Forms and Mathematical Modeling

ERIC Educational Resources Information Center

Lege, Jerry

2009-01-01

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

A Research-Informed Dialogic-Teaching Approach to Early Secondary School Mathematics and Science: The Pedagogical Design and Field Trial of the"epiSTEMe" Intervention

ERIC Educational Resources Information Center

Ruthven, Kenneth; Mercer, Neil; Taber, Keith S.; Guardia, Paula; Hofmann, Riikka; Ilie, Sonia; Luthman, Stefanie; Riga, Fran

2017-01-01

The "Effecting Principled Improvement in STEM Education" ["epiSTEMe"] project undertook pedagogical research aimed at improving pupil engagement and learning in early secondary school physical science and mathematics. Using principles identified as effective in the research literature and drawing on a range of existing…

Cultured Cortical Neurons Can Perform Blind Source Separation According to the Free-Energy Principle

PubMed Central

Isomura, Takuya; Kotani, Kiyoshi; Jimbo, Yasuhiko

2015-01-01

Blind source separation is the computation underlying the cocktail party effect––a partygoer can distinguish a particular talker’s voice from the ambient noise. Early studies indicated that the brain might use blind source separation as a signal processing strategy for sensory perception and numerous mathematical models have been proposed; however, it remains unclear how the neural networks extract particular sources from a complex mixture of inputs. We discovered that neurons in cultures of dissociated rat cortical cells could learn to represent particular sources while filtering out other signals. Specifically, the distinct classes of neurons in the culture learned to respond to the distinct sources after repeating training stimulation. Moreover, the neural network structures changed to reduce free energy, as predicted by the free-energy principle, a candidate unified theory of learning and memory, and by Jaynes’ principle of maximum entropy. This implicit learning can only be explained by some form of Hebbian plasticity. These results are the first in vitro (as opposed to in silico) demonstration of neural networks performing blind source separation, and the first formal demonstration of neuronal self-organization under the free energy principle. PMID:26690814

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

NASA Astrophysics Data System (ADS)

Alawdin, Piotr; Liepa, Liudas

2017-06-01

Classical optimization problems of metal structures confined mainly with 1st class cross-sections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

The Construction of a Square through Multiple Approaches to Foster Learners' Mathematical Thinking

ERIC Educational Resources Information Center

Reyes-Rodriguez, Aaron; Santos-Trigo, Manuel; Barrera-Mora, Fernando

2017-01-01

The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into…

Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

The Learning of Mathematics: 69th NCTM Yearbook [2007 NCTM Yearbook (69th)

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2007

2007-01-01

Learning mathematics is the central goal of mathematics education, yet it is the least frequently addressed of the National Council of Teachers of Mathematics' (NCTM's) Principles and Standards. With an increasing population of English language learners and the inclusion of students with learning disabilities into the regular mathematics…

"Real Teaching" in the Mathematics Classroom: A Comparison of the Instructional Practices of Elementary Teachers in Urban High-Poverty Schools

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Robinson, Jack; Berube, Clair T.

2013-01-01

The National Council of Teachers of Mathematics' "Principles and Standards for School Mathematics" outlines fundamental elements that are crucial for creating a problem-solving and inquiry-driven classroom learning environment that highlights conceptual understandings of mathematics ideas. Even though this document outlines…

Remembering Zoltan Dienes, a Maverick of Mathematics Teaching and Learning: Applying the Variability Principles to Teach Algebra

ERIC Educational Resources Information Center

Gningue, Serigne Mbaye

2016-01-01

This paper is written in honor of Zoltan Paul Dienes, an internationally renowned mathematician and educator, who passed away in January 2014. It is an attempt to describe, analyze and apply Dienes' theory on how mathematical structures can be taught by applying his four principles of learning upon which he believed a teacher can base concept…

There Is More Variation "within" than "across" Domains: An Interview with Paul A. Kirschner about Applying Cognitive Psychology-Based Instructional Design Principles in Mathematics Teaching and Learning

ERIC Educational Resources Information Center

Kirschner, Paul A.; Verschaffel, Lieven; Star, Jon; Van Dooren, Wim

2017-01-01

In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational technology and instructional design, this…

Screening Health Risk Assessment Burn Pit Exposures, Balad Air Base, Iraq and Addendum Report

DTIC Science & Technology

2008-05-01

risk uses principles drawn from many scientific disciplines including chemistry , toxicology, physics, mathematics, and statistics. Because the data...uses principles drawn from many scientific disciplines, including chemistry , toxicology, physics, mathematics, and statistics. Because the data...natural chemicals in plants (called flavonoids ) also act on the Ah-receptor and could potentially block the effects of dioxins. One more reason to

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2014 CFR

2014-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2012 CFR

2012-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2013 CFR

2013-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

Sharing a Birthday Cake

ERIC Educational Resources Information Center

Switzer, J. Matt

2016-01-01

National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" outlines eight teaching practices for effective teaching and learning of mathematics (NCTM 2014). One of the teaching practices, "elicit and use evidence of student thinking," states, "Effective teaching of…

Focus in High School Mathematics: Reasoning and Sense Making

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2009

2009-01-01

Addressing the direction of high school mathematics in the 21st century, this resource builds on the ideas of NCTM's Principles and Standards for School Mathematics and focuses on how high school mathematics can better prepare students for future success. Reasoning and sense making are at the heart of the high school curriculum. Discover the…

An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children

ERIC Educational Resources Information Center

Paolucci, Catherine; Wessels, Helena

2017-01-01

This study examined preservice teachers' (PSTs) capacity to create mathematical modeling problems (MMPs) for grades 1 to 3. PSTs created MMPs for their choice of grade level and aligned the mathematical content of their MMPs with the relevant mathematics curriculum. PSTs were given criteria adapted from Galbraith's MMP design principles to guide…

How Bob Barker Would (Probably) Teach Discrete Mathematics

ERIC Educational Resources Information Center

Urness, Timothy

2010-01-01

This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…

Motivational Qualities of Mathematical Experiences for Turkish Preservice Kindergarten Teachers

ERIC Educational Resources Information Center

Bintas, Jale

2008-01-01

This study is based on the principle that the mathematical anxiety in preservice kindergarten teachers-to-be should be removed and they should be encouraged towards mathematics. It is expected from teachers-to-be who are able to construct this confidence to prepare exercises improving mathematical ideas for their students. This study was carried…

An Examination of the Instructional Practices of Mathematics Teachers in Urban Schools

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Chappell, Shannan; Berry, Robert Q.; Hickman, Bythella T.

2009-01-01

Researchers have given increased attention to the teaching and learning of mathematics since the release of the National Council of Teachers of Mathematics (NCTM)'s Principles and Standards for School Mathematics (PSSM). Despite the clear and focused goals, recommendations, and standards set by the NCTM (2000), a majority of classrooms continue to…

Cardiac mechanics: Physiological, clinical, and mathematical considerations

NASA Technical Reports Server (NTRS)

Mirsky, I. (Editor); Ghista, D. N.; Sandler, H.

1974-01-01

Recent studies concerning the basic physiological and biochemical principles underlying cardiac muscle contraction, methods for the assessment of cardiac function in the clinical situation, and mathematical approaches to cardiac mechanics are presented. Some of the topics covered include: cardiac ultrastructure and function in the normal and failing heart, myocardial energetics, clinical applications of angiocardiography, use of echocardiography for evaluating cardiac performance, systolic time intervals in the noninvasive assessment of left ventricular performance in man, evaluation of passive elastic stiffness for the left ventricle and isolated heart muscle, a conceptual model of myocardial infarction and cardiogenic shock, application of Huxley's sliding-filament theory to the mechanics of normal and hypertrophied cardiac muscle, and a rheological modeling of the intact left ventricle. Individual items are announced in this issue.

To Issue of Mathematical Management Methods Applied for Investment-Building Complex under Conditions of Economic Crisis

NASA Astrophysics Data System (ADS)

Novikova, V.; Nikolaeva, O.

2017-11-01

In the article the authors consider a cognitive management method of the investment-building complex in the crisis conditions. The factors influencing the choice of an investment strategy are studied, the basic lines of the activity in the field of crisis-management from a position of mathematical modelling are defined. The general approach to decision-making on investment in real assets on the basis of the discrete systems based on the optimum control theory is offered. With the use of a discrete maximum principle the task in view of the decision is found. The numerical algorithm to define the optimum control is formulated by investments. Analytical decisions for the case of constant profitability of the basic means are obtained.

Statistical Analysis of Protein Ensembles

NASA Astrophysics Data System (ADS)

Máté, Gabriell; Heermann, Dieter

2014-04-01

As 3D protein-configuration data is piling up, there is an ever-increasing need for well-defined, mathematically rigorous analysis approaches, especially that the vast majority of the currently available methods rely heavily on heuristics. We propose an analysis framework which stems from topology, the field of mathematics which studies properties preserved under continuous deformations. First, we calculate a barcode representation of the molecules employing computational topology algorithms. Bars in this barcode represent different topological features. Molecules are compared through their barcodes by statistically determining the difference in the set of their topological features. As a proof-of-principle application, we analyze a dataset compiled of ensembles of different proteins, obtained from the Ensemble Protein Database. We demonstrate that our approach correctly detects the different protein groupings.

Supporting All Learners in Productive Struggle

ERIC Educational Resources Information Center

Townsend, Cynthia; Slavit, David; McDuffie, Amy Roth

2018-01-01

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

Cognitive Play and Mathematical Learning in Computer Microworlds.

ERIC Educational Resources Information Center

Steffe, Leslie P.; Wiegel, Heide G.

1994-01-01

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Graphing Calculators as Tools

ERIC Educational Resources Information Center

Browning, Christine A.; Garza-Kling, Gina

2010-01-01

Middle school mathematics classrooms are changing. The curriculum has changed as well. Instead of an annual return to previously encountered topics, many middle school students encounter mathematics of a varying nature, characterized in "Principles and Standards for School Mathematics" (NCTM 2000) as the five Content Standards of Number and…

Promoting Mathematical Connections Using Three-Dimensional Manipulatives

ERIC Educational Resources Information Center

Safi, Farshid; Desai, Siddhi

2017-01-01

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

Exploration of Patterns in a Calendar

ERIC Educational Resources Information Center

Huang, Rongjin; Prince, Kyle M.; Schmidt, Teresa

2014-01-01

The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

Fostering Perseverance

ERIC Educational Resources Information Center

Lewis, Jennifer M.; Özgün-Koca, S. Asli

2016-01-01

Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

Spaghetti Bridges: Modeling Linear Relationships

ERIC Educational Resources Information Center

Kroon, Cindy D.

2016-01-01

Mathematics and science are natural partners. One of many examples of this partnership occurs when scientific observations are made, thus providing data that can be used for mathematical modeling. Developing mathematical relationships elucidates such scientific principles. This activity describes a data-collection activity in which students employ…

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-offs on Phenotype Robustness in Biological Networks. Part III: Synthetic Gene Networks in Synthetic Biology

PubMed Central

Chen, Bor-Sen; Lin, Ying-Po

2013-01-01

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental disturbances, is also proposed, together with a simulation example. PMID:23515190

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-offs on Phenotype Robustness in Biological Networks. Part III: Synthetic Gene Networks in Synthetic Biology.

PubMed

Chen, Bor-Sen; Lin, Ying-Po

2013-01-01

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental disturbances, is also proposed, together with a simulation example.

Mathematical Learning Disabilities in Special Populations: Phenotypic Variation and Cross-Disorder Comparisons

PubMed Central

Dennis, Maureen; Berch, Daniel B.; Mazzocco, Michèle M.M.

2011-01-01

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to mathematical learning difficulties and disabilities presented across the reviews. Specifically we consider how each of the reviews contributes to identifying the MLD phenotype by specifying the range of assets and deficits in mathematics, identifying sources of individual variation, and characterizing the natural progression of MLD over the life course. We show how principled comparisons across disorders address issues about the cognitive and behavioral co-morbidities of MLD, and whether commonalities in brain dysmorphology are associated with common mathematics performance profiles. We project the status of MLD research ten years hence with respect to theoretical gains, advances in methodology, and principled intervention studies. PMID:19213019

Study on Fluid-solid Coupling Mathematical Models and Numerical Simulation of Coal Containing Gas

NASA Astrophysics Data System (ADS)

Xu, Gang; Hao, Meng; Jin, Hongwei

2018-02-01

Based on coal seam gas migration theory under multi-physics field coupling effect, fluid-solid coupling model of coal seam gas was build using elastic mechanics, fluid mechanics in porous medium and effective stress principle. Gas seepage behavior under different original gas pressure was simulated. Results indicated that residual gas pressure, gas pressure gradient and gas low were bigger when original gas pressure was higher. Coal permeability distribution decreased exponentially when original gas pressure was lower than critical pressure. Coal permeability decreased rapidly first and then increased slowly when original pressure was higher than critical pressure.

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-off on Phenotype Robustness in Biological Networks Part I: Gene Regulatory Networks in Systems and Evolutionary Biology

PubMed Central

Chen, Bor-Sen; Lin, Ying-Po

2013-01-01

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view. PMID:23515240

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-off on Phenotype Robustness in Biological Networks Part I: Gene Regulatory Networks in Systems and Evolutionary Biology.

PubMed

Chen, Bor-Sen; Lin, Ying-Po

2013-01-01

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view.

Principles for Designing Intervention in Mathematics

ERIC Educational Resources Information Center

National Center on Intensive Intervention, 2016

2016-01-01

The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics. Special education instructors, math interventionists, and others working with students who struggle with mathematics may find this guide helpful. Specific topics covered…

Making Sense of Extraneous Solutions

ERIC Educational Resources Information Center

Zelkowski, Jeremy S.

2013-01-01

Principles and Standards for School Mathematics (NCTM 2000) states, "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." The focus on reasoning and sense making with technology in the lesson presented in this article will enable students to do more…

Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.

2011-01-01

This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…

Las normas de desempeno matematico desde el preescolar hasta el segundo grado (Mathematics Standards for Pre-Kindergarten through Grade 2). ERIC Digest.

ERIC Educational Resources Information Center

Richardson, Kathy

The National Council of Teachers of Mathematics recently published "Principles and Standards for School Mathematics." For the first time, these new standards include pre-kindergarten standards, while outlining the mathematics that children should learn as they progress through school. The standards present a broad view of what…

Mathematics and Living Things. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Faber, Norman J.; And Others

This document is designed for grade eight to enrich and supplement the usual courses of instruction. Mathematics and Living Things (MALT) utilizes exercises in biological science to derive data through which mathematical concepts and principles may be introduced and expanded. Chapters included are: (1) Leaves and Natural Variation: Measurement of…

The Math Wizard in Oz

ERIC Educational Resources Information Center

Christy, Donna; Lambe, Karen; Payson, Christine; Carnevale, Patricia

2011-01-01

The crucial need for a mathematically literate society, coupled with a sustained focus on mathematics standards, continues its center-stage presence. At the same time, "Principles and Standards" states that it is imperative to offer "all students high-quality programs that include significant mathematics presented in a manner that respects both…

The Money Context

ERIC Educational Resources Information Center

Tabach, Michal; Friedlander, Alex

2009-01-01

One of the basic disagreements in mathematics education concerns the roles that rules and procedures, on the one hand, and concepts and principles, on the other hand, should play in students' learning of mathematics. The use of procedures and an understanding of concepts are considered to be two separate aspects of mathematical activity.…

The String Task: Not Just for High School

ERIC Educational Resources Information Center

Isler, Isil; Marum, Tim; Stephens, Ana; Blanton, Maria; Knuth, Eric; Gardiner, Angela Murphy

2014-01-01

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, 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…

The Technological Revolution and the Reform of School Mathematics.

ERIC Educational Resources Information Center

Heid, M. Kathleen

1997-01-01

Evaluates the ways in which empirical research supports the use of technology and technology-intensive mathematics curricula as catalysts for the mathematics education reform movement. It describes the theories, principles, and issues that influence the role of this technological revolution and discusses the ways in which technology influences the…

System principles, mathematical models and methods to ensure high reliability of safety systems

NASA Astrophysics Data System (ADS)

Zaslavskyi, V.

2017-04-01

Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.

Children's Understanding of the Addition/Subtraction Complement Principle

ERIC Educational Resources Information Center

Torbeyns, Joke; Peters, Greet; De Smedt, Bert; Ghesquière, Pol; Verschaffel, Lieven

2016-01-01

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

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

Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can bemore » potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.« less

20 CFR 901.13 - Eligibility for enrollment of individuals applying for enrollment on or after January 1, 1976.

Code of Federal Regulations, 2011 CFR

2011-04-01

... actuarial mathematics and methodology by one of the following: (1) Joint Board basic examination. Successful... basic actuarial mathematics and methodology including compound interest, principles of life... major area of concentration was actuarial mathematics, or (ii) Which included at least as many semester...

Mathematics in the K-8 Classroom and Library

ERIC Educational Resources Information Center

McKinney, Sueanne; Hinton, KaaVonia

2010-01-01

Two experts on education offer a rich and diverse selection of children's literature and teaching strategies for the K-8 mathematics classroom. To date, a vast majority of classrooms continue to fall short in the implementation and direction of NCTM Principles and Standards for School Mathematics (PSSM), in part because most of these classrooms…

A Snowflake Project: Calculating, Analyzing, and Optimizing with the Koch Snowflake.

ERIC Educational Resources Information Center

Bolte, Linda A.

2002-01-01

Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

Handbook of Research Design in Mathematics and Science Education.

ERIC Educational Resources Information Center

Kelly, Anthony E., Ed.; Lesh, Richard A., Ed.

This book attempts to clarify the nature of principles that govern the effective use of merging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research design that have been pioneered recently by mathematics and science educators, have distinctive characteristics when…

Examining Sources of Gender DIF in Mathematics Assessments Using a Confirmatory Multidimensional Model Approach

ERIC Educational Resources Information Center

Mendes-Barnett, Sharon; Ercikan, Kadriye

2006-01-01

This study contributes to understanding sources of gender differential item functioning (DIF) on mathematics tests. This study focused on identifying sources of DIF and differential bundle functioning for boys and girls on the British Columbia Principles of Mathematics Exam (Grade 12) using a confirmatory SIBTEST approach based on a…

STEM and Model-Eliciting Activities: Responsive Professional Development for K-8 Mathematics Coaches

ERIC Educational Resources Information Center

Baker, Courtney; Galanti, Terrie; Birkhead, Sara

2017-01-01

This research highlights a university-school division collaboration to pilot a professional development framework for integrating STEM in K-8 mathematics classrooms. The university researchers worked with mathematics coaches to construct a realistic and reasonable vision of STEM integration built upon the design principles of model-eliciting…

Differential Improvement in Student Understanding of Mathematical Principles following Formative Assessment Intervention

ERIC Educational Resources Information Center

Phelan, Julia; Choi, Kilchan; Vendlinski, Terry; Baker, Eva; Herman, Joan

2011-01-01

The authors describe results from a study of a middle school mathematics formative assessment strategy. They employed a randomized, controlled design to address the following question: Does using our strategy improve student performance on assessments of key mathematical ideas relative to a comparison group? Eighty-five teachers and 4,091 students…

Basic mathematical rules are encoded by primate prefrontal cortex neurons

PubMed Central

Bongard, Sylvia; Nieder, Andreas

2010-01-01

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

Closing the Minority Achievement Gap in Math

ERIC Educational Resources Information Center

Holloway, John H.

2004-01-01

Minority students face numerous academic barriers for achievement in the classroom as well as outside the school. The National Council of Teachers of Mathematics (NCTM) suggests six principles for maintaining the standard of school mathematics.

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Application of a mathematical model for ergonomics in lean manufacturing.

PubMed

Botti, Lucia; Mora, Cristina; Regattieri, Alberto

2017-10-01

The data presented in this article are related to the research article "Integrating ergonomics and lean manufacturing principles in a hybrid assembly line" (Botti et al., 2017) [1]. The results refer to the application of the mathematical model for the design of lean processes in hybrid assembly lines, meeting both the lean principles and the ergonomic requirements for safe assembly work. Data show that the success of a lean strategy is possible when ergonomics of workers is a parameter of the assembly process design.

Modelling nutritional mutualisms: challenges and opportunities for data integration.

PubMed

Clark, Teresa J; Friel, Colleen A; Grman, Emily; Shachar-Hill, Yair; Friesen, Maren L

2017-09-01

Nutritional mutualisms are ancient, widespread, and profoundly influential in biological communities and ecosystems. Although much is known about these interactions, comprehensive answers to fundamental questions, such as how resource availability and structured interactions influence mutualism persistence, are still lacking. Mathematical modelling of nutritional mutualisms has great potential to facilitate the search for comprehensive answers to these and other fundamental questions by connecting the physiological and genomic underpinnings of mutualisms with ecological and evolutionary processes. In particular, when integrated with empirical data, models enable understanding of underlying mechanisms and generalisation of principles beyond the particulars of a given system. Here, we demonstrate how mathematical models can be integrated with data to address questions of mutualism persistence at four biological scales: cell, individual, population, and community. We highlight select studies where data has been or could be integrated with models to either inform model structure or test model predictions. We also point out opportunities to increase model rigour through tighter integration with data, and describe areas in which data is urgently needed. We focus on plant-microbe systems, for which a wealth of empirical data is available, but the principles and approaches can be generally applied to any nutritional mutualism. © 2017 John Wiley & Sons Ltd/CNRS.

Turbulence and the Stabilization Principle

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Connection of Scattering Principles: A Visual and Mathematical Tour

ERIC Educational Resources Information Center

Broggini, Filippo; Snieder, Roel

2012-01-01

Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

A Comparative Analysis of the Minuteman Education Programs as Currently Offered at Six SAC Bases.

DTIC Science & Technology

1980-06-01

Principles of Marketing 3 Business Statistics 3 Business Law 3 Management Total... Principles of Marketing 3 Mathematics Methods I Total prerequisite hours 26 Required Graduate Courses Policy Formulation and Administration 3 Management...Business and Economic Statistics 3 Intermediate Business and Economic Statistics 3 Principles of Management 3 Corporation Finance 3 Principles of Marketing

The role of language in mathematical development: evidence from children with specific language impairments.

PubMed

Donlan, Chris; Cowan, Richard; Newton, Elizabeth J; Lloyd, Delyth

2007-04-01

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.

Quasi-static responses and variational principles in gradient plasticity

NASA Astrophysics Data System (ADS)

Nguyen, Quoc-Son

2016-12-01

Gradient models have been much discussed in the literature for the study of time-dependent or time-independent processes such as visco-plasticity, plasticity and damage. This paper is devoted to the theory of Standard Gradient Plasticity at small strain. A general and consistent mathematical description available for common time-independent behaviours is presented. Our attention is focussed on the derivation of general results such as the description of the governing equations for the global response and the derivation of related variational principles in terms of the energy and the dissipation potentials. It is shown that the quasi-static response under a loading path is a solution of an evolution variational inequality as in classical plasticity. The rate problem and the rate minimum principle are revisited. A time-discretization by the implicit scheme of the evolution equation leads to the increment problem. An increment of the response associated with a load increment is a solution of a variational inequality and satisfies also a minimum principle if the energy potential is convex. The increment minimum principle deals with stables solutions of the variational inequality. Some numerical methods are discussed in view of the numerical simulation of the quasi-static response.

Mathematical Optimization Algorithm for Minimizing the Cost Function of GHG Emission in AS/RS Using Positive Selection Based Clonal Selection Principle

NASA Astrophysics Data System (ADS)

Mahalakshmi; Murugesan, R.

2018-04-01

This paper regards with the minimization of total cost of Greenhouse Gas (GHG) efficiency in Automated Storage and Retrieval System (AS/RS). A mathematical model is constructed based on tax cost, penalty cost and discount cost of GHG emission of AS/RS. A two stage algorithm namely positive selection based clonal selection principle (PSBCSP) is used to find the optimal solution of the constructed model. In the first stage positive selection principle is used to reduce the search space of the optimal solution by fixing a threshold value. In the later stage clonal selection principle is used to generate best solutions. The obtained results are compared with other existing algorithms in the literature, which shows that the proposed algorithm yields a better result compared to others.

Deciphering principles of transcription regulation in eukaryotic genomes

PubMed Central

Nguyen, Dat H; D'haeseleer, Patrik

2006-01-01

Transcription regulation has been responsible for organismal complexity and diversity in the course of biological evolution and adaptation, and it is determined largely by the context-dependent behavior of cis-regulatory elements (CREs). Therefore, understanding principles underlying CRE behavior in regulating transcription constitutes a fundamental objective of quantitative biology, yet these remain poorly understood. Here we present a deterministic mathematical strategy, the motif expression decomposition (MED) method, for deriving principles of transcription regulation at the single-gene resolution level. MED operates on all genes in a genome without requiring any a priori knowledge of gene cluster membership, or manual tuning of parameters. Applying MED to Saccharomyces cerevisiae transcriptional networks, we identified four functions describing four different ways that CREs can quantitatively affect gene expression levels. These functions, three of which have extrema in different positions in the gene promoter (short-, mid-, and long-range) whereas the other depends on the motif orientation, are validated by expression data. We illustrate how nature could use these principles as an additional dimension to amplify the combinatorial power of a small set of CREs in regulating transcription. PMID:16738557

Tablet-Based Math Assessment: What Can We Learn from Math Apps?

ERIC Educational Resources Information Center

Cayton-Hodges, Gabrielle A.; Feng, Gary; Pan, Xingyu

2015-01-01

In this report, we describe a survey of mathematics education apps in the Apple App Store, conducted as part of a research project to develop a tablet-based assessment prototype for elementary mathematics. This survey was performed with the goal of understanding the design principles and techniques used in mathematics apps designed for tablets. We…

Perspectives on Equity and Access in Mathematics and Science for a 21st-Century Democracy: Re-Visioning Our Gaze

ERIC Educational Resources Information Center

Williams, Brian A.; Lemons-Smith, Shonda

2009-01-01

In 1996, the National Research Council (NRC) published the "National Science Education Standards." Similarly in 2000, the National Council of Teachers of Mathematics (NCTM) published the "Principles and Standards for School Mathematics." These standards provided the nation with a framework for conceptualizing what and how…

Examining of Model Eliciting Activities Developed by Mathematics Student Teachers

ERIC Educational Resources Information Center

Dede, Ayse Tekin; Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

2017-01-01

The purpose of this study is to examine the model eliciting activities developed by the mathematics student teachers in the context of the principles of the model eliciting activities. The participants of the study conducted as a case study design were twenty one mathematics student teachers working on seven groups. The data collection tools were…

How Revisions to Mathematical Visuals Affect Cognition: Evidence from Eye Tracking

ERIC Educational Resources Information Center

Clinton, Virginia; Cooper, Jennifer L.; Michaelis, Joseph; Alibali, Martha W.; Nathan, Mitchell J.

2017-01-01

Mathematics curricula are frequently rich with visuals, but these visuals are often not designed for optimal use of students' limited cognitive resources. The authors of this study revised the visuals in a mathematics lesson based on instructional design principles. The purpose of this study is to examine the effects of these revised visuals on…

Licensure tests for special education teachers: how well they assess knowledge of reading instruction and mathematics.

PubMed

Stotsky, Sandra

2009-01-01

To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.

Development of an electromechanical principle for wet and dry milling

NASA Astrophysics Data System (ADS)

Halbedel, Bernd; Kazak, Oleg

2018-05-01

The paper presents a novel electromechanical principle for wet and dry milling of different materials, in which the milling beads are moved under a time- and local-variable magnetic field. A possibility to optimize the milling process in such a milling machine by simulation of the vector gradient distribution of the electromagnetic field in the process room is presented. The mathematical model and simulation methods based on standard software packages are worked out. The results of numerical simulations and experimental measurements of the electromagnetic field in the working chamber of a developed and manufactured laboratory plant correlate well with each other. Using the obtained operating parameters, dry milling experiments with crushed cement clinker and wet milling experiments of organic agents in the laboratory plant are performed and the results are discussed here.

An Assessment of the Level of Mathematics in Introductory Meteorology Textbooks.

NASA Astrophysics Data System (ADS)

Ulanski, Stan L.

1992-10-01

A review of introductory meteorology textbooks shows a wide difference in the level of mathematical treatment of atmospheric principles-from virtually none to fairly high. Particular deficiencies include lack of equations integrated into the text, problem-solving examples, and paucity of end-of-chapter questions requiring mathematical reasoning. These issues are raised in order to generate discussion among the meteorological community with regard to the degree of interaction between mathematics and meteorology in introductory courses.

Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

PubMed

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

The role of mathematical models in understanding pattern formation in developmental biology.

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Design of Learning Objects for Concept Learning: Effects of Multimedia Learning Principles and an Instructional Approach

ERIC Educational Resources Information Center

Chiu, Thomas K. F.; Churchill, Daniel

2016-01-01

Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching…

An Analysis of Statements of the Multiplication Principle in Combinatorics, Discrete, and Finite Mathematics Textbooks

ERIC Educational Resources Information Center

Lockwood, Elise; Reed, Zackery; Caughman, John S.

2017-01-01

The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of…

Approaches to Foster Transfer of Formal Principles: Which Route to Take?

PubMed

Schalk, Lennart; Saalbach, Henrik; Stern, Elsbeth

2016-01-01

Enabling learners to transfer knowledge about formal principles to new problems is a major aim of science and mathematics education, which, however, is notoriously difficult to reach. Previous research advocates different approaches of how to introduce principles to foster the transfer of knowledge about formal principles. One approach suggests teaching a generic formalism of the principles. Another approach suggests presenting (at least) two concrete cases instantiating the principle. A third approach suggests presenting a generic formalism accompanied by a case. As yet, though, empirical results regarding the transfer potential of these approaches are mixed and difficult to integrate as the three approaches have rarely been tested competitively. Furthermore, the approaches have been evaluated in relation to different control conditions, and they have been assessed using varying transfer measures. In the present experiment, we introduced undergraduates to the formal principles of propositional logic with the aim to systematically compare the transfer potential of the different approaches in relation to each other and to a common control condition by using various learning and transfer tasks. Results indicate that all approaches supported successful learning and transfer of the principles, but also caused systematic differences in the magnitude of transfer. Results indicate that the combination of a generic formalism with a case was surprisingly unsuccessful while learners who compared two cases outperformed the control condition. We discuss how the simultaneous assessment of the different approaches allows to more precisely capture the underlying learning mechanisms and to advance theory on how these mechanisms contribute to transfer performance.

Supporting Productive Struggle with Communication Moves

ERIC Educational Resources Information Center

Freeburn, Ben; Arbaugh, Fran

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014, p. 10) contains eight research-informed teaching practices that have been shown to support students' mathematical thinking and learning. Two teaching practices highlighted herein are "to elicit and use evidence of students' thinking" and "support…

Differential Calculus: Concepts and Notation.

ERIC Educational Resources Information Center

Hobbs, David; Relf, Simon

1997-01-01

Suggests that many students with A-level mathematics, and even with a degree in mathematics or a related subject, do not have an understanding of the basic principles of calculus. Describes the approach used in three textbooks currently in use. Contains 14 references. (Author/ASK)

Connecting and Using Multiple Representations

ERIC Educational Resources Information Center

Nielsen, Maria E.; Bostic, Jonathan D.

2018-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) emphasizes eight teaching practices for effective mathematics teaching, one of which is to "use and connect multiple representations" (NCTM 2014, p. 24). An action that describes how teachers might promote this practice is to "allocate substantial…

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints.

PubMed

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M

2016-10-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. Copyright © 2016. Published by Elsevier Ltd.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

PubMed Central

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M.

2017-01-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. PMID:27544910

The Physics and Mathematics of MRI

NASA Astrophysics Data System (ADS)

Ansorge, Richard; Graves, Martin

2016-10-01

Magnetic Resonance Imaging is a very important clinical imaging tool. It combines different fields of physics and engineering in a uniquely complex way. MRI is also surprisingly versatile, `pulse sequences' can be designed to yield many different types of contrast. This versatility is unique to MRI. This short book gives both an in depth account of the methods used for the operation and construction of modern MRI systems and also the principles of sequence design and many examples of applications. An important additional feature of this book is the detailed discussion of the mathematical principles used in building optimal MRI systems and for sequence design. The mathematical discussion is very suitable for undergraduates attending medical physics courses. It is also more complete than usually found in alternative books for physical scientists or more clinically orientated works.

What is the uncertainty principle of non-relativistic quantum mechanics?

NASA Astrophysics Data System (ADS)

Riggs, Peter J.

2018-05-01

After more than ninety years of discussions over the uncertainty principle, there is still no universal agreement on what the principle states. The Robertson uncertainty relation (incorporating standard deviations) is given as the mathematical expression of the principle in most quantum mechanics textbooks. However, the uncertainty principle is not merely a statement of what any of the several uncertainty relations affirm. It is suggested that a better approach would be to present the uncertainty principle as a statement about the probability distributions of incompatible variables and the resulting restrictions on quantum states.

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

ERIC Educational Resources Information Center

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…

Preliminary Investigation of Profiling Tools and Methods

DTIC Science & Technology

2011-06-01

1 Jaccard coefficient is a unique mathematical way to measure behaviour co-occurancesrd’s coefficient (measure similarity) 4 DRDC Toronto TM...a few heuristics (that are the basis for the mathematical algorithms used in GP systems) these individuals perform just as well as the system...route that GP is a holistic method of data interpretation with unsystematic methodologies, practices and varying mathematical principles, then anecdotes

State-of-the-Art Assessment of Testing and Testability of Custom LSI/VLSI Circuits. Volume VI. Redundancy, Testing Circuits, and Codes.

DTIC Science & Technology

1982-10-01

e.g., providing voters in TMR systems and detection-switching requirements in standby-sparing sys- tems. The application of mathematical thoery of...and time redundancy required for error detection and correction, are interrelated. Mathematical modeling, when applied to fault tolerant systems, can...9 1.1 Some Fundamental Principles............................. 11 1.2 Mathematical Theory of

Mechanisms underlying brain monitoring during anesthesia: limitations, possible improvements, and perspectives

PubMed Central

2016-01-01

Currently, anesthesiologists use clinical parameters to directly measure the depth of anesthesia (DoA). This clinical standard of monitoring is often combined with brain monitoring for better assessment of the hypnotic component of anesthesia. Brain monitoring devices provide indices allowing for an immediate assessment of the impact of anesthetics on consciousness. However, questions remain regarding the mechanisms underpinning these indices of hypnosis. By briefly describing current knowledge of the brain's electrical activity during general anesthesia, as well as the operating principles of DoA monitors, the aim of this work is to simplify our understanding of the mathematical processes that allow for translation of complex patterns of brain electrical activity into dimensionless indices. This is a challenging task because mathematical concepts appear remote from clinical practice. Moreover, most DoA algorithms are proprietary algorithms and the difficulty of exploring the inner workings of mathematical models represents an obstacle to accurate simplification. The limitations of current DoA monitors — and the possibility for improvement — as well as perspectives on brain monitoring derived from recent research on corticocortical connectivity and communication are also discussed. PMID:27066200

[Study on balance group in steady-state extraction process of Chinese medicine and experimental verification to Houttuynia cordata].

PubMed

Liu, Wenlong; Zhang, Xili; He, Fuyuan; Zhang, Ping; Wang, Haiqin; Wu, Dezhi; Chen, Zuohong

2011-11-01

To establish and experimental verification the mathematical model of the balance groups that is the steady-state of traditional Chinese medicine in extraction. Using the entropy and genetic principles of statistics, and taking the coefficient of variation of GC fingerprint which is the naphtha of the Houttuynia cordata between strains in the same GAP place as a pivot to establish and verify the mathematical model was established of the balance groups that is the steady-state of traditional Chinese medicine in extraction. A mathematical model that is suitable for the balance groups of the steady-state of traditional Chinese medicine and preparation in extraction, and the balance groups which is 29 683 strains (approximately 118.7 kg) were gained with the same origin of H. cordata as the model drug. Under the GAP of quality control model, controlling the stability of the quality through further using the Hardy-Weinberg balance groups of the H. cordata between strains, the new theory and experiment foundation is established for the steady-state of traditional Chinese medicine in extraction and quality control.

Evaluation of losses in transmission of machinery for development of mineral deposits in conditions of variable load

NASA Astrophysics Data System (ADS)

Zvonarev, I. E.; Ivanov, S. L.

2017-10-01

The influence of individual elements of machines transmissions on the operation of the whole system is shown. The approach of determining the resource of operation of systems elements based on the energy theory is presented. The formulas for determining the total energy resource of the reducer are given. The influence of individual elements of the system on each other is indicated. The principle of researching the system by the method of equivalent circuits is substantiated. The weakest places of transmission (gears, bearing supports and shafts) are determined. A mathematical model of a mechanical transmission was developed. To test the adequacy of the mathematical model, the stand for obtaining experimental data was designed. The description of the stand and the principle of its operation are given. Experimental data are presented. A comparative analysis of modeling and experimental data is carried out and the adequacy of the developed mathematical model is proved. The principle of determining the resource of the system as a whole for the element with the minimal resource of work is suggested.

Examples of testing global identifiability of biological and biomedical models with the DAISY software.

PubMed

Saccomani, Maria Pia; Audoly, Stefania; Bellu, Giuseppina; D'Angiò, Leontina

2010-04-01

DAISY (Differential Algebra for Identifiability of SYstems) is a recently developed computer algebra software tool which can be used to automatically check global identifiability of (linear and) nonlinear dynamic models described by differential equations involving polynomial or rational functions. Global identifiability is a fundamental prerequisite for model identification which is important not only for biological or medical systems but also for many physical and engineering systems derived from first principles. Lack of identifiability implies that the parameter estimation techniques may not fail but any obtained numerical estimates will be meaningless. The software does not require understanding of the underlying mathematical principles and can be used by researchers in applied fields with a minimum of mathematical background. We illustrate the DAISY software by checking the a priori global identifiability of two benchmark nonlinear models taken from the literature. The analysis of these two examples includes comparison with other methods and demonstrates how identifiability analysis is simplified by this tool. Thus we illustrate the identifiability analysis of other two examples, by including discussion of some specific aspects related to the role of observability and knowledge of initial conditions in testing identifiability and to the computational complexity of the software. The main focus of this paper is not on the description of the mathematical background of the algorithm, which has been presented elsewhere, but on illustrating its use and on some of its more interesting features. DAISY is available on the web site http://www.dei.unipd.it/ approximately pia/. 2010 Elsevier Ltd. All rights reserved.

The Dynamic Discograph.

ERIC Educational Resources Information Center

Bell, Garry

1991-01-01

Mechanical devices offer an alternative to computers to explore mathematical concepts in different curricula areas. Described is the discograph, a series of pulleys and wheels, that can be used to teach mathematical principles in pattern drawing, locus, rotation in geared systems, gearing, rotational symmetry, regular plane figures, decimal, and…

Underground Mathematics

ERIC Educational Resources Information Center

Hadlock, Charles R

2013-01-01

The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…

Connecting Representations: Using Predict, Check, Explain

ERIC Educational Resources Information Center

Roy, George J.; Fueyo, Vivian; Vahey, Philip; Knudsen, Jennifer; Rafanan, Ken; Lara-Meloy, Teresa

2016-01-01

Although educators agree that making connections with the real world, as advocated by "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), is important, making such connections while addressing important mathematics is elusive. The authors have found that math content coupled with the instructional strategy of…

Count on It: Congruent Manipulative Displays

ERIC Educational Resources Information Center

Morin, Joe; Samelson, Vicki M.

2015-01-01

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

Designing for Productive Failure

ERIC Educational Resources Information Center

Kapur, Manu; Bielaczyc, Katerine

2012-01-01

In this article, we describe the design principles undergirding "productive failure" (PF; M. Kapur, 2008). We then report findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability. In…

Examining the design features of a communication-rich, problem-centred mathematics professional development

NASA Astrophysics Data System (ADS)

de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik

2018-04-01

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.

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

Does the Budyko curve reflect a maximum power state of hydrological systems? A backward analysis

NASA Astrophysics Data System (ADS)

Westhoff, M.; Zehe, E.; Archambeau, P.; Dewals, B.

2015-08-01

Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving runoff and evaporation for a simple one-box model. We did this in such a way that when the conductances are optimized with the maximum power principle, the steady state behaviour of the model leads exactly to a point on the Budyko curve. Subsequently we derived gradients that, under constant forcing, resulted in a Budyko curve following the asymptotes closely. With these gradients we explored the sensitivity of dry spells and dynamics in actual evaporation. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves derived with dynamics in rainfall and evaporation. This indicates that the maximum power principle may be used (i) to derive the Budyko curve and (ii) to move away from the empiricism in free parameters present in many Budyko functions. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

Equilibrium I: Principles. Independent Learning Project for Advanced Chemistry (ILPAC). Unit P2.

ERIC Educational Resources Information Center

Inner London Education Authority (England).

This unit on the principles of equilibrium is one of 10 first year units produced by the Independent Learning Project for Advanced Chemistry (ILPAC). The unit consists of two levels. After a treatment of non-mathematical aspects in level one (the idea of a reversible reaction, characteristics of an equilibrium state, the Le Chatelier's principle),…

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

NASA Astrophysics Data System (ADS)

Syahrin, Muhammad Alfi; Turmudi, Puspita, Entit

2016-02-01

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

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

Strategically Fostering Dynamic Interactive Environments

ERIC Educational Resources Information Center

Özgün-Koca, S. Asli

2016-01-01

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

A Generic Software Safety Document Generator

NASA Technical Reports Server (NTRS)

Denney, Ewen; Venkatesan, Ram Prasad

2004-01-01

Formal certification is based on the idea that a mathematical proof of some property of a piece of software can be regarded as a certificate of correctness which, in principle, can be subjected to external scrutiny. In practice, however, proofs themselves are unlikely to be of much interest to engineers. Nevertheless, it is possible to use the information obtained from a mathematical analysis of software to produce a detailed textual justification of correctness. In this paper, we describe an approach to generating textual explanations from automatically generated proofs of program safety, where the proofs are of compliance with an explicit safety policy that can be varied. Key to this is tracing proof obligations back to the program, and we describe a tool which implements this to certify code auto-generated by AutoBayes and AutoFilter, program synthesis systems under development at the NASA Ames Research Center. Our approach is a step towards combining formal certification with traditional certification methods.

The effect of gas and fluid flows on nonlinear lateral vibrations of rotating drill strings

NASA Astrophysics Data System (ADS)

Khajiyeva, Lelya; Kudaibergenov, Askar; Kudaibergenov, Askat

2018-06-01

In this work we develop nonlinear mathematical models describing coupled lateral vibrations of a rotating drill string under the effect of external supersonic gas and internal fluid flows. An axial compressive load and a torque also affect the drill string. The mathematical models are derived by the use of Novozhilov's nonlinear theory of elasticity with implementation of Hamilton's variation principle. Expressions for the gas flow pressure are determined according to the piston theory. The fluid flow is considered as added mass inside the curved tube of the drill string. Using an algorithm developed in the Mathematica computation program on the basis of the Galerkin approach and the stiffness switching method the numerical solution of the obtained approximate differential equations is found. Influences of the external loads, drill string angular speed of rotation, parameters of the gas and fluid flows on the drill string vibrations are shown.

Two-dimensional models as testing ground for principles and concepts of local quantum physics

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

Schroer, Bert

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated localmore » covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular 'Euclideanization' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an 'Encyclopedia of Mathematical Physics' contribution hep-th/0502125.« less

Two-dimensional models as testing ground for principles and concepts of local quantum physics

NASA Astrophysics Data System (ADS)

Schroer, Bert

2006-02-01

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff( S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular "Euclideanization" is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an "Encyclopedia of Mathematical Physics" contribution hep-th/0502125.

An ancient rule for constructing dodecagonal quasiperiodic patterns

NASA Astrophysics Data System (ADS)

Ajlouni, Rima

2017-02-01

The discovery of complex dodecagonal patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. By employing a compass and a straightedge, ancient craftsmen utilized consistent design principles that allowed for diverse geometric expressions to be realized throughout the ancient world. Derived from these principles, a global multi-level structural model is proposed that provides a general guiding principle for constructing a wide variety of infinite dodecagon-based quasiperiodic patterns.

Principles of Technology. Workshop Presenter's Handbook for Pennsylvania Educators.

ERIC Educational Resources Information Center

Wichowski, Chester P.

This workshop presenter's handbook was developed to provide assistance to those who will serve as Principles of Technology trainers of science, industrial arts/technology education, and mathematics teachers throughout Pennsylvania. The handbook provides trainers with presentation materials, transparency masters, suggested activities, and selected…

A Classroom Perspective on the Principle of Moderate Challenge in Mathematics.

ERIC Educational Resources Information Center

Turner, Julianne C.; Meyer, Debra K.

2004-01-01

The authors reviewed the research on challenge as a motivator, with a view toward application in mathematics classrooms. The authors conclude that traditional motivational research, with its focus on individual differences and decontextualized tasks, is not readily applicable to classrooms. They argue that a combination of challenging instruction…

Developing the Area of a Trapezoid

ERIC Educational Resources Information Center

Manizade, Agida G.; Mason, Marguerite M.

2014-01-01

A mathematics classroom that reflects the vision of NCTM's "Principles and Standards for School Mathematics" will have the teacher posing problems, asking questions that build on students' thinking, and encouraging students to explore different solutions. In teaching about area, it is not sufficient to give students the…

Using a Card Trick to Teach Discrete Mathematics

ERIC Educational Resources Information Center

Simonson, Shai; Holm, Tara S.

2003-01-01

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

Quantum Theory from Observer's Mathematics Point of View

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

Khots, Dmitriy; Khots, Boris

2010-05-04

This work considers the linear (time-dependent) Schrodinger equation, quantum theory of two-slit interference, wave-particle duality for single photons, and the uncertainty principle in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics, see [1]. Certain theoretical results and communications pertaining to these theorems are also provided.

Using Collective Argumentation to Engage Students in a Primary Mathematics Classroom

ERIC Educational Resources Information Center

Brown, Raymond

2017-01-01

This article focuses on using sociocultural theory to support student engagement with mathematics. The sociocultural approach used, collective argumentation (CA), is based on interactive principles necessary for coordinating student engagement in the discourse of the classroom. A goal of the research was to explore the affordances and constraints…

An Excel-lent Card Trick

ERIC Educational Resources Information Center

Zullo, Holly S.

2011-01-01

Card tricks based on mathematical principles can be a great way to get students interested in exploring some important mathematical ideas. In this article, the author discusses a simple spreadsheet implementation that shows students why the card trick works and allows them to explore several variations. As an added bonus, students are introduced…

Control Engineering, System Theory and Mathematics: The Teacher's Challenge

ERIC Educational Resources Information Center

Zenger, K.

2007-01-01

The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are…

The Relevance and Efficacy of Metacognition for Instructional Design in the Domain of Mathematics

ERIC Educational Resources Information Center

Baten, Elke; Praet, Magda; Desoete, Annemie

2017-01-01

The efficacy of metacognition as theory-based instructional principle or technique in general, and particularly in mathematics, is explored. Starting with an overview of different definitions, conceptualizations, assessment and training models originating from cognitive information processing theory, the role of metacognition in teaching and…

Energy Transfer and a Recurring Mathematical Function

ERIC Educational Resources Information Center

Atkin, Keith

2013-01-01

This paper extends the interesting work of a previous contributor concerning the analogies between physical phenomena such as mechanical collisions and the transfer of power in an electric circuit. Emphasis is placed on a mathematical function linking these different areas of physics. This unifying principle is seen as an exciting opportunity to…

Rethinking Mathematics: Teaching Social Justice by the Numbers

ERIC Educational Resources Information Center

Gutstein, Eric, Ed.; Peterson, Bob, Ed.

2005-01-01

This unique collection of more than 30 articles shows teachers how to weave social-justice principles throughout the math curriculum, and how to integrate social-justice math into other curricular areas as well. "Rethinking Mathematics" presents teaching ideas, lesson plans and reflections by practicing classroom teachers and distinguished…

Professional Learning for Cultural Mathematics in Papua New Guinea's Elementary Schools

ERIC Educational Resources Information Center

Owens, Kay; Edmonds-Wathen, Cris; Kravia, Geori; Sakopa, Priscilla

2014-01-01

A design of principles for teacher professional learning was developed to improve the teaching of "Cultural Mathematics" in elementary schools in Papua New Guinea. The design's appropriateness for PNG elementary schools is the focus of the research implemented through week-long workshops using technology enhancement. Implementation has…

Motivating Mathematics Learning: Changes in Teachers' Practices and Beliefs during a Nine-Month Collaboration

ERIC Educational Resources Information Center

Turner, Julianne C.; Warzon, Kristen Bogner; Christensen, Andrea

2011-01-01

The authors investigated patterns of change in three middle grade teachers' beliefs and practices about motivation in mathematics during a yearlong professional development project with a university researcher. Four principles of motivation (and corresponding instructional strategies) were introduced in this sequence: supporting students'…

Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice

ERIC Educational Resources Information Center

Anderson-Pence, Katie L.

2015-01-01

This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…

Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles

ERIC Educational Resources Information Center

Freeman, Gregory D.; Lucius, Lisa B.

2008-01-01

In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…

Assessing Knowledge of Mathematical Equivalence: A Construct-Modeling Approach

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Matthews, Percival G.; Taylor, Roger S.; McEldoon, Katherine L.

2011-01-01

Knowledge of mathematical equivalence, the principle that 2 sides of an equation represent the same value, is a foundational concept in algebra, and this knowledge develops throughout elementary and middle school. Using a construct-modeling approach, we developed an assessment of equivalence knowledge. Second through sixth graders (N = 175)…

Job-Embedded Professional Development: Its Impact on Teacher Self-Efficacy and Student Performance

ERIC Educational Resources Information Center

Althauser, Krista

2015-01-01

A quantitative approach was used to investigate the impact of a district-wide, job-embedded mathematics professional development program on elementary teachers' general and personal efficacy. This investigation was based on the principles of mathematics professional development, efficacy theory, and student achievement. It was designed to…

A Gauge-generalized Solution for Non-Keplerian Motion in the Frenet-Serret Frame

NASA Astrophysics Data System (ADS)

Garber, Darren D.

2009-05-01

The customary modeling of perturbed planetary and spacecraft motion as a continuous sequence of unperturbed two-body orbits (instantaneous ellipses) is conveniently assigned a physical interpretation through the Keplerian and Delaunay elements and complemented mathematically by the Lagrange-type equations which describe the evolution of these variables. If however the actual motion is very non-Keplerian (i.e. the perturbed orbit varies greatly from a two-body orbit), then its modeling by a sequence of conics is not necessarily optimal in terms of its mathematical description and its resulting physical interpretation. Since, in principle a curve of any type can be represented as a sequence of points from a family of curves of any other type (Efroimsky 2005), alternate non-conic curves can be utilized to better describe the perturbed non-Keplerian motion of the body both mathematically and with a physically relevant interpretation. Non-Keplerian motion exists in both celestial mechanics and astrodynamics as evident by the complex interactions within star clusters and also as the result of a spacecraft accelerating via ion propulsion, solar sails and electro-dynamic tethers. For these cases, the sequence of simple orbits to describe the motion is not based on conics, but instead a family of spirals. The selection of spirals as the underlying simple motion is supported by the fact that it is unnecessary to describe the motion in terms of instantaneous orbits tangent to the actual trajectory (Efroimsky 2002, Newman & Efroimsky 2003) and at times there is an advantage to deviate from osculation, in order to greatly simplify the resulting mathematics via gauge freedom (Efroimsky & Goldreich 2003, Slabinski 2003, Gurfil 2004). From these two principles, (1) spirals as instantaneous orbits, and (2) controlled deviation from osculation, new planetary equations are derived for new non-osculating elements in the Frenet-Serret frame with the gauge function as a measure of non-osculation.

Evaluation methodology for query-based scene understanding systems

NASA Astrophysics Data System (ADS)

Huster, Todd P.; Ross, Timothy D.; Culbertson, Jared L.

2015-05-01

In this paper, we are proposing a method for the principled evaluation of scene understanding systems in a query-based framework. We can think of a query-based scene understanding system as a generalization of typical sensor exploitation systems where instead of performing a narrowly defined task (e.g., detect, track, classify, etc.), the system can perform general user-defined tasks specified in a query language. Examples of this type of system have been developed as part of DARPA's Mathematics of Sensing, Exploitation, and Execution (MSEE) program. There is a body of literature on the evaluation of typical sensor exploitation systems, but the open-ended nature of the query interface introduces new aspects to the evaluation problem that have not been widely considered before. In this paper, we state the evaluation problem and propose an approach to efficiently learn about the quality of the system under test. We consider the objective of the evaluation to be to build a performance model of the system under test, and we rely on the principles of Bayesian experiment design to help construct and select optimal queries for learning about the parameters of that model.

Ethnomathematics Exploration of the Toba Community: Elements of Geometry Transformation Contained in Gorga (Ornament on Bataks House)

NASA Astrophysics Data System (ADS)

Ditasona, C.

2018-04-01

Gorga is an ornament known to the Batak community. As one of the works of art that poured in the form of carvings, gorga become icons for batak society. Long before the Batak people knew formal education, they had made gorga. This is evidenced through several historical sources. Gorga not only contains the value of art but also has a mathematical element. There are many mathematical principles used in the process of making gorga. The principle of geometry transformation is very prominent in the gorga motifs. This article is an ethnomathematics research that will discuss how the thinking process in making gorga. Observations and interviews with the gorga craftsmen (pande) are conducted to find out how the principles of rotation, translation, dilation and reflection are used in making gorga motifs

Approaches to Foster Transfer of Formal Principles: Which Route to Take?

PubMed Central

Schalk, Lennart; Saalbach, Henrik; Stern, Elsbeth

2016-01-01

Enabling learners to transfer knowledge about formal principles to new problems is a major aim of science and mathematics education, which, however, is notoriously difficult to reach. Previous research advocates different approaches of how to introduce principles to foster the transfer of knowledge about formal principles. One approach suggests teaching a generic formalism of the principles. Another approach suggests presenting (at least) two concrete cases instantiating the principle. A third approach suggests presenting a generic formalism accompanied by a case. As yet, though, empirical results regarding the transfer potential of these approaches are mixed and difficult to integrate as the three approaches have rarely been tested competitively. Furthermore, the approaches have been evaluated in relation to different control conditions, and they have been assessed using varying transfer measures. In the present experiment, we introduced undergraduates to the formal principles of propositional logic with the aim to systematically compare the transfer potential of the different approaches in relation to each other and to a common control condition by using various learning and transfer tasks. Results indicate that all approaches supported successful learning and transfer of the principles, but also caused systematic differences in the magnitude of transfer. Results indicate that the combination of a generic formalism with a case was surprisingly unsuccessful while learners who compared two cases outperformed the control condition. We discuss how the simultaneous assessment of the different approaches allows to more precisely capture the underlying learning mechanisms and to advance theory on how these mechanisms contribute to transfer performance. PMID:26871902

What Diagrams Argue in Late Imperial Chinese Combinatorial Texts.

PubMed

Bréard, Andrea

2015-01-01

Attitudes towards diagrammatic reasoning and visualization in mathematics were seldom spelled out in texts from pre-modern China, although illustrations figure prominently in mathematical literature since the eleventh century. Taking the sums of finite series and their combinatorial interpretation as a case study, this article investigates the epistemological function of illustrations from the eleventh to the nineteenth century that encode either the mathematical objects themselves or represent their related algorithms. It particularly focuses on the two illustrations given in Wang Lai's (1768-1813) Mathematical Principles of Sequential Combinations, arguing that they reflect a specific mode of nineteenth-century mathematical argumentative practice and served as a heuristic model for later authors.

Principles for the dynamic maintenance of cortical polarity

PubMed Central

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

2007-01-01

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

Principles of Empiricism and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

The interpretation of quantum mechanics (QM) is discussed in terms of the principles and logic of empiricism. First, we list a set of issues that should be settled before any consistent interpretation is attempted. This includes questions such as whether we can use an exophysical perspective or an endophysical perspective, and whether a completely reductionist approach makes sense or are we forced to incorporate emergent laws of physics. We then list the scientific pr nciples that should be strictly adhered to in any debate on QM. We follow this with a list of cautions and warnings about misleading concepts that should be avoided, such as ignoring contextuality and the meaning of scientific truth values. These principles and warning are then used to decide on the issues we first identified, giving us a basis for an interpretation of QM from the perspective of observers and quantum signal states of apparatus, rather than in terms of qu ntum states of systems under observation. Finally, we review a proposed mathematical formalism that encodes this interpretation in terms of quantum registers.

Boltzmann, Darwin and Directionality theory

NASA Astrophysics Data System (ADS)

Demetrius, Lloyd A.

2013-09-01

Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and extinction. We also elucidate the relation between thermodynamic entropy, which pertains to the extent of energy spreading and sharing within inanimate matter, and evolutionary entropy, which refers to the rate of energy appropriation from the environment and allocation within living systems. We show that the entropic principle of thermodynamics is the limit as R→0, M→∞, (where R denote the resource production rate, and M denote population size) of the entropic principle of evolution. We exploit this relation between the thermodynamic and evolutionary tenets to propose a physico-chemical model of the transition from inanimate matter which is under thermodynamic selection, to living systems which are subject to evolutionary selection. Life history variation and the evolution of senescence The evolutionary dynamics of speciation and extinction Evolutionary trends in body size. The origin of sporadic forms of cancer and neurological diseases, and the evolution of cooperation are important recent applications of directionality theory. These applications, which draw from the medical sciences and sociobiology, appeal to methods which lie outside the formalism described in this report. A companion review, Demetrius and Gundlach (submitted for publication), gives an account of these applications.An important aspect of this report pertains to the connection between statistical mechanics and evolutionary theory and its implications towards understanding the processes which underlie the emergence of living systems from inanimate matter-a problem which has recently attracted considerable attention, Morowitz (1992), Eigen (1992), Dyson (2000), Pross (2012).The connection between the two disciplines can be addressed by appealing to certain extremal principles which are considered the mainstay of the respective theories.The extremal principle in statistical mechanics can be stated as follows:

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Principles and Practices Fostering Inclusive Excellence: Lessons from the Howard Hughes Medical Institute's Capstone Institutions

ERIC Educational Resources Information Center

DiBartolo, Patricia Marten; Gregg-Jolly, Leslie; Gross, Deborah; Manduca, Cathryn A.; Iverson, Ellen; Cooke, David B., III; Davis, Gregory K.; Davidson, Cameron; Hertz, Paul E.; Hibbard, Lisa; Ireland, Shubha K.; Mader, Catherine; Pai, Aditi; Raps, Shirley; Siwicki, Kathleen; Swartz, Jim E.

2016-01-01

Best-practices pedagogy in science, technology, engineering, and mathematics (STEM) aims for inclusive excellence that fosters student persistence. This paper describes principles of inclusivity across 11 primarily undergraduate institutions designated as Capstone Awardees in Howard Hughes Medical Institute's (HHMI) 2012 competition. The Capstones…

The Impact on Student Achievement Following Professional Development on the Principles of Formative Assessment

ERIC Educational Resources Information Center

DeNome, Evonne C.

2015-01-01

This quantitative study reviews the impact on student achievement following professional development on the principles of formative assessment. The study compared mathematics and reading performance data from student populations with teachers who received training in formative assessment to performance data from student populations with teachers…

Bridging Levels of Analysis: Learning, Information Theory, and the Lexicon

ERIC Educational Resources Information Center

Dye, Melody

2017-01-01

While information theory is typically considered in the context of modern computing and engineering, its core mathematical principles provide a potentially useful lens through which to consider human language. Like the artificial communication systems such principles were invented to describe, natural languages involve a sender and receiver, a…

Case Study of an Epistemic Mathematics Computer Game

ERIC Educational Resources Information Center

Buteau, Chantal; Muller, Eric

2018-01-01

E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which "players think and act like real world professionals" has been called epistemic. This article presents an empirical…

A Symbiotic Relationship: The Observe-Orient-Decide-Act (OODA) Loop, Intuition, and Strategic Thought

DTIC Science & Technology

2013-03-01

Incompleteness Theorem (used in mathematics), and Heisenberg’s Uncertainty Principle as it pertains to the mathematical foundations of quantum ...subtlety which normal consciousness cannot even see…”46 It is in our PME system where we can create the time to develop the unconscious realms of the

The True Growth Rate and the Inflation Balancing Principle.

ERIC Educational Resources Information Center

Thompson, Robert C.

1983-01-01

The demise of mathematics of finance as a subject is discussed and a resurgence is seen as possible, but the traditional instructional presentation is seen as in need of modernization. Financial mathematics is referred to as a beautiful subject when inflation is incorporated, provided that calculators are used in computations. (Author/MP)

Learning from Worked-Examples in Mathematics: Students Relate Procedures to Principles

ERIC Educational Resources Information Center

Renkl, Alexander

2017-01-01

This article discusses the relevance of the worked-example effect for mathematics education. This effect refers to the finding that, in initial cognitive skill acquisition, students profit more from studying worked examples as compared to solving problems. One reason for the effectiveness of worked examples is that the students get the opportunity…

Effective Computer-Aided Assessment of Mathematics; Principles, Practice and Results

ERIC Educational Resources Information Center

Greenhow, Martin

2015-01-01

This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and…

Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles

ERIC Educational Resources Information Center

Cigas, John; Hsin, Wen-Jung

2005-01-01

Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…

Common Grounds for Modelling Mathematics in Educational Software

ERIC Educational Resources Information Center

Neuper, Walther

2010-01-01

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

From Square Dance to Mathematics

ERIC Educational Resources Information Center

Bremer, Zoe

2010-01-01

In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…

In Addition Afterschool Mathematics Program: Principles, Practice, and Pitfalls

ERIC Educational Resources Information Center

McVarish, Judith; Birkmeier, Patricia

2004-01-01

Afterschool math hours are most often spent on homework help, tutoring, drill, and test-preparation with instructors who may not be certified teachers or mathematics educators. While such "extra math help" may be of value, it is unreasonable to expect students to enjoy learning experiences based on workbook-style exercises. The In…

Toward a theory of organisms: Three founding principles in search of a useful integration

PubMed Central

SOTO, ANA M.; LONGO, GIUSEPPE; MIQUEL, PAUL-ANTOINE; MONTEVIL, MAËL; MOSSIO, MATTEO; PERRET, NICOLE; POCHEVILLE, ARNAUD; SONNENSCHEIN, CARLOS

2016-01-01

Organisms, be they uni- or multi-cellular, are agents capable of creating their own norms; they are continuously harmonizing their ability to create novelty and stability, that is, they combine plasticity with robustness. Here we articulate the three principles for a theory of organisms proposed in this issue, namely: the default state of proliferation with variation and motility, the principle of variation and the principle of organization. These principles profoundly change both biological observables and their determination with respect to the theoretical framework of physical theories. This radical change opens up the possibility of anchoring mathematical modeling in biologically proper principles. PMID:27498204

The principle of superposition and its application in ground-water hydraulics

USGS Publications Warehouse

Reilly, Thomas E.; Franke, O. Lehn; Bennett, Gordon D.

1987-01-01

The principle of superposition, a powerful mathematical technique for analyzing certain types of complex problems in many areas of science and technology, has important applications in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that problem solutions can be added together to obtain composite solutions. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to ground-water hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader.

Is Logic in the Mind or in the World? Why a Philosophical Question can Affect the Understanding of Intelligence

NASA Astrophysics Data System (ADS)

Sommer, Hanns; Schreiber, Lothar

2012-05-01

Dreyfus' call ‘to make artificial intelligence (AI) more Heideggerian‘ echoes Heidegger's affirmation that pure calculations produce no ‘intelligence’ (Dreyfus, 2007). But what exactly is it that AI needs more than mathematics? The question in the title gives rise to a reexamination of the basic principles of cognition in Husserl's Phenomenology. Using Husserl's Phenomenological Method, a formalization of these principles is presented that provides the principal idea of cognition, and as a consequence, a ‘natural logic’. Only in a second step, mathematics is obtained from this natural logic by abstraction. The limitations of pure reasoning are demonstrated for fundamental considerations (Hilbert's ‘finite Einstellung’) as well as for the task of solving practical problems. Principles will be presented for the design of general intelligent systems, which make use of a natural logic.

The birth of the blues: how physics underlies music

NASA Astrophysics Data System (ADS)

Gibson, J. M.

2009-07-01

Art and science have intimate connections, although these are often underappreciated. Western music provides compelling examples. The sensation of harmony and related melodic development are rooted in physical principles that can be understood with simple mathematics. The focus of this review is not the better known acoustics of instruments, but the structure of music itself. The physical basis of the evolution of Western music in the last half millennium is discussed, culminating with the development of the 'blues'. The paper refers to a number of works which expand the connections, and introduces material specific to the development of the 'blues'. Several conclusions are made: (1) that music is axiomatic like mathematics and that to appreciate music fully listeners must learn the axioms; (2) that this learning does not require specific conscious study but relies on a linkage between the creative and quantitative brain and (3) that a key element of the musical 'blues' comes from recreating missing notes on the modern equal temperament scale. The latter is an example of 'art built on artifacts'. Finally, brief reference is made to the value of music as a tool for teaching physics, mathematics and engineering to non-scientists.

The birth of the blues : how physics underlies music.

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

Gibson, J. M.

Art and science have intimate connections, although these are often underappreciated. Western music provides compelling examples. The sensation of harmony and related melodic development are rooted in physical principles that can be understood with simple mathematics. The focus of this review is not the better known acoustics of instruments, but the structure of music itself. The physical basis of the evolution of Western music in the last half millennium is discussed, culminating with the development of the 'blues'. The paper refers to a number of works which expand the connections, and introduces material specific to the development of the 'blues'.more » Several conclusions are made: (1) that music is axiomatic like mathematics and that to appreciate music fully listeners must learn the axioms; (2) that this learning does not require specific conscious study but relies on a linkage between the creative and quantitative brain and (3) that a key element of the musical 'blues' comes from recreating missing notes on the modern equal temperament scale. The latter is an example of 'art built on artifacts'. Finally, brief reference is made to the value of music as a tool for teaching physics, mathematics and engineering to non-scientists.« less

Globalization and Its Impact on the Medium of Instruction in Higher Education in Malaysia

ERIC Educational Resources Information Center

Mohamed, Mohini

2008-01-01

Understanding bilingualism in science and mathematics education and developing a principled instruction is a pressing issue in Malaysian system of education. With the implementation of government policy of teaching science and mathematics in English starting from year 2003, an increasing number of students are affected with this policy. An initial…

Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics

ERIC Educational Resources Information Center

Sangwin, Christopher J.; Naismith, Laura

2008-01-01

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

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

ERIC Educational Resources Information Center

Kretschmer, Hildrun

2002-01-01

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

A Case Study of an Expert Problem Poser for Mathematics Competitions

ERIC Educational Resources Information Center

Kontorovich, Igor'; Koichu, Boris

2016-01-01

This paper is concerned with organizational principles of a pool of familiar problems of expert problem posers and the ways by which they are utilized for creating new problems. The presented case of Leo is part of a multiple-case study with expert problem posers for mathematics competitions. We present and inductively analyze the data collected…

Task Design for Ways of Working: Making Distinctions in Teaching and Learning Mathematics

ERIC Educational Resources Information Center

Coles, Alf; Brown, Laurinda

2016-01-01

A problem identified in the literature around task design is the persistence of a gap between teacher intention and student activity. We show how principles designed around the making of distinctions and having an explicit language of mathematical thinking can eliminate the "gap" by guiding teacher planning, teacher actions in the…

Development of a Mathematics, Science, and Technology Education Integrated Program for a Maglev

ERIC Educational Resources Information Center

Park, Hyoung Seo

2006-01-01

The purpose of the study was to develop an MST Integrated Program for making a Maglev hands-on activity for higher elementary school students in Korea. In this MST Integrated Program, students will apply Mathematics, Science, and Technology principles and concepts to the design, construction, and evaluation of a magnetically levitated vehicle. The…

The Patterns of Music: Young Children Learning Mathematics through Beat, Rhythm, and Melody

ERIC Educational Resources Information Center

Geist, Kamile; Geist, Eugene A.; Kuznik, Kathleen

2012-01-01

Research on music and music therapy suggests that math and music are related in the brain from very early in life. Musical elements such as steady beat, rhythm, melody, and tempo possess inherent mathematical principles such as spatial properties, sequencing, counting, patterning, and one-to-one correspondence. With new understanding about the…

Promoting Self-Explanation to Improve Mathematics Learning: A Meta-Analysis and Instructional Design Principles

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Loehr, Abbey M.; Durkin, Kelley

2017-01-01

Promoting self-explanation (i.e., generating explanations for oneself in an attempt to make sense of new information) is a recommended study strategy and instructional practice. A meta-analysis of the literature on prompting self-explanation to improve mathematics learning confirmed that prompted self-explanation leads to a small to moderate…

Proofs without Words: A Visual Application of Reasoning and Proof

ERIC Educational Resources Information Center

Bell, Carol J.

2011-01-01

Reasoning and Proof is one of the Process Standards set forth in National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics." Thus, it is important to give students opportunities to build their reasoning skills and aid their understanding of the proof process. Teaching students how to do proofs is a…

Especially for High School Teachers

NASA Astrophysics Data System (ADS)

Howell, J. Emory

2001-05-01

Literature Cited

1. National Science Education Standards; National Academy Press: Washington, DC, 1996; http://www. nap.edu/readingroom/books/nses/.
2. Principles and Standards for School Mathematics; National Council of Teachers of Mathematics: Washington, DC, 2000; http://standards.nctm.org/.

Devising Principles of Design for Numeracy Tasks

ERIC Educational Resources Information Center

Geiger, Vince; Forgasz, Helen; Goos, Merrilyn; Bennison, Anne

2014-01-01

Numeracy is a fundamental component of the Australian National Curriculum as a General Capability identified in each F-10 subject. In this paper, we consider the principles of design necessary for the development of numeracy tasks specific to subjects other than mathematics--in this case, the subject of English. We explore the nature of potential…

Design-Based Research for Professional Learning for "Cultural Mathematics"

ERIC Educational Resources Information Center

Kravia, Geori; Owens, Kay

2014-01-01

Design-based research is being used to develop and refine the principles used in professional learning workshops with teachers from three different Papua New Guinean ecologies: highlands, coastal, and inland in a coastal province. The appropriateness of the design of principles for Papua New Guinean Elementary Schools is tried over several phases…

Principled Improvement in Science: Forces and Proportional Relations in Early Secondary-School Teaching

ERIC Educational Resources Information Center

Howe, Christine; Ilie, Sonia; Guardia, Paula; Hofmann, Riikka; Mercer, Neil; Riga, Fran

2015-01-01

In response to continuing concerns about student attainment and participation in science and mathematics, the "epiSTEMe" project took a novel approach to pedagogy in these two disciplines. Using principles identified as effective in the research literature (and combining these in a fashion not previously attempted), the project developed…

An Educational Development Tool Based on Principles of Formal Ontology

ERIC Educational Resources Information Center

Guzzi, Rodolfo; Scarpanti, Stefano; Ballista, Giovanni; Di Nicolantonio, Walter

2005-01-01

Computer science provides with virtual laboratories, places where one can merge real experiments with the formalism of algorithms and mathematics and where, with the advent of multimedia, sounds and movies can also be added. In this paper we present a method, based on principles of formal ontology, allowing one to develop interactive educational…

Five Easy Principles to Make Math Moments Count

ERIC Educational Resources Information Center

Cutler, Carrie S.

2011-01-01

Preschool children are learning so many skills--how to cut with scissors, zip zippers, recognize the alphabet and their names, and share toys with others. A strong academic curriculum also requires that children learn more about math (National Council of Teachers of Mathematics [NCTM], 2000). By following the five easy principles outlined here,…

Designing Learning Personalized to Students' Interests: Balancing Rich Experiences with Mathematical Goals

ERIC Educational Resources Information Center

Walkington, Candace; Hayata, Carole A.

2017-01-01

Context personalization is an instructional design principle where tasks are presented to students in the context of their interest areas like sports, music, or video games. Personalization allows for understanding of domain principles to be grounded in concrete and familiar experiences. By making connections to prior knowledge, personalization…

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

Superposition Quantification

NASA Astrophysics Data System (ADS)

Chang, Li-Na; Luo, Shun-Long; Sun, Yuan

2017-11-01

The principle of superposition is universal and lies at the heart of quantum theory. Although ever since the inception of quantum mechanics a century ago, superposition has occupied a central and pivotal place, rigorous and systematic studies of the quantification issue have attracted significant interests only in recent years, and many related problems remain to be investigated. In this work we introduce a figure of merit which quantifies superposition from an intuitive and direct perspective, investigate its fundamental properties, connect it to some coherence measures, illustrate it through several examples, and apply it to analyze wave-particle duality. Supported by Science Challenge Project under Grant No. TZ2016002, Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Grant under No. 2008DP173182

Handicap principle implies emergence of dimorphic ornaments

PubMed Central

2016-01-01

Species spanning the animal kingdom have evolved extravagant and costly ornaments to attract mating partners. Zahavi's handicap principle offers an elegant explanation for this: ornaments signal individual quality, and must be costly to ensure honest signalling, making mate selection more efficient. Here, we incorporate the assumptions of the handicap principle into a mathematical model and show that they are sufficient to explain the heretofore puzzling observation of bimodally distributed ornament sizes in a variety of species. PMID:27903876

Children's understanding of the addition/subtraction complement principle.

PubMed

Torbeyns, Joke; Peters, Greet; De Smedt, Bert; Ghesquière, Pol; Verschaffel, Lieven

2016-09-01

In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal techniques. This contribution aimed at deepening our understanding of children's knowledge of the addition/subtraction complement principle, combining verbal and non-verbal techniques. Participants were 67 third and fourth graders (9- to 10-year-olds). Children solved two tasks in which verbal reports as well as accuracy and speed data were collected. These two tasks differed only in the order of the problems and the instructions. In the looking-back task, children were told that sometimes the preceding problem might help to answer the next problem. In the baseline task, no helpful preceding items were offered. The looking-back task included 10 trigger-target problem pairs on the complement relation. Children verbally reported looking back on about 40% of all target problems in the looking-back task; the target problems were also solved faster and more accurately than in the baseline task. These results suggest that children used their understanding of the complement principle. The verbal and non-verbal data were highly correlated. This study complements previous work on children's understanding of mathematical principles by highlighting interindividual differences in 9- to 10-year-olds' understanding of the complement principle and indicating the potential of combining verbal and non-verbal techniques to investigate (the acquisition of) this understanding. © 2016 The British Psychological Society.

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

NASA Astrophysics Data System (ADS)

Rodríguez, Clara Rojas; Fernández Calvo, Gabriel; Ramis-Conde, Ignacio; Belmonte-Beitia, Juan

2017-08-01

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology

PubMed Central

Balduzzi, Mathilde; Binder, Brad M.; Bucksch, Alexander; Chang, Cynthia; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Pradal, Christophe; Sparks, Erin E.

2017-01-01

An emerging challenge in plant biology is to develop qualitative and quantitative measures to describe the appearance of plants through the integration of mathematics and biology. A major hurdle in developing these metrics is finding common terminology across fields. In this review, we define approaches for analyzing plant geometry, topology, and shape, and provide examples for how these terms have been and can be applied to plants. In leaf morphological quantifications both geometry and shape have been used to gain insight into leaf function and evolution. For the analysis of cell growth and expansion, we highlight the utility of geometric descriptors for understanding sepal and hypocotyl development. For branched structures, we describe how topology has been applied to quantify root system architecture to lend insight into root function. Lastly, we discuss the importance of using morphological descriptors in ecology to assess how communities interact, function, and respond within different environments. This review aims to provide a basic description of the mathematical principles underlying morphological quantifications. PMID:28217137

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

PubMed

Wong, Terry Tin-Yau

2017-12-01

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

System for corrosion monitoring in pipeline applying fuzzy logic mathematics

NASA Astrophysics Data System (ADS)

Kuzyakov, O. N.; Kolosova, A. L.; Andreeva, M. A.

2018-05-01

A list of factors influencing corrosion rate on the external side of underground pipeline is determined. Principles of constructing a corrosion monitoring system are described; the system performance algorithm and program are elaborated. A comparative analysis of methods for calculating corrosion rate is undertaken. Fuzzy logic mathematics is applied to reduce calculations while considering a wider range of corrosion factors.

Teaching Guide and Problem Supplement. A Publication of the Exemplary Project Problem Solving Computer Style 1969-1970.

ERIC Educational Resources Information Center

New Orleans Public Schools, LA.

Secondary school teachers incorporating the use of a computer in algebra, trigonometry, advanced mathematics, chemistry, or physics classes are the individuals for whom this book is intended. The content included in it is designed to aid the learning of programing techniques and basic scientific or mathematical principles, and to offer some…

Journeys of Transformation: A Statewide Effort by Mathematics and Science Professors To Improve Student Understanding. Case Reports from Participants in the Maryland Collaborative for Teacher Preparation.

ERIC Educational Resources Information Center

Gardner, Maureen B., Ed.

This document presents the Maryland Collaborative for Teacher Preparation (MCTP) faculty's reviews on instructional issues of different disciplines. Contents include: (1) "The Maryland Collaborative for Teacher Preparation"; (2) "Guiding Principles: New Thinking in Mathematics and Science Teaching"; (3) "Introduction: Parallel Journeys of Risk and…

Promoting Secondary Teachers' Diagnostic Competence with Respect to Functions: Development of a Scalable Unit in Continuous Professional Development

ERIC Educational Resources Information Center

Busch, Julia; Barzel, Bärbel; Leuders, Timo

2015-01-01

Diagnosing student achievement in a formative way is a crucial skill for planning and carrying out effective mathematics lessons. This study takes a subject-specific view and aims at investigating diagnostic competence in the field of mathematical functions at secondary level and how to improve it. Following three evidence-based design principles,…

Formal logic rewrite system bachelor in teaching mathematical informatics

NASA Astrophysics Data System (ADS)

Habiballa, Hashim; Jendryscik, Radek

2017-07-01

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

Towards the Solution of Abysmal Performance in Mathematics in Junior High Schools: Comparing the Pedagogical Potential of Two Designed Interventions

ERIC Educational Resources Information Center

Sarfo, Frederick Kwaku; Eshun, Grace; Elen, Jan; Adentwi, Kobina Impraim

2014-01-01

Introduction: In this study, the effectiveness of two different interventions was investigated. The effects of a concrete abstract intervention and a regular method of teaching intervention were compared. Both interventions were designed in line with the specifications of classical principles of instructional design for learning mathematics in the…

An optimal brain can be composed of conflicting agents

PubMed Central

Livnat, Adi; Pippenger, Nicholas

2006-01-01

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under natural physiological limitations, an optimal decision-making system can involve “selfish” agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only. PMID:16492775

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2014-12-01

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

Using "First Principles of Instruction" to Design Secondary School Mathematics Flipped Classroom: The Findings of Two Exploratory Studies

ERIC Educational Resources Information Center

Lo, Chung Kwan; Hew, Khe Foon

2017-01-01

Flipping the classroom is a current pedagogical innovation in many schools and universities. Although interest in flipped classroom (or Inverted Classroom) continues to grow, its implementation so far has been driven more by teachers' intuitive beliefs, rather than empirically-based principles. Many studies merely replace in-class instructions…

Conceptual Learning in a Principled Design Problem Solving Environment

ERIC Educational Resources Information Center

Prusak, Naomi; Hershkowitz, Rina; Schwarz, Baruch B.

2013-01-01

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…

It Is All about Inquiry: A Cross-Disciplinary Conversation about the Shared Foundations for Teaching

ERIC Educational Resources Information Center

Firkins Nordstrom, Jennifer A.; Sumner, David Thomas

2017-01-01

This paper brings together general principles for teaching inquiry across disciplines with those generally employed in mathematics classrooms. It describes some broad principles of teaching inquiry to first-year writing students and shows how these can be employed in the context of a course on game theory in popular culture. Although undergraduate…

A Study of Visualization for Mathematics Education

NASA Technical Reports Server (NTRS)

Daugherty, Sarah C.

2008-01-01

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

The principle of finiteness - a guideline for physical laws

NASA Astrophysics Data System (ADS)

Sternlieb, Abraham

2013-04-01

I propose a new principle in physics-the principle of finiteness (FP). It stems from the definition of physics as a science that deals with measurable dimensional physical quantities. Since measurement results including their errors, are always finite, FP postulates that the mathematical formulation of legitimate laws in physics should prevent exactly zero or infinite solutions. I propose finiteness as a postulate, as opposed to a statement whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories or principles. Some consequences of FP are discussed, first in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The corrected Lorentz transformations include an additional translation term depending on the minimum length epsilon. The relativistic gamma is replaced by a corrected gamma, that is finite for v=c. To comply with FP, physical laws should include the relevant extremum finite values in their mathematical formulation. An important prediction of FP is that there is a maximum attainable relativistic mass/energy which is the same for all subatomic particles, meaning that there is a maximum theoretical value for cosmic rays energy. The Generalized Uncertainty Principle required by Quantum Gravity is actually a necessary consequence of FP at Planck's scale. Therefore, FP may possibly contribute to the axiomatic foundation of Quantum Gravity.

Mathematical modeling of molecular diffusion through mucus

PubMed Central

Cu, Yen; Saltzman, W. Mark

2008-01-01

The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488

Tropical mathematics and the financial catastrophe of the 17th century. Thermoeconomics of Russia in the early 20th century

NASA Astrophysics Data System (ADS)

Maslov, V. P.

2010-03-01

In the paper, an example is presented concerning relationships (which cannot be neglected) between mathematics and other sciences. In particular, the relationship between the tropical mathematics and the humanitarian-economic catastrophe of 17th century (related to slavery of Africans) is considered. The notion of critical state of economy of the 19th century is introduced by using the refined Fisher equation. A correspondence principle for thermodynamics of fluids and economics of the 19th century is presented.

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

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Khramushin, Vasily

2016-02-01

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

Handicap principle implies emergence of dimorphic ornaments.

PubMed

Clifton, Sara M; Braun, Rosemary I; Abrams, Daniel M

2016-11-30

Species spanning the animal kingdom have evolved extravagant and costly ornaments to attract mating partners. Zahavi's handicap principle offers an elegant explanation for this: ornaments signal individual quality, and must be costly to ensure honest signalling, making mate selection more efficient. Here, we incorporate the assumptions of the handicap principle into a mathematical model and show that they are sufficient to explain the heretofore puzzling observation of bimodally distributed ornament sizes in a variety of species. © 2016 The Author(s).

Universal Decoherence under Gravity: A Perspective through the Equivalence Principle.

PubMed

Pang, Belinda H; Chen, Yanbei; Khalili, Farid Ya

2016-08-26

Pikovski et al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's equivalence principle to be valid, we analyze a physical realization of the (1+1)D thought experiment of Pikovski et al. to demonstrate that the dephasing between the different internal states arises not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Pikovski et al., where we propose that gravity plays a kinematic role by providing a relative velocity to the detector frame with respect to the particle; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We then apply this insight to their thought experiment in (1+1)D to draw a direct correspondence, and obtain the same mathematical result for dephasing. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the equivalence principle is violated.

The utilization of the seven principles for good practices of full-time and adjunct faculty in teaching health & science in community colleges

NASA Astrophysics Data System (ADS)

Musaitif, Linda M.

Purpose. The purpose of this study was to determine the degree to which undergraduate full-time and adjunct faculty members in the health and science programs at community colleges in Southern California utilize the seven principles of good practice as measured by the Faculty Inventory of the Seven Principles for Good Practice in Undergraduate Education. A second purpose was to compare degree of utilization for gender and class size. Methodology. This is a quantitative study wherein there exists a systematic and mathematical assessment of data gathered through the use of a Likert scale survey to process and determine the mathematical model of the use of the principles by the target population of both full-time and adjunct faculty of health/science programs of community colleges in Southern California. Findings. Examination of the data revealed that both full-time and adjunct faculty members of Southern California community colleges perceive themselves a high degree of utilization of the seven principles of good practice. There was no statistically significant data to suggest a discrepancy between full-time and adjunct professors' perceptions among the utilization of the seven principles. Overall, male faculty members perceived themselves as utilizing the principles to a greater degree than female faculty. Data suggest that faculty with class size 60 or larger showed to utilize the seven principles more frequently than the professors with smaller class sizes. Conclusions. Full-time and adjunct professors of the health and sciences in Southern California community colleges perceive themselves as utilizing the seven principles of good practice to a high degree. Recommendations. This study suggests many recommendations for future research, including the degree to which negative economic factors such as budget cuts and demands affect the utilization of the seven principles. Also recommended is a study comparing students' perceptions of faculty's utilization of the seven principles of good practice in the classroom with faculty's self-perception.

The Convallis Rule for Unsupervised Learning in Cortical Networks

PubMed Central

Yger, Pierre; Harris, Kenneth D.

2013-01-01

The phenomenology and cellular mechanisms of cortical synaptic plasticity are becoming known in increasing detail, but the computational principles by which cortical plasticity enables the development of sensory representations are unclear. Here we describe a framework for cortical synaptic plasticity termed the “Convallis rule”, mathematically derived from a principle of unsupervised learning via constrained optimization. Implementation of the rule caused a recurrent cortex-like network of simulated spiking neurons to develop rate representations of real-world speech stimuli, enabling classification by a downstream linear decoder. Applied to spike patterns used in in vitro plasticity experiments, the rule reproduced multiple results including and beyond STDP. However STDP alone produced poorer learning performance. The mathematical form of the rule is consistent with a dual coincidence detector mechanism that has been suggested by experiments in several synaptic classes of juvenile neocortex. Based on this confluence of normative, phenomenological, and mechanistic evidence, we suggest that the rule may approximate a fundamental computational principle of the neocortex. PMID:24204224

Consistent Quantum Theory

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2001-11-01

Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics

Galileo as an intellectual heretic and why that matters

NASA Astrophysics Data System (ADS)

Palmieri, Paolo

2014-03-01

What was physics like before Galileo? Five centuries ago physics was taught in universities all over Europe as part of a broader field of knowledge known as natural philosophy. It was neither quantitative, nor experimental, but mostly an a-priori, logical type of inquiry about principles concerning notions such as space, time, and motion, from which deductions could be made about the natural world. Galileo changed all that. He claimed that inquiry about nature should be experimental, and that reasoning in natural philosophy should be mathematical. It was a bold enough move. But Galileo's intellectual heresy was the discovery that knowledge of the natural world could only be achieved by relaxing the requirement that principles be known with absolute certainty. He demonstrated that a new mathematical physics could be built upon principles based on experiment. Thus the new physics could be extended recklessly by starting from less than certain foundations. Galileo's startling insight was that scientific truth need not be localized but can be diffused throughout the structure of science.

Strategy Choices in Simple and Complex Addition: Contributions of Working Memory and Counting Knowledge for Children with Mathematical Disability

ERIC Educational Resources Information Center

Geary, David C.; Hoard, Mary K.; Byrd-Craven, Jennifer; DeSoto, M. Catherine

2004-01-01

Groups of first-grade (mean age = 82 months), third-grade (mean age = 107 months), and fifth-grade (mean age = 131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n = 91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to…

A Computer-Assisted Framework Based on a Cognitivist Learning Theory for Teaching Mathematics in the Early Primary Years

ERIC Educational Resources Information Center

Moradmand, Nasrin; Datta, Amitava; Oakley, Grace

2012-01-01

With the world moving rapidly into digital media and information, the ways in which learning activities in mathematics can be created and delivered are changing. However, to get the best results from the integration of ICTs in education, any application's design and development needs to be based on pedagogically appropriate principles, in terms of…

Who Is Doing the Engineering, the Student or the Teacher? The Development and Use of a Rubric to Categorize Level of Design for the Elementary Classroom

ERIC Educational Resources Information Center

Nadelson, Louis S.; Pfiester, Joshua; Callahan, Janet; Pyke, Patricia

2015-01-01

Science, technology, engineering, and mathematics (STEM) professional development for K-5 teachers often includes engineering design as a focus. Because engineering applications provide perspective to both teachers and their students in terms of how mathematic and scientific principles are employed to solve real-world problems (Baine, 2004; Roden,…

A Mathematical Analysis of Semantic Maps, with Theoretical and Applied Implications for Blended Learning Software

ERIC Educational Resources Information Center

Tang, Michael; David, Hyerle; Byrne, Roxanne; Tran, John

2012-01-01

This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps[R], based on Albert Upton's semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of…

ACHIEVEMENT OF STUDENTS FROM GROUPS INSTRUCTED BY PROGRAMED MATERIALS, CLASSROOM TEACHER, OR BOTH. COMPARATIVE STUDIES OF PRINCIPLES FOR PROGRAMMING MATHEMATICS IN AUTOMATED INSTRUCTION, TECHNICAL REPORT NO. 12.

ERIC Educational Resources Information Center

BROWN, O. ROBERT, JR.

THE EXPERIMENTAL DESIGN IN THIS STUDY OF THE USE OF PROGRAMED MATERIALS TO TEACH HIGH SCHOOL MATHEMATICS DESIGNATED FOUR GROUPS--A CONTROL GROUP TAUGHT CONVENTIONALLY BY TEACHERS TRAINED TO USE PROGRAMED MATERIALS, A "PURE" GROUP USING PROGRAMED MATERIALS ONLY, AND "ANTICIPATING" AND "FOLLOWING" GROUPS THAT USED…

Wave-Particle Duality and Uncertainty Principle: Phenomenographic Categories of Description of Tertiary Physics Students' Depictions

ERIC Educational Resources Information Center

Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie

2011-01-01

Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students' depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an…

Synthesis of an optoelectronic system for tracking (OEST) the information track of the optical record carrier based on the acceleration control principle

NASA Astrophysics Data System (ADS)

Zalogin, Stanislav M.; Zalogin, M. S.

1997-02-01

The problem for construction of control algorithm in OEST the information track of the optical record carrier the realization of which is based on the use of accelerations is considered. Such control algorithms render the designed system the properties of adaptability, feeble sensitivity to the system parameter change and the action of disturbing forces what gives known advantages to information carriers with such system under operation in hard climate conditions as well as at maladjustment, workpieces wear and change of friction in the system. In the paper are investigated dynamic characteristics of a closed OEST, it is shown, that the designed stable system with given quality indices is a high-precision one. The validated recommendations as to design of control algorithms parameters are confirmed by results of mathematical simulation of controlled processes. The proposed methods for OEST synthesis on the basis of the control acceleration principle can be recommended for the use at industrial production of optical information record carriers.

[Application of numerical convolution in in vivo/in vitro correlation research].

PubMed

Yue, Peng

2009-01-01

This paper introduced the conception and principle of in vivo/in vitro correlation (IVIVC) and convolution/deconvolution methods, and elucidated in details the convolution strategy and method for calculating the in vivo absorption performance of the pharmaceutics according to the their pharmacokinetic data in Excel, then put the results forward to IVIVC research. Firstly, the pharmacokinetic data ware fitted by mathematical software to make up the lost points. Secondly, the parameters of the optimal fitted input function were defined by trail-and-error method according to the convolution principle in Excel under the hypothesis that all the input functions fit the Weibull functions. Finally, the IVIVC between in vivo input function and the in vitro dissolution was studied. In the examples, not only the application of this method was demonstrated in details but also its simplicity and effectiveness were proved by comparing with the compartment model method and deconvolution method. It showed to be a powerful tool for IVIVC research.

Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles

NASA Astrophysics Data System (ADS)

Tzirtzilakis, E. E.

2015-06-01

In this study, the fundamental problem of biomagnetic fluid flow in an aneurysmal geometry under the influence of a steady localized magnetic field is numerically investigated. The mathematical model used to formulate the problem is consistent with the principles of ferrohydrodynamics. Blood is considered to be an electrically non-conducting, homogeneous, non-isothermal Newtonian magnetic fluid. For the numerical solution of the problem, which is described by a coupled, non-linear system of Partial Differential Equations (PDEs), with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by applying an efficient pseudotransient numerical methodology using finite differences. This methodology is based on the application of a semi-implicit numerical technique, transformations, stretching of the grid, and construction of the boundary conditions for the vorticity. The results regarding the velocity and temperature field, skin friction, and rate of heat transfer indicate that the presence of a magnetic field considerably influences the flow field, particularly in the region of the aneurysm.

Maintaining homeostasis by decision-making.

PubMed

Korn, Christoph W; Bach, Dominik R

2015-05-01

Living organisms need to maintain energetic homeostasis. For many species, this implies taking actions with delayed consequences. For example, humans may have to decide between foraging for high-calorie but hard-to-get, and low-calorie but easy-to-get food, under threat of starvation. Homeostatic principles prescribe decisions that maximize the probability of sustaining appropriate energy levels across the entire foraging trajectory. Here, predictions from biological principles contrast with predictions from economic decision-making models based on maximizing the utility of the endpoint outcome of a choice. To empirically arbitrate between the predictions of biological and economic models for individual human decision-making, we devised a virtual foraging task in which players chose repeatedly between two foraging environments, lost energy by the passage of time, and gained energy probabilistically according to the statistics of the environment they chose. Reaching zero energy was framed as starvation. We used the mathematics of random walks to derive endpoint outcome distributions of the choices. This also furnished equivalent lotteries, presented in a purely economic, casino-like frame, in which starvation corresponded to winning nothing. Bayesian model comparison showed that--in both the foraging and the casino frames--participants' choices depended jointly on the probability of starvation and the expected endpoint value of the outcome, but could not be explained by economic models based on combinations of statistical moments or on rank-dependent utility. This implies that under precisely defined constraints biological principles are better suited to explain human decision-making than economic models based on endpoint utility maximization.

Maintaining Homeostasis by Decision-Making

PubMed Central

Korn, Christoph W.; Bach, Dominik R.

2015-01-01

Living organisms need to maintain energetic homeostasis. For many species, this implies taking actions with delayed consequences. For example, humans may have to decide between foraging for high-calorie but hard-to-get, and low-calorie but easy-to-get food, under threat of starvation. Homeostatic principles prescribe decisions that maximize the probability of sustaining appropriate energy levels across the entire foraging trajectory. Here, predictions from biological principles contrast with predictions from economic decision-making models based on maximizing the utility of the endpoint outcome of a choice. To empirically arbitrate between the predictions of biological and economic models for individual human decision-making, we devised a virtual foraging task in which players chose repeatedly between two foraging environments, lost energy by the passage of time, and gained energy probabilistically according to the statistics of the environment they chose. Reaching zero energy was framed as starvation. We used the mathematics of random walks to derive endpoint outcome distributions of the choices. This also furnished equivalent lotteries, presented in a purely economic, casino-like frame, in which starvation corresponded to winning nothing. Bayesian model comparison showed that—in both the foraging and the casino frames—participants’ choices depended jointly on the probability of starvation and the expected endpoint value of the outcome, but could not be explained by economic models based on combinations of statistical moments or on rank-dependent utility. This implies that under precisely defined constraints biological principles are better suited to explain human decision-making than economic models based on endpoint utility maximization. PMID:26024504

Didactic trajectory of research in mathematics education using research-based learning

NASA Astrophysics Data System (ADS)

Charitas Indra Prahmana, Rully; Kusumah, Yaya S.; Darhim

2017-10-01

This study aims to describe the role of research-based learning in design a learning trajectory of research in mathematics education to enhance research and academic writing skills for pre-service mathematics teachers. The method used is a design research with three stages, namely the preliminary design, teaching experiment, and retrospective analysis. The research subjects are pre-service mathematics teacher class of 2012 from one higher education institution in Tangerang - Indonesia. The use of research-based learning in designing learning trajectory of research in mathematics education plays a crucial role as a trigger to enhancing math department preservice teachers research and academic writing skills. Also, this study also describes the design principles and characteristics of the learning trajectory namely didactic trajectory generated by the role of research-based learning syntax.

Mathematical models for principles of gyroscope theory

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2017-01-01

Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.

Contributions from sociology of science to mathematics education in Brazil: logic as a system of beliefs

NASA Astrophysics Data System (ADS)

de Andrade, Thales Haddad Novaes; Vilela, Denise Silva

2013-09-01

In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor's theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the "naturalization of logic" was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.

Mathematical modelling in developmental biology.

PubMed

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

2013-06-01

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

A New Principle in Physiscs: the Principle "Finiteness", and Some Consequences

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

Abraham Sternlieb

2010-06-25

In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of "legitimate" laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory ormore » principle in physics. I propose "finiteness" as a postulate (like the constancy of the speed of light in vacuum, "c"), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.« less

Malaysian Secondary Physics Teachers' Perceptions towards the Teaching and Learning of Archimedes' Principle

NASA Astrophysics Data System (ADS)

Salleh, Khalijah Mohd; Abdullah, Abu Bakar Bin

2008-05-01

An explorative study was carried out to confirm Malaysian Physics teachers' perception that Archimedes' principle is a difficult topic for secondary level students. The interview method was used for data collection. The study sample was made of nine national secondary schools teachers from Miri, Sarawak. The data was analysed qualitatively using the Atlas-ti version 5.2 software. The findings of the study showed that i) Archimedes' principle as compared to Bernoulli's and Pascal's is the most difficult principle of hydrodynamics for students, ii) more time was given in the teaching and learning (TL) of Archimedes principle compared to the other two principles, iii) the major TL problems include conceptual understanding, application of physics principles and ideas, and lack of mathematical skills. These findings implicate the need to develop corresponding instructional materials and learning kits that can assist students' understanding of Archimedes' principle.

Irreversibility in physics stemming from unpredictable symbol-handling agents

NASA Astrophysics Data System (ADS)

Myers, John M.; Madjid, F. Hadi

2016-05-01

The basic equations of physics involve a time variable t and are invariant under the transformation t --> -t. This invariance at first sight appears to impose time reversibility as a principle of physics, in conflict with thermodynamics. But equations written on the blackboard are not the whole story in physics. In prior work we sharpened a distinction obscured in today's theoretical physics, the distinction between obtaining evidence from experiments on the laboratory bench and explaining that evidence in mathematical symbols on the blackboard. The sharp distinction rests on a proof within the mathematics of quantum theory that no amount of evidence, represented in quantum theory in terms of probabilities, can uniquely determine its explanation in terms of wave functions and linear operators. Building on the proof we show here a role in physics for unpredictable symbol-handling agents acting both at the blackboard and at the workbench, communicating back and forth by means of transmitted symbols. Because of their unpredictability, symbol-handling agents introduce a heretofore overlooked source of irreversibility into physics, even when the equations they write on the blackboard are invariant under t --> -t. Widening the scope of descriptions admissible to physics to include the agents and the symbols that link theory to experiments opens up a new source of time-irreversibility in physics.

Mathematics, anxiety, and the brain.

PubMed

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Organizing principles as tools for bridging the gap between system theory and biological experimentation.

PubMed

Mekios, Constantinos

2016-04-01

Twentieth-century theoretical efforts towards the articulation of general system properties came short of having the significant impact on biological practice that their proponents envisioned. Although the latter did arrive at preliminary mathematical formulations of such properties, they had little success in showing how these could be productively incorporated into the research agenda of biologists. Consequently, the gap that kept system-theoretic principles cut-off from biological experimentation persisted. More recently, however, simple theoretical tools have proved readily applicable within the context of systems biology. In particular, examples reviewed in this paper suggest that rigorous mathematical expressions of design principles, imported primarily from engineering, could produce experimentally confirmable predictions of the regulatory properties of small biological networks. But this is not enough for contemporary systems biologists who adopt the holistic aspirations of early systemologists, seeking high-level organizing principles that could provide insights into problems of biological complexity at the whole-system level. While the presented evidence is not conclusive about whether this strategy could lead to the realization of the lofty goal of a comprehensive explanatory integration, it suggests that the ongoing quest for organizing principles is pragmatically advantageous for systems biologists. The formalisms postulated in the course of this process can serve as bridges between system-theoretic concepts and the results of molecular experimentation: they constitute theoretical tools for generalizing molecular data, thus producing increasingly accurate explanations of system-wide phenomena.

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

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

Khots, Boris, E-mail: bkhots@cccglobal.com; Khots, Dmitriy, E-mail: dkhots@imathconsulting.com

2014-12-10

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We considermore » the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.« less

A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.

PubMed

Montévil, Maël

2018-01-01

Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

A perceptual account of symbolic reasoning

PubMed Central

Landy, David; Allen, Colin; Zednik, Carlos

2014-01-01

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

The basic science and mathematics of random mutation and natural selection.

PubMed

Kleinman, Alan

2014-12-20

The mutation and natural selection phenomenon can and often does cause the failure of antimicrobial, herbicidal, pesticide and cancer treatments selection pressures. This phenomenon operates in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures. The mathematical behavior of mutation and selection is derived using the principles given by probability theory. The derivation of the equations describing the mutation and selection phenomenon is carried out in the context of an empirical example. Copyright © 2014 John Wiley & Sons, Ltd.

Ethnomathematics: Exploration in Javanese culture

NASA Astrophysics Data System (ADS)

Risdiyanti, Irma; Charitas Indra Prahmana, Rully

2017-12-01

This research is the exploration study to indicate the correlation between mathematics and Javanese culture. These studies have a purpose of exploring Javanese culture in Yogyakarta that contains mathematics concept namely Batik. The activity of society in making Batik in all regency at Yogyakarta is the focus of this study. The research use ethnography method. The technic to collection data uses principles in ethnography such as observation, interview, documentation, and field note making with the original ethnography description. The result is exploration ethnomathematics in the several motifs of Yogyakarta batik that contains philosophy, deep cultural value, and mathematics concept, especially geometry transform subject.

Particles, Waves, and the Interpretation of Quantum Mechanics

ERIC Educational Resources Information Center

Christoudouleas, N. D.

1975-01-01

Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)

Microgravity

NASA Image and Video Library

1996-01-01

Dr. Michael Wargo, program scientist for materials science at NASA headquarters, explains the math and physics principles associated with freefall research to attendees at the arnual conference of the National Council of Teachers of Mathematics.

Suggested criteria for evaluating systems engineering methodologies

NASA Technical Reports Server (NTRS)

Gates, Audrey; Paul, Arthur S.; Gill, Tepper L.

1989-01-01

Systems engineering is the application of mathematical and scientific principles to practical ends in the life-cycle of a system. A methodology for systems engineering is a carefully developed, relatively complex procedure or process for applying these mathematical and scientific principles. There are many systems engineering methodologies (or possibly many versions of a few methodologies) currently in use in government and industry. These methodologies are usually designed to meet the needs of a particular organization. It has been observed, however, that many technical and non-technical problems arise when inadequate systems engineering methodologies are applied by organizations to their systems development projects. Various criteria for evaluating systems engineering methodologies are discussed. Such criteria are developed to assist methodology-users in identifying and selecting methodologies that best fit the needs of the organization.

Mathematic simulation of soil-vegetation condition and land use structure applying basin approach

NASA Astrophysics Data System (ADS)

Mishchenko, Natalia; Shirkin, Leonid; Krasnoshchekov, Alexey

2016-04-01

Ecosystems anthropogenic transformation is basically connected to the changes of land use structure and human impact on soil fertility. The Research objective is to simulate the stationary state of river basins ecosystems. Materials and Methods. Basin approach has been applied in the research. Small rivers basins of the Klyazma river have been chosen as our research objects. They are situated in the central part of the Russian plain. The analysis is carried out applying integrated characteristics of ecosystems functioning and mathematic simulation methods. To design mathematic simulator functional simulation methods and principles on the basis of regression, correlation and factor analysis have been applied in the research. Results. Mathematic simulation resulted in defining possible permanent conditions of "phytocenosis-soil" system in coordinates of phytomass, phytoproductivity, humus percentage in soil. Ecosystem productivity is determined not only by vegetation photosynthesis activity but also by the area ratio of forest and meadow phytocenosis. Local maximums attached to certain phytomass areas and humus content in soil have been defined on the basin phytoproductivity distribution diagram. We explain the local maximum by synergetic effect. It appears with the definite ratio of forest and meadow phytocenosis. In this case, utmost values of phytomass for the whole area are higher than just a sum of utmost values of phytomass for the forest and meadow phytocenosis. Efficient correlation of natural forest and meadow phytocenosis has been defined for the Klyazma river. Conclusion. Mathematic simulation methods assist in forecasting the ecosystem conditions under various changes of land use structure. Nowadays overgrowing of the abandoned agricultural lands is very actual for the Russian Federation. Simulation results demonstrate that natural ratio of forest and meadow phytocenosis for the area will restore during agricultural overgrowing.

Dynamics of Bacterial Gene Regulatory Networks.

PubMed

Shis, David L; Bennett, Matthew R; Igoshin, Oleg A

2018-05-20

The ability of bacterial cells to adjust their gene expression program in response to environmental perturbation is often critical for their survival. Recent experimental advances allowing us to quantitatively record gene expression dynamics in single cells and in populations coupled with mathematical modeling enable mechanistic understanding on how these responses are shaped by the underlying regulatory networks. Here, we review how the combination of local and global factors affect dynamical responses of gene regulatory networks. Our goal is to discuss the general principles that allow extrapolation from a few model bacteria to less understood microbes. We emphasize that, in addition to well-studied effects of network architecture, network dynamics are shaped by global pleiotropic effects and cell physiology.

General Principles for Brain Design

NASA Astrophysics Data System (ADS)

Josephson, Brian D.

2006-06-01

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

Effects of SKF-83566 and haloperidol on performance on progressive ratio schedules maintained by sucrose and corn oil reinforcement: quantitative analysis using a new model derived from the Mathematical Principles of Reinforcement (MPR).

PubMed

Olarte-Sánchez, C M; Valencia-Torres, L; Cassaday, H J; Bradshaw, C M; Szabadi, E

2013-12-01

Mathematical models can assist the interpretation of the effects of interventions on schedule-controlled behaviour and help to differentiate between processes that may be confounded in traditional performance measures such as response rate and the breakpoint in progressive ratio (PR) schedules. The effects of a D1-like dopamine receptor antagonist, 8-bromo-2,3,4,5-tetrahydro-3-methyl-5-phenyl-1H-3-benzazepin-7-ol hydrobromide (SKF-83566), and a D2-like receptor antagonist, haloperidol, on rats' performance on PR schedules maintained by sucrose and corn oil reinforcers were assessed using a new model derived from Killeen's (Behav Brain Sci 17:105-172, 1994) Mathematical Principles of Reinforcement. Separate groups of rats were trained under a PR schedule using sucrose or corn oil reinforcers. SKF-83566 (0.015 and 0.03 mg kg(-1)) and haloperidol (0.05 and 0.1 mg kg(-1)) were administered intraperitoneally (five administrations of each treatment). Running and overall response rates in successive ratios were analysed using the new model, and estimates of the model's parameters were compared between treatments. Haloperidol reduced a (the parameter expressing incentive value) in the case of both reinforcers, but did not affect the parameters related to response time and post-reinforcement pausing. SKF-83566 reduced a and k (the parameter expressing sensitivity of post-reinforcement pausing to the prior inter-reinforcement interval) in the case of sucrose, but did not affect any of the parameters in the case of corn oil. The results are consistent with the hypothesis that blockade of both D1-like and D2-like receptors reduces the incentive value of sucrose, whereas the incentive value of corn oil is more sensitive to blockade of D2-like than D1-like receptors.

Opting in and Creating Demand: Why Young People Choose to Teach Mathematics to Each Other

NASA Astrophysics Data System (ADS)

Tucker-Raymond, Eli; Lewis, Naama; Moses, Maisha; Milner, Chad

2016-12-01

Access to science, technology, engineering, and mathematics fields serves as a key entry point to economic mobility and civic enfranchisement. Such access must take seriously the intellectual power of the knowledge and practices of non-dominant youth. In our case, this has meant to shift epistemic authority in mathematics from academic institutions to young people themselves. This article is about why high school-aged students, from underrepresented groups, choose to participate in an out-of-school time program in which they teach younger children in the domains of mathematics and computer science. It argues for programmatic principles based on access, identity engagement, relationship building, and connections to community to support underrepresented youth as learners, teachers, leaders, and organizers in mathematics-related activities using game design as the focus of activity.

The Work of Dr. Ladislav Kosc on Dyscalculia.

ERIC Educational Resources Information Center

Sharma, Mahesh C., Ed.; Loveless, Eugene J., Ed.

1986-01-01

The work of Ladislav Kosc on dyscalculia is presented. His work on meanings, forms, terminology, diagnosis, correction principles, factors in mathematical ability, language dysfunctions, and publications are each included. (MNS)

22 CFR 120.10 - Technical data.

Code of Federal Regulations, 2010 CFR

2010-04-01

... scientific, mathematical or engineering principles commonly taught in schools, colleges and universities or information in the public domain as defined in § 120.11. It also does not include basic marketing information...

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

PubMed

Bates, Jason H T; Sobel, Burton E

2003-04-01

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

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

PubMed

Bates, Jason H T; Sobel, Burton E

2003-05-01

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

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

PubMed

Bates, Jason H T; Sobel, Burton E

2003-06-01

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

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

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

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

AN ATTEMPT TO FIND AN A PRIORI MEASURE OF STEP SIZE. COMPARATIVE STUDIES OF PRINCIPLES FOR PROGRAMMING MATHEMATICS IN AUTOMATED INSTRUCTION, TECHNICAL REPORT NO. 13.

ERIC Educational Resources Information Center

ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.

IN ORDER TO FIND A GOOD PREDICTOR OF EMPIRICAL DIFFICULTY, AN OPERATIONAL DEFINITION OF STEP SIZE, TEN PROGRAMER-JUDGES RATED CHANGE IN COMPLEXITY IN TWO VERSIONS OF A MATHEMATICS PROGRAM, AND THESE RATINGS WERE THEN COMPARED WITH MEASURES OF EMPIRICAL DIFFICULTY OBTAINED FROM STUDENT RESPONSE DATA. THE TWO VERSIONS, A 54 FRAME BOOKLET AND A 35…

Introduction to the Theory of Atmospheric Radiative Transfer

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1986-01-01

The fundamental physical and mathematical principles governing the transmission of radiation through the atmosphere are presented, with emphasis on the scattering of visible and near-IR radiation. The classical two-stream, thin-atmosphere, and Eddington approximations, along with some of their offspring, are developed in detail, along with the discrete ordinates method of Chandrasekhar. The adding and doubling methods are discussed from basic principles, and references for further reading are suggested.

Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

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

Barletti, Luigi, E-mail: luigi.barletti@unifi.it

2014-08-15

The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.

The Theories of Turbulence

NASA Technical Reports Server (NTRS)

Bass, J; Agostini, L

1955-01-01

The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form. During the war, some isolated scientists - von Weizsacker and Heisenberg in Germany, Kolmogoroff in Russia, Onsager in the U.S.A. - started a program of research. By a system of assumptions which make it possible to approach the structure of turbulence in well-defined limiting conditions quantitatively, they obtained a certain number of laws on the correlations and the spectrum. Since the late reports have improved the mathematical language of turbulence, it was deemed advisable to start with a detailed account of the mathematical methods applicable to turbulence, inspired at first by the work of the French school, above all for the basic principles, then the work of the foreigners, above all for the theory of the spectrum.

Freefall Research Education Outreach

NASA Technical Reports Server (NTRS)

1996-01-01

Dr. Michael Wargo, program scientist for materials science at NASA headquarters, explains the math and physics principles associated with freefall research to attendees at the arnual conference of the National Council of Teachers of Mathematics.

A combined approach of self-referencing and Principle Component Thermography for transient, steady, and selective heating scenarios

NASA Astrophysics Data System (ADS)

Omar, M. A.; Parvataneni, R.; Zhou, Y.

2010-09-01

Proposed manuscript describes the implementation of a two step processing procedure, composed of the self-referencing and the Principle Component Thermography (PCT). The combined approach enables the processing of thermograms from transient (flash), steady (halogen) and selective (induction) thermal perturbations. Firstly, the research discusses the three basic processing schemes typically applied for thermography; namely mathematical transformation based processing, curve-fitting processing, and direct contrast based calculations. Proposed algorithm utilizes the self-referencing scheme to create a sub-sequence that contains the maximum contrast information and also compute the anomalies' depth values. While, the Principle Component Thermography operates on the sub-sequence frames by re-arranging its data content (pixel values) spatially and temporally then it highlights the data variance. The PCT is mainly used as a mathematical mean to enhance the defects' contrast thus enabling its shape and size retrieval. The results show that the proposed combined scheme is effective in processing multiple size defects in sandwich steel structure in real-time (<30 Hz) and with full spatial coverage, without the need for a priori defect-free area.

Gravitational attraction until relativistic equipartition of internal and translational kinetic energies

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. E.

2018-02-01

Translational ordering of the internal kinematic chaos provides the Special Relativity referents for the geodesic motion of warm thermodynamical bodies. Taking identical mathematics, relativistic physics of the low speed transport of time-varying heat-energies differs from Newton's physics of steady masses without internal degrees of freedom. General Relativity predicts geodesic changes of the internal heat-energy variable under the free gravitational fall and the geodesic turn in the radial field center. Internal heat variations enable cyclic dynamics of decelerated falls and accelerated takeoffs of inertial matter and its structural self-organization. The coordinate speed of the ordered spatial motion takes maximum under the equipartition of relativistic internal and translational kinetic energies. Observable predictions are discussed for verification/falsification of the principle of equipartition as a new basic for the ordered motion and self-organization in external fields, including gravitational, electromagnetic, and thermal ones.

Hands-On Fractals and the Unexpected in Mathematics

ERIC Educational Resources Information Center

Gluchoff, Alan

2006-01-01

This article describes a hands-on project in which unusual fractal images are produced using only a photocopy machine and office supplies. The resulting images are an example of the contraction mapping principle.

3 CFR 9052 - Proclamation 9052 of October 31, 2013. National Entrepreneurship Month, 2013

Code of Federal Regulations, 2014 CFR

2014-01-01

... inventions that changed American life and startups that lifted our economy as they grew, entrepreneurs helped... science, technology, engineering, and mathematics. These principles are consistent with ensuring our...

Annette Bunge: developing the principles in percutaneous absorption using chemical engineering principles.

PubMed

Stinchcomb, A L

2013-01-01

Annette Bunge and her research group have had the central theme of mathematically modeling the dermal absorption process. Most of the research focus has been on estimating dermal absorption for the purpose of risk assessment, for exposure scenarios in the environment and in the occupational setting. Her work is the basis for the United States Environmental Protection Agency's estimations for dermal absorption from contaminated water. It is also the basis of the dermal absorption estimates used in determining if chemicals should be assigned a 'skin notation' for potential systemic toxicity following occupational skin exposure. The work is truly translational in that it started with mathematical theory, is validated with preclinical and human experiments, and then is used in guidelines to protect human health. Her valued research has also extended into the topical drug bioavailability and bioequivalence assessment field.

Principles and Practices Fostering Inclusive Excellence: Lessons from the Howard Hughes Medical Institute's Capstone Institutions.

PubMed

DiBartolo, Patricia Marten; Gregg-Jolly, Leslie; Gross, Deborah; Manduca, Cathryn A; Iverson, Ellen; Cooke, David B; Davis, Gregory K; Davidson, Cameron; Hertz, Paul E; Hibbard, Lisa; Ireland, Shubha K; Mader, Catherine; Pai, Aditi; Raps, Shirley; Siwicki, Kathleen; Swartz, Jim E

Best-practices pedagogy in science, technology, engineering, and mathematics (STEM) aims for inclusive excellence that fosters student persistence. This paper describes principles of inclusivity across 11 primarily undergraduate institutions designated as Capstone Awardees in Howard Hughes Medical Institute's (HHMI) 2012 competition. The Capstones represent a range of institutional missions, student profiles, and geographical locations. Each successfully directed activities toward persistence of STEM students, especially those from traditionally underrepresented groups, through a set of common elements: mentoring programs to build community; research experiences to strengthen scientific skill/identity; attention to quantitative skills; and outreach/bridge programs to broaden the student pool. This paper grounds these program elements in learning theory, emphasizing their essential principles with examples of how they were implemented within institutional contexts. We also describe common assessment approaches that in many cases informed programming and created traction for stakeholder buy-in. The lessons learned from our shared experiences in pursuit of inclusive excellence, including the resources housed on our companion website, can inform others' efforts to increase access to and persistence in STEM in higher education. © 2016 P. M. DiBartolo, L. Gregg-Jolly, D. Gross, C. A. Manduca, E. Iverson, et al. CBE—Life Sciences Education © 2016 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Using collective argumentation to engage students in a primary mathematics classroom

NASA Astrophysics Data System (ADS)

Brown, Raymond

2017-02-01

This article focuses on using sociocultural theory to support student engagement with mathematics. The sociocultural approach used, collective argumentation (CA), is based on interactive principles necessary for coordinating student engagement in the discourse of the classroom. A goal of the research was to explore the affordances and constraints of using CA to enrich student engagement with mathematics. The design of the research was based on a teaching experiment that sought to capture the influence of social and cultural processes on learning and development. Participants included primary and secondary school teachers and their mathematics classes. This article focuses on the practice of one female primary school teacher. Data sources included interview transcripts, report writings, journal entries and observational records. Data were analysed using a participation framework. Findings suggest that aspects of CA such as students explaining and justifying ideas and presenting ideas to the whole class can be used by teachers to promote student engagement with mathematics.

Primary school student teachers’ perception to Pendidikan Matematika Realistik Indonesia (PMRI) instruction

NASA Astrophysics Data System (ADS)

Fauziah, A.; Putri, R. I. I.; Zulkardi; Somakim

2017-12-01

This article aimed to report the perceptions of the students of primary school education to PMRI. PMRI or Realistic Mathematics Education (RME) in Indonesian version is one of the promising mathematics learning innovations developed in Indonesia. The research method consisted of three steps, namely preliminary, teaching experiment, and retrospective Analysis. The participants were six students of the primary school teacher education. In the second phase, the participants took an PMRI lesson. Then, they filled in the perception questionnaire (open and closed). The results of the study showed that the participants agreed that learning by realistic mathematics education principles helped them understand the topic.

The enhancement of students' mathematical self-efficacy through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, S.

2018-05-01

This research aims to investigate the enhancement of students’ mathematical self- efficacy through teaching with metacognitive scaffolding approach. This research used a quasi- experimental design with pre-post respon control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 students who acquire teaching mathematics under metacognitive approach, while the control group consists of 58 students who acquire teaching mathematics under direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical self-efficacy instruments. By using mean difference test, two conclusions of the research: (1) there is a significant difference in the enhancement of mathematical self-efficacy between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and (2) there is no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students’ mathematical self-efficacy.

Theory of Connectivity: Nature and Nurture of Cell Assemblies and Cognitive Computation.

PubMed

Li, Meng; Liu, Jun; Tsien, Joe Z

2016-01-01

Richard Semon and Donald Hebb are among the firsts to put forth the notion of cell assembly-a group of coherently or sequentially-activated neurons-to represent percept, memory, or concept. Despite the rekindled interest in this century-old idea, the concept of cell assembly still remains ill-defined and its operational principle is poorly understood. What is the size of a cell assembly? How should a cell assembly be organized? What is the computational logic underlying Hebbian cell assemblies? How might Nature vs. Nurture interact at the level of a cell assembly? In contrast to the widely assumed randomness within the mature but naïve cell assembly, the Theory of Connectivity postulates that the brain consists of the developmentally pre-programmed cell assemblies known as the functional connectivity motif (FCM). Principal cells within such FCM is organized by the power-of-two-based mathematical principle that guides the construction of specific-to-general combinatorial connectivity patterns in neuronal circuits, giving rise to a full range of specific features, various relational patterns, and generalized knowledge. This pre-configured canonical computation is predicted to be evolutionarily conserved across many circuits, ranging from these encoding memory engrams and imagination to decision-making and motor control. Although the power-of-two-based wiring and computational logic places a mathematical boundary on an individual's cognitive capacity, the fullest intellectual potential can be brought about by optimized nature and nurture. This theory may also open up a new avenue to examining how genetic mutations and various drugs might impair or improve the computational logic of brain circuits.

Theory of Connectivity: Nature and Nurture of Cell Assemblies and Cognitive Computation

PubMed Central

Li, Meng; Liu, Jun; Tsien, Joe Z.

2016-01-01

Richard Semon and Donald Hebb are among the firsts to put forth the notion of cell assembly—a group of coherently or sequentially-activated neurons—to represent percept, memory, or concept. Despite the rekindled interest in this century-old idea, the concept of cell assembly still remains ill-defined and its operational principle is poorly understood. What is the size of a cell assembly? How should a cell assembly be organized? What is the computational logic underlying Hebbian cell assemblies? How might Nature vs. Nurture interact at the level of a cell assembly? In contrast to the widely assumed randomness within the mature but naïve cell assembly, the Theory of Connectivity postulates that the brain consists of the developmentally pre-programmed cell assemblies known as the functional connectivity motif (FCM). Principal cells within such FCM is organized by the power-of-two-based mathematical principle that guides the construction of specific-to-general combinatorial connectivity patterns in neuronal circuits, giving rise to a full range of specific features, various relational patterns, and generalized knowledge. This pre-configured canonical computation is predicted to be evolutionarily conserved across many circuits, ranging from these encoding memory engrams and imagination to decision-making and motor control. Although the power-of-two-based wiring and computational logic places a mathematical boundary on an individual’s cognitive capacity, the fullest intellectual potential can be brought about by optimized nature and nurture. This theory may also open up a new avenue to examining how genetic mutations and various drugs might impair or improve the computational logic of brain circuits. PMID:27199674

Cosmological Models and Stability

NASA Astrophysics Data System (ADS)

Andersson, Lars

Principles in the form of heuristic guidelines or generally accepted dogma play an important role in the development of physical theories. In particular, philosophical considerations and principles figure prominently in the work of Albert Einstein. As mentioned in the talk by Jiří Bičák at this conference, Einstein formulated the equivalence principle, an essential step on the road to general relativity, during his time in Prague 1911-1912. In this talk, I would like to discuss some aspects of cosmological models. As cosmology is an area of physics where "principles" such as the "cosmological principle" or the "Copernican principle" play a prominent role in motivating the class of models which form part of the current standard model, I will start by comparing the role of the equivalence principle to that of the principles used in cosmology. I will then briefly describe the standard model of cosmology to give a perspective on some mathematical problems and conjectures on cosmological models, which are discussed in the later part of this paper.

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

PubMed Central

ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN

2013-01-01

In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation. PMID:23645963

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.

Formulae as Scientific Stories

ERIC Educational Resources Information Center

Horsewell, Ian

2017-01-01

In science lessons many students struggle to apply the principles of rearranging formulae, even after coverage in maths. A structured approach is suggested that focuses on describing a narrative linking cause and effect before explicit mathematical terms are introduced.

Statistical mechanical theory for steady state systems. VI. Variational principles

NASA Astrophysics Data System (ADS)

Attard, Phil

2006-12-01

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

Pre-Service Teachers' Free and Structured Mathematical Problem Posing

ERIC Educational Resources Information Center

Silber, Steven; Cai, Jinfa

2017-01-01

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

Quantum theory and Aquinas's doctrine on matter

NASA Astrophysics Data System (ADS)

Grove, Stanley F.

The Aristotelian conception of the material principle, deepened by Aquinas, is today widely misunderstood and largely alien to modern mathematical physics, despite the latter's preoccupation with matter and the spatiotemporal. The present dissertation seeks to develop a coherent understanding of matter in the Aristotelian-Thomistic sense, and to apply it to some key interpretive issues in quantum physics. I begin with a brief historical analysis of the Aristotelian, Newtonian ("classical"), and modern (quantum) approaches to physics, in order to highlight their commonality as well as their differences. Next, matter---especially prime matter---is investigated, in an Aristotelian-Thomistic perspective, under several rationes: as principle of individuation, as principle of extension or spatiality, as principle of corruptibility, as related to essence and existence, and as ground of intelligibility. An attempt is made to order these different rationes according to primordiality. A number of topics concerning the formal structure of hylomorphic being are then addressed: elementarity, virtual presence, the "dispositions of matter," entia vialia, natural minima, atomism, the nature of local motion, the plenum and instantaneous action at a distance---all with a view to their incorporation in a unified account of formed matter at or near the elementary level. Finally I take up several interpretive problems in quantum physics which were introduced early in the dissertation, and show how the material and formal principles expounded in the central chapters can render these problems intelligible. Thus I propose that wave and particle aspects in the quantum realm are related substantially rather than accidentally, and that characteristics of substantial (prime) matter and substantial form are therefore being evidenced directly at this level---in the reversibility of the wave-particle transition, in the spatial and temporal instantaneity of quantum events, and in the probabilism encountered in such phenomena. I offer related hypotheses for Heisenberg uncertainty and for quantum nonlocality. In closing, I address some strengths and weaknesses in others' work on quantum interpretation in the light of Aristotelian principles. Three Appendices explore further aspects of matter as a cosmic principle.

Design principles for elementary gene circuits: Elements, methods, and examples

NASA Astrophysics Data System (ADS)

Savageau, Michael A.

2001-03-01

The control of gene expression involves complex circuits that exhibit enormous variation in design. For years the most convenient explanation for these variations was historical accident. According to this view, evolution is a haphazard process in which many different designs are generated by chance; there are many ways to accomplish the same thing, and so no further meaning can be attached to such different but equivalent designs. In recent years a more satisfying explanation based on design principles has been found for at least certain aspects of gene circuitry. By design principle we mean a rule that characterizes some biological feature exhibited by a class of systems such that discovery of the rule allows one not only to understand known instances but also to predict new instances within the class. The central importance of gene regulation in modern molecular biology provides strong motivation to search for more of these underlying design principles. The search is in its infancy and there are undoubtedly many design principles that remain to be discovered. The focus of this three-part review will be the class of elementary gene circuits in bacteria. The first part reviews several elements of design that enter into the characterization of elementary gene circuits in prokaryotic organisms. Each of these elements exhibits a variety of realizations whose meaning is generally unclear. The second part reviews mathematical methods used to represent, analyze, and compare alternative designs. Emphasis is placed on particular methods that have been used successfully to identify design principles for elementary gene circuits. The third part reviews four design principles that make specific predictions regarding (1) two alternative modes of gene control, (2) three patterns of coupling gene expression in elementary circuits, (3) two types of switches in inducible gene circuits, and (4) the realizability of alternative gene circuits and their response to phased environmental cues. In each case, the predictions are supported by experimental evidence. These results are important for understanding the function, design, and evolution of elementary gene circuits.

Anticipatory precrash restraint sensor feasibility study: Final report

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

Kercel, S.W.; Dress, W.B.

1995-08-01

This report explores feasibility of an anticipatory precrash restraint sensor. The foundation principle is the anticipation mechanism found at a primitive level of biological intelligence and originally formalized by the mathematical biologist Robert Rosen. A system based on formal anticipatory principles should significantly outperform conventional technologies. It offers the prospect of high payoff in prevention of death and injury. Sensors and processes are available to provide a good, fast, and inexpensive description of the present dynamical state of the vehicle to the embedded system model in the anticipation engine. The experimental part of this study found that inexpensive radar inmore » a real-world setting does return useful data on target dynamics. The data produced by a radar system can be converted to target dynamical information by good, fast and inexpensive signal-processing techniques. Not only is the anticipatory sensor feasible, but further development under the sponsorship of the National Highway Traffic Safety Administration is necessary and desirable. There are a number of possible lines of follow-on investigation. The level of effort and expected benefits of various alternatives are discussed.« less

Bacterial responses to antibiotics and their combinations.

PubMed

Mitosch, Karin; Bollenbach, Tobias

2014-12-01

Antibiotics affect bacterial cell physiology at many levels. Rather than just compensating for the direct cellular defects caused by the drug, bacteria respond to antibiotics by changing their morphology, macromolecular composition, metabolism, gene expression and possibly even their mutation rate. Inevitably, these processes affect each other, resulting in a complex response with changes in the expression of numerous genes. Genome-wide approaches can thus help in gaining a comprehensive understanding of bacterial responses to antibiotics. In addition, a combination of experimental and theoretical approaches is needed for identifying general principles that underlie these responses. Here, we review recent progress in our understanding of bacterial responses to antibiotics and their combinations, focusing on effects at the levels of growth rate and gene expression. We concentrate on studies performed in controlled laboratory conditions, which combine promising experimental techniques with quantitative data analysis and mathematical modeling. While these basic research approaches are not immediately applicable in the clinic, uncovering the principles and mechanisms underlying bacterial responses to antibiotics may, in the long term, contribute to the development of new treatment strategies to cope with and prevent the rise of resistant pathogenic bacteria.

Ethnomathematics study: uncovering units of length, area, and volume in Kampung Naga Society

NASA Astrophysics Data System (ADS)

Septianawati, T.; Turmudi; Puspita, E.

2017-02-01

During this time, mathematics is considered as something neutral and not associated with culture. It can be seen from mathematics learning in the school which adopt many of foreign mathematics learning are considered more advanced (western). In fact, Indonesia is a rich country in cultural diversity. In the cultural activities, there are mathematical ideas that were considered a important thing in the mathematics learning. A study that examines the idea or mathematical practices in a variety of cultural activities are known as ethnomathematics. In Indonesia, there are some ethnic maintain their ancestral traditions, one of them is Kampung Naga. Therefore, this study was conducted in Kampung Naga. This study aims to uncover units of length, area, and volume used by Kampung Naga society. This study used a qualitative approach and ethnography methods. In this research, data collection is done through the principles of ethnography such as observation, interviews, documentation, and field notes. The results of this study are units of length, area, and volume used by Kampung Naga society and its conversion into standard units. This research is expected to give information to the public that mathematics has a relationship with culture and become recommendation to mathematics curriculum in Indonesia.

Magnetic storms and solar flares: can be analysed within similar mathematical framework with other extreme events?

NASA Astrophysics Data System (ADS)

Balasis, Georgios; Potirakis, Stelios M.; Papadimitriou, Constantinos; Zitis, Pavlos I.; Eftaxias, Konstantinos

2015-04-01

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up to different extreme events, in order to support the suggestion that a dynamical analogy characterizes the generation of a single magnetic storm, solar flare, earthquake (in terms of pre-seismic electromagnetic signals) , epileptic seizure, and economic crisis. The analysis reveals that all the above mentioned different extreme events can be analyzed within similar mathematical framework. More precisely, we show that the populations of magnitudes of fluctuations included in all the above mentioned pulse-like-type time series follow the traditional Gutenberg-Richter law as well as a nonextensive model for earthquake dynamics, with similar nonextensive q-parameter values. Moreover, based on a multidisciplinary statistical analysis we show that the extreme events are characterized by crucial common symptoms, namely: (i) high organization, high compressibility, low complexity, high information content; (ii) strong persistency; and (iii) existence of clear preferred direction of emerged activities. These symptoms clearly discriminate the appearance of the extreme events under study from the corresponding background noise.

Organizing principles underlying microorganism's growth-robustness trade-off.

PubMed

Bolli, Alessandro; Salvador, Armindo

2014-10-01

Growth Robustness Reciprocity (GRR) is an intriguing microbial manifestation: the impairment of microorganism's growth enhances their ability to resist acute stresses, and vice-versa. This is caused by regulatory interactions that determine higher expression of protection mechanisms in response to low growth rates. But because such regulatory mechanisms are species-specific, GRR must result from convergent evolution. Why does natural selection favor such an outcome? We used mathematical models of optimal cellular resource allocation to identify the general principles underlying GRR. Non-linear optimization allowed to predict allocation patterns of biosynthetic resources (ribosomes devoted to the synthesis of each cell component) that maximize growth. These models predict the down-regulation of stress defenses under high substrate availabilities and low stress levels. Under these conditions, stress tolerance ensues from growth-related damage dilution: the higher the substrate availability, the fastest the dilution of damaged proteins by newly synthesized proteins, the lower the accumulation of damaged components into the cell. In turn, under low substrate availability growth is too slow for effective damage dilution, and the expression of the defenses up to some optimal level then increases growth. As a consequence, slow-growing cells are pre-adapted to withstand acute stresses. Therefore, the observed negative correlation between growth and stress tolerance can be explained as a consequence of optimal resource allocation for maximal growth. We acknowledge fellowship SFRH/BPD/90065/2012 and grants PEst-C/SAU/LA0001/2013-2014 and FCOMP-01-0124-FEDER-020978 financed by FEDER through the "Programa Operacional Factores de Competitividade, COMPETE" and by national funds through "FCT, Fundação para a Ciência e a Tecnologia" (project PTDC/QUI-BIQ/119657/2010). Copyright © 2014. Published by Elsevier Inc.

Mathematics education for social justice

NASA Astrophysics Data System (ADS)

Suhendra

2016-02-01

Mathematics often perceived as a difficult subject with many students failing to understand why they learn mathematics. This situation has been further aggravated by the teaching and learning processes used, which is mechanistic without considering students' needs. The learning of mathematics tends to be just a compulsory subject, in which all students have to attend its classes. Social justice framework facilitates individuals or groups as a whole and provides equitable approaches to achieving equitable outcomes by recognising disadvantage. Applying social justice principles in educational context is related to how the teachers treat their students, dictates that all students the right to equal treatment regardless of their background and completed with applying social justice issues integrated with the content of the subject in order to internalise the principles of social justice simultaneously the concepts of the subject. The study examined the usefulness of implementing the social justice framework as a means of improving the quality of mathematics teaching in Indonesia involved four teacher-participants and their mathematics classes. The study used action research as the research methodology in which the teachers implemented and evaluated their use of social justice framework in their teaching. The data were collected using multiple research methods while analysis and interpretation of the data were carried out throughout the study. The findings of the study indicated that there were a number of challengesrelated to the implementation of the social justice framework. The findings also indicated that, the teachers were provided with a comprehensive guide that they could draw on to make decisions about how they could improve their lessons. The interactions among students and between the teachers and the students improved, they became more involved in teaching and learning process. Using social justice framework helped the teachers to make mathematics more relevant to students. This increased relevance led to increasing students' engagement in the teaching and learning process and becoming more accessible to all students. Additionally, the findings have the potential to make a contribution to those seeking to reform mathematics teaching in Indonesia. The results could inform policy makers and professional development providers about how social justice framework might contribute to the educational reform in Indonesia.

Design of a universal two-layered neural network derived from the PLI theory

NASA Astrophysics Data System (ADS)

Hu, Chia-Lun J.

2004-05-01

The if-and-only-if (IFF) condition that a set of M analog-to-digital vector-mapping relations can be learned by a one-layered-feed-forward neural network (OLNN) is that all the input analog vectors dichotomized by the i-th output bit must be positively, linearly independent, or PLI. If they are not PLI, then the OLNN just cannot learn no matter what learning rules is employed because the solution of the connection matrix does not exist mathematically. However, in this case, one can still design a parallel-cascaded, two-layered, perceptron (PCTLP) to acheive this general mapping goal. The design principle of this "universal" neural network is derived from the major mathematical properties of the PLI theory - changing the output bits of the dependent relations existing among the dichotomized input vectors to make the PLD relations PLI. Then with a vector concatenation technique, the required mapping can still be learned by this PCTLP system with very high efficiency. This paper will report in detail the mathematical derivation of the general design principle and the design procedures of the PCTLP neural network system. It then will be verified in general by a practical numerical example.

A Mathematical Model of the Thermo-Anemometric Flowmeter

PubMed Central

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-01-01

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed. PMID:26378535

A Mathematical Model of the Thermo-Anemometric Flowmeter.

PubMed

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-09-11

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

Power and Efficiency.

ERIC Educational Resources Information Center

Boyd, James N.

1991-01-01

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)

Playful Physics

NASA Technical Reports Server (NTRS)

Weaver, David

2008-01-01

Effectively communicate qualitative and quantitative information orally and in writing. Explain the application of fundamental physical principles to various physical phenomena. Apply appropriate problem-solving techniques to practical and meaningful problems using graphical, mathematical, and written modeling tools. Work effectively in collaborative groups.

Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro

This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.

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

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

On Two-Scale Modelling of Heat and Mass Transfer

NASA Astrophysics Data System (ADS)

Vala, J.; Št'astník, S.

2008-09-01

Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.

Self-reports of mathematics self-concept and educational outcomes: the roles of ego-dimensions and self-consciousness.

PubMed

Martin, A J; Debus, R L

1998-12-01

There is a need for research to (a) explore more fully the academic outcomes that follow from under-/over-rating of self-concept and (b) identify factors that predict the nature of self-reports of self-concept as well as under- and over-rating of this self-concept. The study examines the link between students' self-appraisals of both mathematics self-concept and under-/over-rating of this self-concept and educational outcomes in mathematics such as achievement and motivation (future plans for mathematics). Ego-dimensions (ego-orientation and competence-valuation) and public self-consciousness were examined as two factors that might contribute to predicting these self-appraisals. Findings are drawn from a sample of 382 male and female high school students ranging in age from 14 to 16 years. Students responded to a questionnaire (at Time 1) that assessed self-concept, motivation orientation, competence-valuation, self-consciousness, and mathematics motivation. Teachers rated each student using a brief mathematics self-concept scale. Higher mathematics self-concept and over-rating of this self-concept were predictive of higher levels of mathematics motivation and later mathematics achievement (Time 2). Findings also indicate that ego-orientation and competence-valuation are positively associated with mathematics self-concept and over-rating, whilst public self-consciousness negatively predicts mathematics self-concept and is also associated with a tendency to under-rate oneself in this domain.

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

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

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Thermodynamics and evolution.

PubMed

Demetrius, L

2000-09-07

The science of thermodynamics is concerned with understanding the properties of inanimate matter in so far as they are determined by changes in temperature. The Second Law asserts that in irreversible processes there is a uni-directional increase in thermodynamic entropy, a measure of the degree of uncertainty in the thermal energy state of a randomly chosen particle in the aggregate. The science of evolution is concerned with understanding the properties of populations of living matter in so far as they are regulated by changes in generation time. Directionality theory, a mathematical model of the evolutionary process, establishes that in populations subject to bounded growth constraints, there is a uni-directional increase in evolutionary entropy, a measure of the degree of uncertainty in the age of the immediate ancestor of a randomly chosen newborn. This article reviews the mathematical basis of directionality theory and analyses the relation between directionality theory and statistical thermodynamics. We exploit an analytic relation between temperature, and generation time, to show that the directionality principle for evolutionary entropy is a non-equilibrium extension of the principle of a uni-directional increase of thermodynamic entropy. The analytic relation between these directionality principles is consistent with the hypothesis of the equivalence of fundamental laws as one moves up the hierarchy, from a molecular ensemble where the thermodynamic laws apply, to a population of replicating entities (molecules, cells, higher organisms), where evolutionary principles prevail. Copyright 2000 Academic Press.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

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

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

PubMed

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

2010-01-01

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

Cross-sectional comparisons of the mathematical performance of children with learning disabilities: are we on the right track toward comprehensive programming?

PubMed

Cawley, J F; Miller, J H

1989-04-01

This study examines the mathematical performance of 220 children from 8 years through 17 years of age diagnosed as having learning disabilities. Student records were searched for data indicating performance on standardized test instruments relating to mathematics. Data for the Woodcock-Johnson Psycho-Educational Achievement Battery math subtests and for the IQ scores from the Wechsler Intelligence Scale for Children-Revised were obtained. Comparisons were made among children at different ages and among specific age clusters. Primary attention was directed toward calculations and applications of math concepts and principles. Developmental patterns across the ages studied were discovered. Implications for long-term comprehensive programming are presented.

Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory

NASA Astrophysics Data System (ADS)

Masriyah; Firmansyah, M. H.

2018-01-01

This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic operation as well as symbol and graphic representation. In employing, he devised and implemented strategies using additional plane forming on area-subtraction principle; declared truth of result according calculation process; used and switched between symbol and graphic representation. In interpreting, he declared result as house area within terrace and wall; declared reasonableness according measurement estimation. In formulating, idealist subject identified mathematical aspects are sides length; significant variables are terms/condition in problem; translated into mathematical language those are measurement, variables, arithmetic operations as well as symbol and graphic representation. In employing, he devised and implemented strategies using trial and error and two design in process of finding solutions; declared truth of result according the use of two design of solution; used and switched between symbol and graphic representation. In interpreting, he declared result as floor area of house; declared reasonableness according measurement estimation.

BOOK REVIEW: Conversations on the Dark Secrets of Physics

NASA Astrophysics Data System (ADS)

Teller, Edward

2003-07-01

Over many years Edward Teller delivered a course of Physical Science Appreciation Lectures. This book is based on those lectures, which must have been very stimulating. In the preparation of the book, Edward Teller was assisted by his daughter, Wendy Teller, and also by Wilson Talley. On many pages there are footnotes in the form of conversations between 'ET', who explains, and 'WT', who asks intelligent questions. (It is never clear which 'WT' is which.) I mention these footnotes as they contribute enormously to the charm and humour of the book. The book contains numerous anecdotes, many of which were new to me. The verse in the New Yorker, by Harold Furth, recording the famous meeting between Dr Teller and Dr Anti-Teller, is included. Dr Teller's comment is `The remarkable fact is that Harold got paid for the poem'. Dr Anti-Teller's comment is anti-recorded. The topics in the book include simple mechanics, statistical mechanics, electromagnetism, quantum mechanics and 'uses of new knowledge'. Despite its origins, the book does not avoid mathematics ('I will use mathematics because physics without mathematics is meaningless' (p1)), but Teller does attempt to explain the mathematics he uses. In much of the book the mathematics is at school level, but in his treatment of quantum mechanics he uses differential equations. If one skips past the equations then his final chapters are less mathematically demanding. I have enjoyed reading this book. Teller's approach is refreshing, and his coverage comprehensive and generally authoritative. My only disquiet is over his coverage of electrons in solids, where it would be clearer to consider the one-dimensional case first, before treating the three-dimensional case. There is a substantial discussion on the correspondence principle, wave-particle duality and on the uncertainty principle. His disposal of Schrödinger's notorious cat is masterly. There are questions at the end of each chapter. One question is based on a possible experiment suggested by Einstein to measure both energy and time precisely, thus violating the uncertainty principle. (We are reminded that Einstein was unhappy with the uncertainty principle.) The question is to find the flaw in the argument: we are told it took Bohr a (sleepless?) night to find it. Answers to all the questions are included at the end of the book. The last chapter is the epilogue, 'After the Revolution', in which Teller makes clear his belief that there will continue to be new discoveries in the physical sciences for a long time to come. This is a book which all readers of this journal should enjoy. It may give you fresh insight into some of the topics. Buy a copy, read it and then keep it at your bedside for occasional browsing. Make sure your institutional library has a copy, and recommend it to all physics students, both graduates and undergraduates. P Borcherds

The development of mathematics courseware for learning line and angle

NASA Astrophysics Data System (ADS)

Halim, Noor Dayana Abd; Han, Ong Boon; Abdullah, Zaleha; Yusup, Junaidah

2015-05-01

Learning software is a teaching aid which is often used in schools to increase students' motivation, attract students' attention and also improve the quality of teaching and learning process. However, the development of learning software should be followed the phases in Instructional Design (ID) Model, therefore the process can be carried out systematic and orderly. Thus, this concept paper describes the application of ADDIE model in the development of mathematics learning courseware for learning Line and Angle named CBL-Math. ADDIE model consists of five consecutive phases which are Analysis, Design, Development, Implementation and Evaluation. Each phase must be properly planned in order to achieve the objectives stated. Other than to describe the processes occurring in each phase, this paper also demonstrating how cognitive theory of multimedia learning principles are integrated in the developed courseware. The principles that applied in the courseware reduce the students' cognitive load while learning the topic of line and angle. With well prepared development process and the integration of appropriate principles, it is expected that the developed software can help students learn effectively and also increase students' achievement in the topic of Line and Angle.

Prokaryotic regulatory systems biology: Common principles governing the functional architectures of Bacillus subtilis and Escherichia coli unveiled by the natural decomposition approach.

PubMed

Freyre-González, Julio A; Treviño-Quintanilla, Luis G; Valtierra-Gutiérrez, Ilse A; Gutiérrez-Ríos, Rosa María; Alonso-Pavón, José A

2012-10-31

Escherichia coli and Bacillus subtilis are two of the best-studied prokaryotic model organisms. Previous analyses of their transcriptional regulatory networks have shown that they exhibit high plasticity during evolution and suggested that both converge to scale-free-like structures. Nevertheless, beyond this suggestion, no analyses have been carried out to identify the common systems-level components and principles governing these organisms. Here we show that these two phylogenetically distant organisms follow a set of common novel biologically consistent systems principles revealed by the mathematically and biologically founded natural decomposition approach. The discovered common functional architecture is a diamond-shaped, matryoshka-like, three-layer (coordination, processing, and integration) hierarchy exhibiting feedback, which is shaped by four systems-level components: global transcription factors (global TFs), locally autonomous modules, basal machinery and intermodular genes. The first mathematical criterion to identify global TFs, the κ-value, was reassessed on B. subtilis and confirmed its high predictive power by identifying all the previously reported, plus three potential, master regulators and eight sigma factors. The functionally conserved cores of modules, basal cell machinery, and a set of non-orthologous common physiological global responses were identified via both orthologous genes and non-orthologous conserved functions. This study reveals novel common systems principles maintained between two phylogenetically distant organisms and provides a comparison of their lifestyle adaptations. Our results shed new light on the systems-level principles and the fundamental functions required by bacteria to sustain life. Copyright © 2012 Elsevier B.V. All rights reserved.

Celestial Navigation

ERIC Educational Resources Information Center

Rosenkrantz, Kurt

2005-01-01

In the unit described in this article, students discover the main principles of navigation, build tools to observe celestial bodies, and apply their new skills to finding their position on Earth. Along the way students see how science, mathematics, technology, and history are intertwined.

Reducible or irreducible? Mathematical reasoning and the ontological method.

PubMed

Fisher, William P

2010-01-01

Science is often described as nothing but the practice of measurement. This perspective follows from longstanding respect for the roles mathematics and quantification have played as media through which alternative hypotheses are evaluated and experience becomes better managed. Many figures in the history of science and psychology have contributed to what has been called the "quantitative imperative," the demand that fields of study employ number and mathematics even when they do not constitute the language in which investigators think together. But what makes an area of study scientific is, of course, not the mere use of number, but communities of investigators who share common mathematical languages for exchanging quantitative and quantitative value. Such languages require rigorous theoretical underpinning, a basis in data sufficient to the task, and instruments traceable to reference standard quantitative metrics. The values shared and exchanged by such communities typically involve the application of mathematical models that specify the sufficient and invariant relationships necessary for rigorous theorizing and instrument equating. The mathematical metaphysics of science are explored with the aim of connecting principles of quantitative measurement with the structures of sufficient reason.

Black-box Brain Experiments, Causal Mathematical Logic, and the Thermodynamics of Intelligence

NASA Astrophysics Data System (ADS)

Pissanetzky, Sergio; Lanzalaco, Felix

2013-12-01

Awareness of the possible existence of a yet-unknown principle of Physics that explains cognition and intelligence does exist in several projects of emulation, simulation, and replication of the human brain currently under way. Brain simulation projects define their success partly in terms of the emergence of non-explicitly programmed biophysical signals such as self-oscillation and spreading cortical waves. We propose that a recently discovered theory of Physics known as Causal Mathematical Logic (CML) that links intelligence with causality and entropy and explains intelligent behavior from first principles, is the missing link. We further propose the theory as a roadway to understanding more complex biophysical signals, and to explain the set of intelligence principles. The new theory applies to information considered as an entity by itself. The theory proposes that any device that processes information and exhibits intelligence must satisfy certain theoretical conditions irrespective of the substrate where it is being processed. The substrate can be the human brain, a part of it, a worm's brain, a motor protein that self-locomotes in response to its environment, a computer. Here, we propose to extend the causal theory to systems in Neuroscience, because of its ability to model complex systems without heuristic approximations, and to predict emerging signals of intelligence directly from the models. The theory predicts the existence of a large number of observables (or "signals"), all of which emerge and can be directly and mathematically calculated from non-explicitly programmed detailed causal models. This approach is aiming for a universal and predictive language for Neuroscience and AGI based on causality and entropy, detailed enough to describe the finest structures and signals of the brain, yet general enough to accommodate the versatility and wholeness of intelligence. Experiments are focused on a black-box as one of the devices described above of which both the input and the output are precisely known, but not the internal implementation. The same input is separately supplied to a causal virtual machine, and the calculated output is compared with the measured output. The virtual machine, described in a previous paper, is a computer implementation of CML, fixed for all experiments and unrelated to the device in the black box. If the two outputs are equivalent, then the experiment has quantitatively succeeded and conclusions can be drawn regarding details of the internal implementation of the device. Several small black-box experiments were successfully performed and demonstrated the emergence of non-explicitly programmed cognitive function in each case

Physical principles of filamentous protein self-assembly kinetics

NASA Astrophysics Data System (ADS)

Michaels, Thomas C. T.; Liu, Lucie X.; Meisl, Georg; Knowles, Tuomas P. J.

2017-04-01

The polymerization of proteins and peptides into filamentous supramolecular structures is an elementary form of self-organization of key importance to the functioning biological systems, as in the case of actin biofilaments that compose the cellular cytoskeleton. Aberrant filamentous protein self-assembly, however, is associated with undesired effects and severe clinical disorders, such as Alzheimer’s and Parkinson’s diseases, which, at the molecular level, are associated with the formation of certain forms of filamentous protein aggregates known as amyloids. Moreover, due to their unique physicochemical properties, protein filaments are finding extensive applications as biomaterials for nanotechnology. With all these different factors at play, the field of filamentous protein self-assembly has experienced tremendous activity in recent years. A key question in this area has been to elucidate the microscopic mechanisms through which filamentous aggregates emerge from dispersed proteins with the goal of uncovering the underlying physical principles. With the latest developments in the mathematical modeling of protein aggregation kinetics as well as the improvement of the available experimental techniques it is now possible to tackle many of these complex systems and carry out detailed analyses of the underlying microscopic steps involved in protein filament formation. In this paper, we review some classical and modern kinetic theories of protein filament formation, highlighting their use as a general strategy for quantifying the molecular-level mechanisms and transition states involved in these processes.

On the Uniqueness and Consistency of Scattering Amplitudes

NASA Astrophysics Data System (ADS)

Rodina, Laurentiu

In this dissertation, we study constraints imposed by locality, unitarity, gauge invariance, the Adler zero, and constructability (scaling under BCFW shifts). In the first part we study scattering amplitudes as the unique mathematical objects which can satisfy various combinations of such principles. In all cases we find that locality and unitarity may be derived from gauge invariance (for Yang-Mills and General Relativity) or from the Adler zero (for the non-linear sigma model and the Dirac-Born-Infeld model), together with mild assumptions on the singularity structure and mass dimension. We also conjecture that constructability and locality together imply gauge invariance, hence also unitarity. All claims are proved through a soft expansion, and in the process we end re-deriving the well-known leading soft theorems for all four theories. Unlike other proofs of these theorems, we do not assume any form of factorization (unitarity). In the second part we show how tensions arising between gauge invariance (as encoded by spinor helicity variables in four dimensions), locality, unitarity and constructability give rise to various physical properties. These include high-spin no-go theorems, the equivalence principle, and the emergence of supersymmetry from spin 3/2 particles. We also complete the fully on-shell constructability proof of gravity amplitudes, by showing that the improved "bonus'' behavior of gravity under BCFW shifts is a simple consequence of Bose symmetry.

Study of the extra-ionic electron distributions in semi-metallic structures by nuclear quadrupole resonance techniques

NASA Technical Reports Server (NTRS)

Murty, A. N.

1976-01-01

A straightforward self-consistent method was developed to estimate solid state electrostatic potentials, fields and field gradients in ionic solids. The method is a direct practical application of basic electrostatics to solid state and also helps in the understanding of the principles of crystal structure. The necessary mathematical equations, derived from first principles, were presented and the systematic computational procedure developed to arrive at the solid state electrostatic field gradients values was given.

The study on the Layout of the Charging Station in Chengdu

NASA Astrophysics Data System (ADS)

Cai, yun; Zhang, wanquan; You, wei; Mao, pan

2018-03-01

In this paper, the comprehensive analysis of the factors affecting the layout of the electric car, considering the principle of layout of the charging station. Using queuing theory in operational research to establish mathematical model and basing on the principle of saving resource and convenient owner to optimize site number. Combining the theory of center to determine the service radius, Using the Gravity method to determine the initial location, Finally using the method of center of gravity to locate the charging station’s location.

Endobiogeny: a global approach to systems biology (part 1 of 2).

PubMed

Lapraz, Jean-Claude; Hedayat, Kamyar M

2013-01-01

Endobiogeny is a global systems approach to human biology that may offer an advancement in clinical medicine based in scientific principles of rigor and experimentation and the humanistic principles of individualization of care and alleviation of suffering with minimization of harm. Endobiogeny is neither a movement away from modern science nor an uncritical embracing of pre-rational methods of inquiry but a synthesis of quantitative and qualitative relationships reflected in a systems-approach to life and based on new mathematical paradigms of pattern recognition.

Adapting mudharabah principle in Islamic option

NASA Astrophysics Data System (ADS)

Suhaimi, Siti Noor Aini binti; Salleh, Hassilah binti

2013-04-01

Most of the options today use the Black-Scholes model as the basis in valuing their price. This conventional model involves the elements that are strictly prohibited in Islam namely riba, gharar and maisir. Hence, this paper introduces a new mathematical model that has been adapted with mudharabah principle to replace the Black-Scholes model. This new model which is more compatible with Islamic values produces a new Islamic option which avoids any form of oppression and injustice to all parties involved.

A new method of search design of refrigerating systems containing a liquid and gaseous working medium based on the graph model of the physical operating principle

NASA Astrophysics Data System (ADS)

Yakovlev, A. A.; Sorokin, V. S.; Mishustina, S. N.; Proidakova, N. V.; Postupaeva, S. G.

2017-01-01

The article describes a new method of search design of refrigerating systems, the basis of which is represented by a graph model of the physical operating principle based on thermodynamical description of physical processes. The mathematical model of the physical operating principle has been substantiated, and the basic abstract theorems relatively semantic load applied to nodes and edges of the graph have been represented. The necessity and the physical operating principle, sufficient for the given model and intended for the considered device class, were demonstrated by the example of a vapour-compression refrigerating plant. The example of obtaining a multitude of engineering solutions of a vapour-compression refrigerating plant has been considered.

WORKSHOP ON APPLICATION OF STATISTICAL METHODS TO BIOLOGICALLY-BASED PHARMACOKINETIC MODELING FOR RISK ASSESSMENT

EPA Science Inventory

Biologically-based pharmacokinetic models are being increasingly used in the risk assessment of environmental chemicals. These models are based on biological, mathematical, statistical and engineering principles. Their potential uses in risk assessment include extrapolation betwe...

40 CFR 280.12 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... a minimum, such persons must have education and experience in soil resistivity, stray current, structure-to-soil potential, and component electrical isolation measurements of buried metal piping and tank... reason of thorough knowledge of the physical sciences and the principles of engineering and mathematics...

40 CFR 280.12 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... a minimum, such persons must have education and experience in soil resistivity, stray current, structure-to-soil potential, and component electrical isolation measurements of buried metal piping and tank... reason of thorough knowledge of the physical sciences and the principles of engineering and mathematics...

40 CFR 280.12 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... a minimum, such persons must have education and experience in soil resistivity, stray current, structure-to-soil potential, and component electrical isolation measurements of buried metal piping and tank... reason of thorough knowledge of the physical sciences and the principles of engineering and mathematics...

Viscosity Meaurement Technique for Metal Fuels

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

Ban, Heng; Kennedy, Rory

2015-02-09

Metallic fuels have exceptional transient behavior, excellent thermal conductivity, and a more straightforward reprocessing path, which does not separate out pure plutonium from the process stream. Fabrication of fuel containing minor actinides and rare earth (RE) elements for irradiation tests, for instance, U-20Pu-3Am-2Np-1.0RE-15Zr samples at the Idaho National Laboratory, is generally done by melt casting in an inert atmosphere. For the design of a casting system and further scale up development, computational modeling of the casting process is needed to provide information on melt flow and solidification for process optimization. Therefore, there is a need for melt viscosity data, themore » most important melt property that controls the melt flow. The goal of the project was to develop a measurement technique that uses fully sealed melt sample with no Americium vapor loss to determine the viscosity of metallic melts and at temperatures relevant to the casting process. The specific objectives of the project were to: develop mathematical models to establish the principle of the measurement method, design and build a viscosity measurement prototype system based on the established principle, and calibrate the system and quantify the uncertainty range. The result of the project indicates that the oscillation cup technique is applicable for melt viscosity measurement. Detailed mathematical models of innovative sample ampoule designs were developed to not only determine melt viscosity, but also melt density under certain designs. Measurement uncertainties were analyzed and quantified. The result of this project can be used as the initial step toward the eventual goal of establishing a viscosity measurement system for radioactive melts.« less

On the stability of lung parenchymal lesions with applications to early pneumothorax diagnosis.

PubMed

Bhandarkar, Archis R; Banerjee, Rohan; Seshaiyer, Padmanabhan

2013-01-01

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

Mathematical modeling of zika virus disease with nonlinear incidence and optimal control

NASA Astrophysics Data System (ADS)

Goswami, Naba Kumar; Srivastav, Akhil Kumar; Ghosh, Mini; Shanmukha, B.

2018-04-01

The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. However, there is documented evidence of sexual transmission of this disease too. In this paper, a nonlinear mathematical model for Zika virus by considering nonlinear incidence is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The stability of the different equilibria of the model is discussed in detail. When the basic reproduction number R0 < 1, the disease-free equilibrium is locally and globally stable i.e. in this case disease dies out. For R0 > 1, we have endemic equilibrium which is locally stable under some restriction on parameters. Further this model is extended to optimal control model and is analyzed by using Pontryagin’s Maximum Principle. It has been observed that optimal control plays a significant role in reducing the number of zika infectives. Finally, numerical simulation is performed to illustrate the analytical findings.

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.

Preface.

PubMed

Ditlevsen, Susanne; Lansky, Petr

2016-06-01

This Special Issue of Mathematical Biosciences and Engineering contains 11 selected papers presented at the Neural Coding 2014 workshop. The workshop was held in the royal city of Versailles in France, October 6-10, 2014. This was the 11th of a series of international workshops on this subject, the first held in Prague (1995), then Versailles (1997), Osaka (1999), Plymouth (2001), Aulla (2003), Marburg (2005), Montevideo (2007), Tainan (2009), Limassol (2010), and again in Prague (2012). Also selected papers from Prague were published as a special issue of Mathematical Biosciences and Engineering and in this way a tradition was started. Similarly to the previous workshops, this was a single track multidisciplinary event bringing together experimental and computational neuroscientists. The Neural Coding Workshops are traditionally biennial symposia. They are relatively small in size, interdisciplinary with major emphasis on the search for common principles in neural coding. The workshop was conceived to bring together scientists from different disciplines for an in-depth discussion of mathematical model-building and computational strategies. Further information on the meeting can be found at the NC2014 website at https://colloque6.inra.fr/neural_coding_2014. The meeting was supported by French National Institute for Agricultural Research, the world's leading institution in this field. This Special Issue of Mathematical Biosciences and Engineering contains 11 selected papers presented at the Neural Coding 2014 workshop. The workshop was held in the royal city of Versailles in France, October 6-10, 2014. This was the 11th of a series of international workshops on this subject, the first held in Prague (1995), then Versailles (1997), Osaka (1999), Plymouth (2001), Aulla (2003), Marburg (2005), Montevideo (2007), Tainan (2009), Limassol (2010), and again in Prague (2012). Also selected papers from Prague were published as a special issue of Mathematical Biosciences and Engineering and in this way a tradition was started. Similarly to the previous workshops, this was a single track multidisciplinary event bringing together experimental and computational neuroscientists. The Neural Coding Workshops are traditionally biennial symposia. They are relatively small in size, interdisciplinary with major emphasis on the search for common principles in neural coding. The workshop was conceived to bring together scientists from different disciplines for an in-depth discussion of mathematical model-building and computational strategies. Further information on the meeting can be found at the NC2014 website at https://colloque6.inra.fr/neural_coding_2014. The meeting was supported by French National Institute for Agricultural Research, the world's leading institution in this field. Understanding how the brain processes information is one of the most challenging subjects in neuroscience. The papers presented in this special issue show a small corner of the huge diversity of this field, and illustrate how scientists with different backgrounds approach this vast subject. The diversity of disciplines engaged in these investigations is remarkable: biologists, mathematicians, physicists, psychologists, computer scientists, and statisticians, all have original tools and ideas by which to try to elucidate the underlying mechanisms. In this issue, emphasis is put on mathematical modeling of single neurons. A variety of problems in computational neuroscience accompanied with a rich diversity of mathematical tools and approaches are presented. We hope it will inspire and challenge the readers in their own research. We would like to thank the authors for their valuable contributions and the referees for their priceless effort of reviewing the manuscripts. Finally, we would like to thank Yang Kuang for supporting us and making this publication possible.

Existence and characterization of optimal control in mathematics model of diabetics population

NASA Astrophysics Data System (ADS)

Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.

2018-03-01

Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.

A single-cell spiking model for the origin of grid-cell patterns

PubMed Central

Kempter, Richard

2017-01-01

Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity. PMID:28968386

An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Universality in the Evolution of Orientation Columns in the Visual Cortex

PubMed Central

Kaschube, Matthias; Schnabel, Michael; Löwel, Siegrid; Coppola, David M.; White, Leonard E.; Wolf, Fred

2011-01-01

The brain’s visual cortex processes information concerning form, pattern, and motion within functional maps that reflect the layout of neuronal circuits. We analyzed functional maps of orientation preference in the ferret, tree shrew, and galago—three species separated since the basal radiation of placental mammals more than 65 million years ago—and found a common organizing principle. A symmetry-based class of models for the self-organization of cortical networks predicts all essential features of the layout of these neuronal circuits, but only if suppressive long-range interactions dominate development. We show mathematically that orientation-selective long-range connectivity can mediate the required interactions. Our results suggest that self-organization has canalized the evolution of the neuronal circuitry underlying orientation preference maps into a single common design. PMID:21051599

Mars 1064-nm Spectral Radiance Measurements from the Receiver Noise Response of the Mars Orbiter Laser Altimeter

NASA Technical Reports Server (NTRS)

Sun, Xiaoli; Neumann, Gregory A.; Abshire, James B.; Zuber, Maria T.

2005-01-01

The Mars Orbiter Laser Altimeter not only provides surface topography from the laser pulse time-of-flight, but also two radiometric measurements, the active measurement of transmitted and reflected laser pulse energy, and the passive measurement of reflected solar illumination. The passive radiometry measurement is accomplished in a novel fashion by monitoring the noise density at the output of the photodetector and solving for the amount of background light. The passive radiometry measurements provide images of Mars at 1064-nm wavelength over a 2 nm bandwidth with sub-km spatial resolution and with 2% or better precision under full illumination. We describe in this paper the principle of operation, the receiver mathematical model, its calibration, and performance assessment from sample measurement data.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit.

PubMed

Eriksson, O; Brinne, B; Zhou, Y; Björkegren, J; Tegnér, J

2009-03-01

Complex regulatory dynamics is ubiquitous in molecular networks composed of genes and proteins. Recent progress in computational biology and its application to molecular data generate a growing number of complex networks. Yet, it has been difficult to understand the governing principles of these networks beyond graphical analysis or extensive numerical simulations. Here the authors exploit several simplifying biological circumstances which thereby enable to directly detect the underlying dynamical regularities driving periodic oscillations in a dynamical nonlinear computational model of a protein-protein network. System analysis is performed using the cell cycle, a mathematically well-described complex regulatory circuit driven by external signals. By introducing an explicit time delay and using a 'tearing-and-zooming' approach the authors reduce the system to a piecewise linear system with two variables that capture the dynamics of this complex network. A key step in the analysis is the identification of functional subsystems by identifying the relations between state-variables within the model. These functional subsystems are referred to as dynamical modules operating as sensitive switches in the original complex model. By using reduced mathematical representations of the subsystems the authors derive explicit conditions on how the cell cycle dynamics depends on system parameters, and can, for the first time, analyse and prove global conditions for system stability. The approach which includes utilising biological simplifying conditions, identification of dynamical modules and mathematical reduction of the model complexity may be applicable to other well-characterised biological regulatory circuits. [Includes supplementary material].

Teaching One Thing at a Time or Several Things Together?--Teachers Changing Their Way of Handling the Object of Learning by Being Engaged in a Theory-Based Professional Learning Community in Mathematics and Science

ERIC Educational Resources Information Center

Kullberg, Angelika; Runesson, Ulla; Marton, Ference; Vikström, Anna; Nilsson, Pernilla; Mårtensson, Pernilla; Häggström, Johan

2016-01-01

Twelve lower secondary schoolteachers in mathematics and science were asked to teach a topic of their choice during a lesson that was video-recorded. We were able to analyse 10 of the cases and we found that all of them were similar in one respect: concepts and principles were introduced one at a time, each one followed by examples of the concept…

Aerodynamic mathematical modeling - basic concepts

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1981-01-01

The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

Surveillance theory applied to virus detection: a case for targeted discovery

USGS Publications Warehouse

Bogich, Tiffany L.; Anthony, Simon J.; Nichols, James D.

2013-01-01

Virus detection and mathematical modeling have gone through rapid developments in the past decade. Both offer new insights into the epidemiology of infectious disease and characterization of future risk; however, modeling has not yet been applied to designing the best surveillance strategies for viral and pathogen discovery. We review recent developments and propose methods to integrate viral and pathogen discovery and mathematical modeling through optimal surveillance theory, arguing for a more targeted approach to novel virus detection guided by the principles of adaptive management and structured decision-making.

A formulation of the foundations of genetics and evolution.

PubMed

Bahr, Brian Edward

2016-05-01

This paper proposes a formulation of theories of the foundations of genetics and evolution that can be used to mathematically simulate phenotype expression, reproduction, mutation, and natural selection. It will be shown that Mendelian inheritance can be mathematically simulated with expressions involving matrices and that these expressions can also simulate phenomena that are modifications to Mendel's basic principles, like alleles that give rise to quantitative effects and traits that are the expression of multiple alleles and/or multiple genetic loci. Copyright © 2016 Elsevier Inc. All rights reserved.

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields.

PubMed

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge-in particular in mathematics domains-influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of their ability, in particular in response to the potentially inhibiting influence of stereotype threat on their pathways to scientific degrees.

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields

PubMed Central

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of their ability, in particular in response to the potentially inhibiting influence of stereotype threat on their pathways to scientific degrees. PMID:26113823

Foundational concepts and underlying theories for majors in "biochemistry and molecular biology".

PubMed

Tansey, John T; Baird, Teaster; Cox, Michael M; Fox, Kristin M; Knight, Jennifer; Sears, Duane; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members and science educators from around the country that focused on identifying: 1) core principles of biochemistry and molecular biology, 2) essential concepts and underlying theories from physics, chemistry, and mathematics, and 3) foundational skills that undergraduate majors in biochemistry and molecular biology must understand to complete their major coursework. Using information gained from these workshops, as well as from the ASBMB accreditation working group and the NSF Vision and Change report, the Core Concepts working group has developed a consensus list of learning outcomes and objectives based on five foundational concepts (evolution, matter and energy transformation, homeostasis, information flow, and macromolecular structure and function) that represent the expected conceptual knowledge base for undergraduate degrees in biochemistry and molecular biology. This consensus will aid biochemistry and molecular biology educators in the development of assessment tools for the new ASBMB recommended curriculum. © 2013 by The International Union of Biochemistry and Molecular Biology.

[Study on the characteristics of radiance calibration using nonuniformity extended source].

PubMed

Wang, Jian-Wei; Huang, Min; Xiangli, Bin; Tu, Xiao-Long

2013-07-01

Integrating sphere and diffuser are always used as extended source, and they have different effects on radiance calibration of imaging spectrometer with parameter difference. In the present paper, a mathematical model based on the theory of radiative transfer and calibration principle is founded to calculate the irradiance and calibration coefficients on CCD, taking relatively poor uniformity lights-board calibration system for example. The effects of the nonuniformity on the calibration was analyzed, which makes up the correlation of calibration coefficient matrix under ideal and unideal situation. The results show that the nonuniformity makes the viewing angle and the position of the point of intersection of the optical axis and the diffuse reflection plate have relatively large effects on calibration, while the observing distance's effect is small; under different viewing angles, a deviation value can be found that makes the calibration results closest to the desired results. So, the calibration error can be reduced by choosing appropriate deviation value.

Jet Topics: Disentangling Quarks and Gluons at Colliders

NASA Astrophysics Data System (ADS)

Metodiev, Eric M.; Thaler, Jesse

2018-06-01

We introduce jet topics: a framework to identify underlying classes of jets from collider data. Because of a close mathematical relationship between distributions of observables in jets and emergent themes in sets of documents, we can apply recent techniques in "topic modeling" to extract jet topics from the data with minimal or no input from simulation or theory. As a proof of concept with parton shower samples, we apply jet topics to determine separate quark and gluon jet distributions for constituent multiplicity. We also determine separate quark and gluon rapidity spectra from a mixed Z -plus-jet sample. While jet topics are defined directly from hadron-level multidifferential cross sections, one can also predict jet topics from first-principles theoretical calculations, with potential implications for how to define quark and gluon jets beyond leading-logarithmic accuracy. These investigations suggest that jet topics will be useful for extracting underlying jet distributions and fractions in a wide range of contexts at the Large Hadron Collider.

Case Study: Audio-Guided Learning, with Computer Graphics.

ERIC Educational Resources Information Center

Koumi, Jack; Daniels, Judith

1994-01-01

Describes teaching packages which involve the use of audiotape recordings with personal computers in Open University (United Kingdom) mathematics courses. Topics addressed include software development; computer graphics; pedagogic principles for distance education; feedback, including course evaluations and student surveys; and future plans.…

A Quasi-Practical Interstellar Rocket Trip

ERIC Educational Resources Information Center

Edmonds, James D., Jr.

1974-01-01

Mathematically shows that in principle a spaceship could travel eight light years in ten earth years, with the passengers arriving 4.6 years older than when they left earth and having experienced an acceleration induced effective gravity of one g for the entire trip. (MLH)

Reduce Confusion about Diffusion.

ERIC Educational Resources Information Center

Hebrank, Mary R.

1997-01-01

Presents activities that allow students to explore the fundamental but poorly understood concept of diffusion by appealing to their kinesthetic senses first, then challenging their analytical skills as they try to deduce the mathematical principle involved. Presents a computer simulation of diffusion and discusses diffusion's limitations and…

Information Processing Technology. Final Report.

ERIC Educational Resources Information Center

Choate, Larry; And Others

A tech prep/associate degree program in information technology was developed to prepare workers for entry into and advancement in occupations entailing applications of scientific principles and higher mathematics in situations involving various office machines. According to the articulation agreement reached, students from five country regional…

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.

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles

PubMed Central

Wheeler, Richard John

2015-01-01

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point “snapshot” of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes—cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)—as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. PMID:26543196

Does Early Mathematics Intervention Change the Processes Underlying Children’s Learning?

PubMed Central

Watts, Tyler W.; Clements, Douglas H.; Sarama, Julie; Wolfe, Christopher B.; Spitler, Mary Elaine; Bailey, Drew H.

2017-01-01

Early educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of children’s mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in children’s mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group. PMID:29399243

Least action and entropy considerations of self-organization in Benard cells

NASA Astrophysics Data System (ADS)

Georgiev, Georgi; Iannacchione, Germano

We study self-organization in complex systems using first principles in physics. Our approach involves the principle of least action and the second law of thermodynamics. In far from equilibrium systems, energy gradients cause internal ordering to facilitate the dissipation of energy in the environment. This internal ordering decreases their internal entropy in order to obey the principle of least action, minimizing the product of time and energy for transport through the system. We are considering the connection between action and entropy decrease inside Benard cells in order to derive some general features of self-organization. We are developing mathematical treatment of this coupling and comparing it to results from experiments and simulations.

Advances in modeling the pressure correlation terms in the second moment equations

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Shabbir, Aamir; Lumley, John L.

1991-01-01

In developing turbulence models, various model constraints were proposed in an attempt to make the model equations more general (or universal). The most recent of these are the realizability principle, the linearity principle, the rapid distortion theory, and the material indifference principle. Several issues are discussed concerning these principles and special attention is payed to the realizability principle. Realizability (defined as the requirement of non-negative energy and Schwarz' inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. The principle of realizability is described in detail, the realizability conditions are derived for various turbulence models, and the model forms are proposed for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models with experiments and direct numerical simulations are presented. As a special case of turbulence, the two dimensional two-component turbulence modeling is also discussed.

Point to point multispectral light projection applied to cultural heritage

NASA Astrophysics Data System (ADS)

Vázquez, D.; Alvarez, A.; Canabal, H.; Garcia, A.; Mayorga, S.; Muro, C.; Galan, T.

2017-09-01

Use of new of light sources based on LED technology should allow the develop of systems that combine conservation and exhibition requirements and allow to make these art goods available to the next generations according to sustainability principles. The goal of this work is to develop light systems and sources with an optimized spectral distribution for each specific point of the art piece. This optimization process implies to maximize the color fidelity reproduction and the same time to minimize the photochemical damage. Perceived color under these sources will be similar (metameric) to technical requirements given by the restoration team uncharged of the conservation and exhibition of the goods of art. Depending of the fragility of the exposed art objects (i.e. spectral responsivity of the material) the irradiance must be kept under a critical level. Therefore, it is necessary to develop a mathematical model that simulates with enough accuracy both the visual effect of the illumination and the photochemical impact of the radiation. Spectral reflectance of a reference painting The mathematical model is based on a merit function that optimized the individual intensity of the LED-light sources taking into account the damage function of the material and color space coordinates. Moreover the algorithm used weights for damage and color fidelity in order to adapt the model to a specific museal application. In this work we show a sample of this technology applied to a picture of Sorolla (1863-1923) an important Spanish painter title "woman walking at the beach".

Livestock Nutrition and Feeding. Student Manual. Second Edition.

ERIC Educational Resources Information Center

Ridenour, Harlan E.

This manual is designed to help agricultural education students and teachers to apply scientific facts and principles to problem-solving procedures in determining nutritious and economical livestock feeding programs. The manual provides applied scientific activities in biological science and chemistry, mathematics, and communication skills. It…

A Personalized Study Method for Learning University Physics

ERIC Educational Resources Information Center

Aravind, Vasudeva Rao; Croyle, Kevin

2017-01-01

Students learn scientific concepts and mathematical calculations relating to scientific principles by repetition and reinforcement. Teachers and instructors cannot practically spend the long time required during tutorials to patiently teach students the calculations. Usually, teachers assign homework to provide practice to students, hoping that…

Earth Algebra: Real-Life Mathematics in Navajoland.

ERIC Educational Resources Information Center

Schaufele, Christopher; Srivastava, Ravindra

1995-01-01

An algebra class at Navajo Community College (Shiprock, New Mexico) uses traditional algebra topics to study real-life situations, focuses on environmental issues, encourages collaborative learning, uses modern technology, and promotes development of critical thinking and decision-making skills. Students follow principles of Dine educational…

A Theory of Intellectual Development: Part 1.

ERIC Educational Resources Information Center

Confrey, Jere

1994-01-01

Part 1 of a three-part article analyzing radical constructivism (as one interpretation of Piaget) and the socio-cultural perspective (as one interpretation of Vygotsky), including major principles, primary contributions to mathematics education, and potential limitations. Introduces an integration of the two theories through a feminist…

The Computer Simulation of Liquids by Molecular Dynamics.

ERIC Educational Resources Information Center

Smith, W.

1987-01-01

Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

Weather to Make a Decision

ERIC Educational Resources Information Center

Hoyle, Julie E.; Mjelde, James W.; Litzenberg, Kerry K.

2006-01-01

DECIDE is a teacher-friendly, integrated approach designed to stimulate learning by allowing students to make decisions about situations they face in their lives while using scientific weather principles. This learning unit integrates weather science, decision theory, mathematics, statistics, geography, and reading in a context of decision…

Communication Speaks

ERIC Educational Resources Information Center

Kinman, Robin Lynn

2010-01-01

When the author recently turned her attention to the National Council of Teachers of Mathematics (NCTM) "Principles and Standards," she was startled to see communication as key. She adjusted her teaching to meet the NCTM Communication Standard and promote communication in her classroom by providing a safe environment, developing discourse and…

Mathematic and the Quest for Fundamental Principles of Biology

DTIC Science & Technology

2017-05-05

stochasticity as part of the process, rather than as extrinsic noise. In some sense, like all organisms, we must continually solve inverse problems...predictions that could not be made before, ideally while simultaneously elucidating new mechanisms and proposing new experiments. The meeting concluded with

Generalization and Training.

ERIC Educational Resources Information Center

Jenkins, W. O.

This paper contends that human organisms are not qualitatively different from infra-human ones. The same principles apply to the acquisition, maintenance and weakening of complex verbal skills as mathematics as to rats pressing bars or pigeons pecking windows. Two aspects of child research are assessment and training. Assessment involves…

Observing Ben Wyckoff: From Basic Research to Programmed Instruction and Social Issues

PubMed Central

Escobar, Rogelio; Lattal, Kennon A

2011-01-01

L. Benjamin Wyckoff's seminal contributions to both psychological theory and application are the subject of this review. Wyckoff started his academic career as a graduate student at Indiana University, where he developed the observing-response procedure under the guidance of B. F. Skinner and C. J. Burke. At the University of Wisconsin–Madison, Wyckoff refined his mathematical theory of secondary reinforcement. This theory was the impetus for his creation of an electronic simulation of a rat running a T maze, one of the first “computer models” of learning. Wyckoff next went to Emory University, leaving there to help create two of the most successful companies dedicated to the advancement of programmed instruction and teaching machines: Teaching Machines, Inc. and the Human Development Institute. Wyckoff's involvement in these companies epitomizes the application of basic behavior-analytic principles in the development of technology to improve education and human relationships. The emergent picture of Wyckoff is that of a man who, through his research, professional work in educational applications of behavioral principles, and active involvement in the civil rights movement of the 1960s, was strongly committed to applying behavioral science to positively influence human behavior change. PMID:22532737

A Minimal Model Describing Hexapedal Interlimb Coordination: The Tegotae-Based Approach

PubMed Central

Owaki, Dai; Goda, Masashi; Miyazawa, Sakiko; Ishiguro, Akio

2017-01-01

Insects exhibit adaptive and versatile locomotion despite their minimal neural computing. Such locomotor patterns are generated via coordination between leg movements, i.e., an interlimb coordination, which is largely controlled in a distributed manner by neural circuits located in thoracic ganglia. However, the mechanism responsible for the interlimb coordination still remains elusive. Understanding this mechanism will help us to elucidate the fundamental control principle of animals' agile locomotion and to realize robots with legs that are truly adaptive and could not be developed solely by conventional control theories. This study aims at providing a “minimal" model of the interlimb coordination mechanism underlying hexapedal locomotion, in the hope that a single control principle could satisfactorily reproduce various aspects of insect locomotion. To this end, we introduce a novel concept we named “Tegotae,” a Japanese concept describing the extent to which a perceived reaction matches an expectation. By using the Tegotae-based approach, we show that a surprisingly systematic design of local sensory feedback mechanisms essential for the interlimb coordination can be realized. We also use a hexapod robot we developed to show that our mathematical model of the interlimb coordination mechanism satisfactorily reproduces various insects' gait patterns. PMID:28649197

Physics of the Mind.

PubMed

Perlovsky, Leonid I

2016-01-01

Is it possible to turn psychology into "hard science"? Physics of the mind follows the fundamental methodology of physics in all areas where physics have been developed. What is common among Newtonian mechanics, statistical physics, quantum physics, thermodynamics, theory of relativity, astrophysics… and a theory of superstrings? The common among all areas of physics is a methodology of physics discussed in the first few lines of the paper. Is physics of the mind possible? Is it possible to describe the mind based on the few first principles as physics does? The mind with its variabilities and uncertainties, the mind from perception and elementary cognition to emotions and abstract ideas, to high cognition. Is it possible to turn psychology and neuroscience into "hard" sciences? The paper discusses established first principles of the mind, their mathematical formulations, and a mathematical model of the mind derived from these first principles, mechanisms of concepts, emotions, instincts, behavior, language, cognition, intuitions, conscious and unconscious, abilities for symbols, functions of the beautiful and musical emotions in cognition and evolution. Some of the theoretical predictions have been experimentally confirmed. This research won national and international awards. In addition to summarizing existing results the paper describes new development theoretical and experimental. The paper discusses unsolved theoretical problems as well as experimental challenges for future research.

Physics of the Mind

PubMed Central

Perlovsky, Leonid I.

2016-01-01

Is it possible to turn psychology into “hard science”? Physics of the mind follows the fundamental methodology of physics in all areas where physics have been developed. What is common among Newtonian mechanics, statistical physics, quantum physics, thermodynamics, theory of relativity, astrophysics… and a theory of superstrings? The common among all areas of physics is a methodology of physics discussed in the first few lines of the paper. Is physics of the mind possible? Is it possible to describe the mind based on the few first principles as physics does? The mind with its variabilities and uncertainties, the mind from perception and elementary cognition to emotions and abstract ideas, to high cognition. Is it possible to turn psychology and neuroscience into “hard” sciences? The paper discusses established first principles of the mind, their mathematical formulations, and a mathematical model of the mind derived from these first principles, mechanisms of concepts, emotions, instincts, behavior, language, cognition, intuitions, conscious and unconscious, abilities for symbols, functions of the beautiful and musical emotions in cognition and evolution. Some of the theoretical predictions have been experimentally confirmed. This research won national and international awards. In addition to summarizing existing results the paper describes new development theoretical and experimental. The paper discusses unsolved theoretical problems as well as experimental challenges for future research. PMID:27895558

Representations of spacetime: Formalism and ontological commitment

NASA Astrophysics Data System (ADS)

Bain, Jonathan Stanley

This dissertation consists of two parts. The first is on the relation between formalism and ontological commitment in the context of theories of spacetime, and the second is on scientific realism. The first part begins with a look at how the substantivalist/relationist debate over the ontological status of spacetime has been influenced by a particular mathematical formalism, that of tensor analysis on differential manifolds (TADM). This formalism has motivated the substantivalist position known as manifold substantivalism. Chapter 1 focuses on the hole argument which maintains that manifold substantivalism is incompatible with determinism. I claim that the realist motivations underlying manifold substantivalism can be upheld, and the hole argument avoided, by adopting structural realism with respect to spacetime. In this context, this is the claim that it is the structure that spacetime points enter into that warrants belief and not the points themselves. In Chapter 2, an elimination principle is defined by means of which a distinction can be made between surplus structure and essential structure with respect to formulations of a theory in two distinct mathematical formulations and some prior ontological commitments. This principle is then used to demonstrate that manifold points may be considered surplus structure in the formulation of field theories. This suggests that, if we are disposed to read field theories literally, then, at most, it should be the essential structure common to all alternative formulations of such theories that should be taken literally. I also investigate how the adoption of alternative formalisms informs other issues in the philosophy of spacetime. Chapter 3 offers a realist position which takes a semantic moral from the preceding investigation and an epistemic moral from work done on reliability. The semantic moral advises us to read only the essential structure of our theories literally. The epistemic moral shows us that such structure is robust under theory change, given an adequate reliabilist notion of epistemic warrant. I call the realist position that subscribes to these morals structural realism and attempt to demonstrate that it is immune to the semantic and epistemic versions of the underdetermination argument posed by the anti-realist.

Model-Based Policymaking: A Framework to Promote Ethical "Good Practice" in Mathematical Modeling for Public Health Policymaking.

PubMed

Boden, Lisa A; McKendrick, Iain J

2017-01-01

Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical "good practice" and are thus "fit for purpose" as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science-policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy.

47 CFR 36.2 - Fundamental principles underlying procedures.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 2 2010-10-01 2010-10-01 false Fundamental principles underlying procedures... Fundamental principles underlying procedures. (a) The following general principles underlie the procedures... operating forces on a unit basis (e.g., conversation-minute-kilometers per message, weighted standard work...

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

PubMed Central

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

2011-01-01

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

Mathematical modeling of a process the rolling delivery

NASA Astrophysics Data System (ADS)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

Differential equation methods for simulation of GFP kinetics in non-steady state experiments.

PubMed

Phair, Robert D

2018-03-15

Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non-steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis. © 2018 Phair. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

ERIC Educational Resources Information Center

Artzt, Alice F.; Armour-Thomas, Eleanor

1998-01-01

Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

Foundations of quantum gravity: The role of principles grounded in empirical reality

NASA Astrophysics Data System (ADS)

Holman, Marc

2014-05-01

When attempting to assess the strengths and weaknesses of various principles in their potential role of guiding the formulation of a theory of quantum gravity, it is crucial to distinguish between principles which are strongly supported by empirical data - either directly or indirectly - and principles which instead (merely) rely heavily on theoretical arguments for their justification. Principles in the latter category are not necessarily invalid, but their a priori foundational significance should be regarded with due caution. These remarks are illustrated in terms of the current standard models of cosmology and particle physics, as well as their respective underlying theories, i.e., essentially general relativity and quantum (field) theory. For instance, it is clear that both standard models are severely constrained by symmetry principles: an effective homogeneity and isotropy of the known universe on the largest scales in the case of cosmology and an underlying exact gauge symmetry of nuclear and electromagnetic interactions in the case of particle physics. However, in sharp contrast to the cosmological situation, where the relevant symmetry structure is more or less established directly on observational grounds, all known, nontrivial arguments for the "gauge principle" are purely theoretical (and far less conclusive than usually advocated). Similar remarks apply to the larger theoretical structures represented by general relativity and quantum (field) theory, where - actual or potential - empirical principles, such as the (Einstein) equivalence principle or EPR-type nonlocality, should be clearly differentiated from theoretical ones, such as general covariance or renormalizability. It is argued that if history is to be of any guidance, the best chance to obtain the key structural features of a putative quantum gravity theory is by deducing them, in some form, from the appropriate empirical principles (analogous to the manner in which, say, the idea that gravitation is a curved spacetime phenomenon is arguably implied by the equivalence principle). Theoretical principles may still be useful however in formulating a concrete theory (analogous to the manner in which, say, a suitable form of general covariance can still act as a sieve for separating theories of gravity from one another). It is subsequently argued that the appropriate empirical principles for deducing the key structural features of quantum gravity should at least include (i) quantum nonlocality, (ii) irreducible indeterminacy (or, essentially equivalently, given (i), relativistic causality), (iii) the thermodynamic arrow of time, (iv) homogeneity and isotropy of the observable universe on the largest scales. In each case, it is explained - when appropriate - how the principle in question could be implemented mathematically in a theory of quantum gravity, why it is considered to be of fundamental significance and also why contemporary accounts of it are insufficient. For instance, the high degree of uniformity observed in the Cosmic Microwave Background is usually regarded as theoretically problematic because of the existence of particle horizons, whereas the currently popular attempts to resolve this situation in terms of inflationary models are, for a number of reasons, less than satisfactory. However, rather than trying to account for the required empirical features dynamically, an arguably much more fruitful approach consists in attempting to account for these features directly, in the form of a lawlike initial condition within a theory of quantum gravity.

The education of perception.

PubMed

Goldstone, Robert L; Landy, David H; Son, Ji Y

2010-04-01

Although the field of perceptual learning has mostly been concerned with low- to middle-level changes to perceptual systems due to experience, we consider high-level perceptual changes that accompany learning in science and mathematics. In science, we explore the transfer of a scientific principle (competitive specialization) across superficially dissimilar pedagogical simulations. We argue that transfer occurs when students develop perceptual interpretations of an initial simulation and simply continue to use the same interpretational bias when interacting with a second simulation. In arithmetic and algebraic reasoning, we find that proficiency in mathematics involves executing spatially explicit transformations to notational elements. People learn to attend mathematical operations in the order in which they should be executed, and the extent to which students employ their perceptual attention in this manner is positively correlated with their mathematical experience. For both science and mathematics, relatively sophisticated performance is achieved not by ignoring perceptual features in favor of deep conceptual features, but rather by adapting perceptual processing so as to conform with and support formally sanctioned responses. These "rigged-up perceptual systems" offer a promising approach to educational reform. Copyright © 2009 Cognitive Science Society, Inc.

Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2014-10-01

The so-called non-locality theorems aim to show that Quantum Mechanics is not consistent with the Locality Principle. Their proofs require, besides the standard postulates of Quantum Theory, further conditions, as for instance the Criterion of Reality, which cannot be formulated in the language of Standard Quantum Theory; this difficulty makes the proofs not verifiable according to usual logico-mathematical methods, and therefore it is a source of the controversial debate about the real implications of these theorems. The present work addresses this difficulty for Bell-type and Stapp's arguments of non-locality. We supplement the formalism of Quantum Mechanics with formal statements inferred from the further conditions in the two different cases. Then an analysis of the two arguments is performed according to ordinary mathematical logic.

Circular Samples as Objects for Magnetic Resonance Imaging - Mathematical Simulation, Experimental Results

NASA Astrophysics Data System (ADS)

Frollo, Ivan; Krafčík, Andrej; Andris, Peter; Přibil, Jiří; Dermek, Tomáš

2015-12-01

Circular samples are the frequent objects of "in-vitro" investigation using imaging method based on magnetic resonance principles. The goal of our investigation is imaging of thin planar layers without using the slide selection procedure, thus only 2D imaging or imaging of selected layers of samples in circular vessels, eppendorf tubes,.. compulsorily using procedure "slide selection". In spite of that the standard imaging methods was used, some specificity arise when mathematical modeling of these procedure is introduced. In the paper several mathematical models were presented that were compared with real experimental results. Circular magnetic samples were placed into the homogenous magnetic field of a low field imager based on nuclear magnetic resonance. For experimental verification an MRI 0.178 Tesla ESAOTE Opera imager was used.

Using mathematics to solve real world problems: the role of enablers

NASA Astrophysics Data System (ADS)

Geiger, Vincent; Stillman, Gloria; Brown, Jill; Galbriath, Peter; Niss, Mogens

2018-03-01

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of "enablers" within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students' development as modellers.

Designs of goal-free problems for trigonometry learning

NASA Astrophysics Data System (ADS)

Retnowati, E.; Maulidya, S. R.

2018-03-01

This paper describes the designs of goal-free problems particularly for trigonometry, which may be considered a difficult topic for high school students.Goal-free problem is an instructional design developed based on a Cognitive load theory (CLT). Within the design, instead of asking students to solve a specific goal of a mathematics problem, the instruction is to solve as many Pythagoras as possible. It was assumed that for novice students, goal-free problems encourage students to pay attention more to the given information and the mathematical principles that can be applied to reveal the unknown variables. Hence, students develop more structured knowledge while solving the goal-free problems. The resulted design may be used in regular mathematics classroom with some adjustment on the difficulty level and the allocated lesson time.

Is Computer Science Compatible with Technological Literacy?

ERIC Educational Resources Information Center

Buckler, Chris; Koperski, Kevin; Loveland, Thomas R.

2018-01-01

Although technology education evolved over time, and pressure increased to infuse more engineering principles and increase links to STEM (science technology, engineering, and mathematics) initiatives, there has never been an official alignment between technology and engineering education and computer science. There is movement at the federal level…

Ship Hydrodynamics

ERIC Educational Resources Information Center

Lafrance, Pierre

1978-01-01

Explores in a non-mathematical treatment some of the hydrodynamical phenomena and forces that affect the operation of ships, especially at high speeds. Discusses the major components of ship resistance such as the different types of drags and ways to reduce them and how to apply those principles for the hovercraft. (GA)

How Computer Graphics Work.

ERIC Educational Resources Information Center

Prosise, Jeff

This document presents the principles behind modern computer graphics without straying into the arcane languages of mathematics and computer science. Illustrations accompany the clear, step-by-step explanations that describe how computers draw pictures. The 22 chapters of the book are organized into 5 sections. "Part 1: Computer Graphics in…

Counting It Twice.

ERIC Educational Resources Information Center

Schattschneider, Doris

1991-01-01

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

Technology-Enhancement for Papua New Guinean Professional Learning

ERIC Educational Resources Information Center

Bino, Vagi; Edmonds-Wathen, Cris

2014-01-01

Technology facilitated the implementation of teacher professional learning based on a design of principles to improve the teaching of "Cultural Mathematics" in elementary schools in Papua New Guinea. An offline "website", a set of interlinked resource materials was used in workshops to enhance the professional learning.…

Classroom Analysis of Rotating Space Vehicles in 2001: A Space Odyssey.

ERIC Educational Resources Information Center

Borgwald, James M.; Schreiner, Serge

1993-01-01

This article describes the use of modern science fiction movies as a vehicle to teach scientific principles. The resulting artificial gravity from a spinning space station in movie "2001" is calculated from measurements taken off of the screen. A mathematical explanation is provided. (MVL)

Epidemic classification of phytosanitary situations on cereal crops using mathematical modeling

USDA-ARS?s Scientific Manuscript database

Most plant protection researchers and experts divide emerging phytosanitary situations into three classes: epidemic, moderate development of disease, and yield depression. The known principles and methods for estimating these situations (Van der Plank J.E., Kranz J. et al.) do not fully describe th...

Activities in Elementary Probability, Monograph No. 9.

ERIC Educational Resources Information Center

Fouch, Daniel J.

This monograph on elementary probability for middle school, junior high, or high school consumer mathematics students is divided into two parts. Part one emphasizes lessons which cover the fundamental counting principle, permutations, and combinations. The 5 lessons of part I indicate the objectives, examples, methods, application, and problems…

A Field Exercise in Fluvial Sediment Transport.

ERIC Educational Resources Information Center

Tharp, Thomas M.

1983-01-01

Describes an investigation which introduces the mathematical principles of stream hydraulics and fluvial sediment in a practical context. The investigation has four stages: defining hydrology of the stream; defining channel hydraulics in a study reach; measuring grain size; and calculating transportable grain size and comparing measure stream-bed…

What Teaching for Understanding Looks Like.

ERIC Educational Resources Information Center

Unger, Chris

1994-01-01

To apply four principles of Teaching for Understanding framework developed at Harvard University, researchers worked with team of four teachers at two Massachusetts high schools. One history teacher revised Industrial Revolution unit to emphasize human progress. Mathematics teacher had students design a dance floor based on several different…

Laser-acoustic transcutaneous drug delivery: A new trend in administration of drugs

NASA Astrophysics Data System (ADS)

Zharov, Vladimir P.; Latyshev, Alexei S.

1999-03-01

This work deals with the principles of transcutaneous drug delivery technique which uses optoacoustic (OA) effect. Laser OA impregnation, enhanced laser OA impregnation, simple laser and laser OA injections are presented. Drug impregnation mathematical model and preliminary experiments on laser injection are described.

The Effects of Constructivist Learning Environment on Prospective Mathematics Teachers' Opinions

ERIC Educational Resources Information Center

Narli, Serkan; Baser, Nes'e

2010-01-01

To explore the effects of constructivist learning environment on prospective teachers' opinions about "mathematics, department of mathematics, discrete mathematics, countable and uncountable infinity" taught under the subject of Cantorian Set Theory in discrete mathematics class, 60 first-year students in the Division of Mathematics…

Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

ERIC Educational Resources Information Center

Sriraman, Bharath, Ed.

2012-01-01

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

Violations of the ceiling principle: exact conditions and statistical evidence.

PubMed Central

Slimowitz, J R; Cohen, J E

1993-01-01

The National Research Council recommended the use of the ceiling principle in forensic applications of DNA testing on the grounds that the ceiling principle was believed to be "conservative," giving estimates greater than or equal to the actual genotype frequencies in the appropriate reference population. We show here that the ceiling principle can fail to be conservative in a population with two subpopulations and two loci, each with two alleles at Hardy-Weinberg equilibrium, if there is some linkage disequilibrium between loci. We also show that the ceiling principle can fail in a population with two subpopulations and a single locus with two alleles if Hardy-Weinberg equilibrium does not hold. We give explicit analytical formulas to describe when the ceiling principle fails. By showing that the ceiling principle is not always mathematically reliable, this analysis gives users of the ceiling principle the responsibility of demonstrating that it is conservative for the particular data with which it is used. Our reanalysis of VNTR data bases of the FBI provides compelling evidence of two-locus associations within three major ethnic groups (Caucasian, black, and Hispanic) in the United States, even though the loci tested are located on different chromosomes. Before the ceiling principle is implemented, more research should be done to determine whether it may be violated in practice. PMID:8328450

Sines and Cosines. Part 1 of 3

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1992-01-01

Applying the concept of similarities, the mathematical principles of circular motion and sine and cosine waves are presented utilizing both film footage and computer animation in this 'Project Mathematics' series video. Concepts presented include: the symmetry of sine waves; the cosine (complementary sine) and cosine waves; the use of sines and cosines on coordinate systems; the relationship they have to each other; the definitions and uses of periodic waves, square waves, sawtooth waves; the Gibbs phenomena; the use of sines and cosines as ratios; and the terminology related to sines and cosines (frequency, overtone, octave, intensity, and amplitude).

Antibiotics in Animal Products

NASA Astrophysics Data System (ADS)

Falcão, Amílcar C.

The administration of antibiotics to animals to prevent or treat diseases led us to be concerned about the impact of these antibiotics on human health. In fact, animal products could be a potential vehicle to transfer drugs to humans. Using appropri ated mathematical and statistical models, one can predict the kinetic profile of drugs and their metabolites and, consequently, develop preventive procedures regarding drug transmission (i.e., determination of appropriate withdrawal periods). Nevertheless, in the present chapter the mathematical and statistical concepts for data interpretation are strictly given to allow understanding of some basic pharma-cokinetic principles and to illustrate the determination of withdrawal periods

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

PubMed

Allen, Edward J

2014-06-01

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

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

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Hierarchical analytical and simulation modelling of human-machine systems with interference

NASA Astrophysics Data System (ADS)

Braginsky, M. Ya; Tarakanov, D. V.; Tsapko, S. G.; Tsapko, I. V.; Baglaeva, E. A.

2017-01-01

The article considers the principles of building the analytical and simulation model of the human operator and the industrial control system hardware and software. E-networks as the extension of Petri nets are used as the mathematical apparatus. This approach allows simulating complex parallel distributed processes in human-machine systems. The structural and hierarchical approach is used as the building method for the mathematical model of the human operator. The upper level of the human operator is represented by the logical dynamic model of decision making based on E-networks. The lower level reflects psychophysiological characteristics of the human-operator.

Thermal oil recovery method using self-contained windelectric sets

NASA Astrophysics Data System (ADS)

Belsky, A. A.; Korolyov, I. A.

2018-05-01

The paper reviews challenges associated with questions of efficiency of thermal methods of impact on productive oil strata. The concept of using electrothermal complexes with WEG power supply for the indicated purposes was proposed and justified, their operating principles, main advantages and disadvantages, as well as a schematechnical solution for the implementation of the intensification of oil extraction, were considered. A mathematical model for finding the operating characteristics of WEG is presented and its main energy parameters are determined. The adequacy of the mathematical model is confirmed by laboratory simulation stand tests with nominal parameters.

Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Ye-Hua; Iazzi, Mauro; Troyer, Matthias; Harcos, Gergely

2015-12-01

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.

Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar

2007-09-01

We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.

Can Sophie's Choice Be Adequately Captured by Cold Computation of Minimizing Losses? An fMRI Study of Vital Loss Decisions

PubMed Central

Li, Qi; Qin, Shaozheng; Rao, Li-Lin; Zhang, Wencai; Ying, Xiaoping; Guo, Xiuyan; Guo, Chunyan; Ding, Jinghong; Li, Shu; Luo, Jing

2011-01-01

The vast majority of decision-making research is performed under the assumption of the value maximizing principle. This principle implies that when making decisions, individuals try to optimize outcomes on the basis of cold mathematical equations. However, decisions are emotion-laden rather than cool and analytic when they tap into life-threatening considerations. Using functional magnetic resonance imaging (fMRI), this study investigated the neural mechanisms underlying vital loss decisions. Participants were asked to make a forced choice between two losses across three conditions: both losses are trivial (trivial-trivial), both losses are vital (vital-vital), or one loss is trivial and the other is vital (vital-trivial). Our results revealed that the amygdala was more active and correlated positively with self-reported negative emotion associated with choice during vital-vital loss decisions, when compared to trivial-trivial loss decisions. The rostral anterior cingulate cortex was also more active and correlated positively with self-reported difficulty of choice during vital-vital loss decisions. Compared to the activity observed during trivial-trivial loss decisions, the orbitofrontal cortex and ventral striatum were more active and correlated positively with self-reported positive emotion of choice during vital-trivial loss decisions. Our findings suggest that vital loss decisions involve emotions and cannot be adequately captured by cold computation of minimizing losses. This research will shed light on how people make vital loss decisions. PMID:21412428

Effect of Directed Study of Mathematics Vocabulary on Standardized Mathematics Assessment Questions

ERIC Educational Resources Information Center

Waite, Adel Marlane

2017-01-01

The problems under investigation included (a) Did a directed study of mathematics vocabulary significantly affect student performance levels on standardized mathematical questions? and (b) Did the strategies used in this study significantly affect student performance levels on standardized mathematical questions? The population consisted of…

Teaching Undergraduate Mathematics Using CAS Technology: Issues and Prospects

ERIC Educational Resources Information Center

Tobin, Patrick C.; Weiss, Vida

2016-01-01

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

Communicational Perspectives on Learning and Teaching Mathematics: Prologue

ERIC Educational Resources Information Center

Tabach, Michal; Nachlieli, Talli

2016-01-01

This special issue comprises five studies which vary in their focus and mathematical content, yet they all share an underlying communicational theoretical framework--commognition. Within this framework, learning mathematics is defined as a change in one's mathematical discourse, that is, in the form of communication known as mathematical. Teaching…

Computerization of a telescope at secondary education

NASA Astrophysics Data System (ADS)

García Santiago, A.; Martos Jumillas, J.

2017-03-01

The work we are presenting in this paper is the computerization of a refractor telescope on an EQ3 type equatorial mount through Arduino. The control of the mount is done via three different interfaces: Stellarium, an Android interface for mobile phones and a second interface for PC made with Processing. The aforementioned work was done by the authors with a double purpose: presenting the interest in astronomy in the Mathematics department, and the development of applications within the subject of Technology in 4th ESO. So, it is a collaborative project between both departments. Except for the telescope and the mount, all the resources we have used can be found in any high school: free software (Guadalinex v9), App Inventor and Processing.The project was carried out under the principle of reducing all possible costs given the economic possibilities of the institution.

Conditional uncertainty principle

NASA Astrophysics Data System (ADS)

Gour, Gilad; Grudka, Andrzej; Horodecki, Michał; Kłobus, Waldemar; Łodyga, Justyna; Narasimhachar, Varun

2018-04-01

We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations, (1) a monotone-based conditional uncertainty relation and (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent.

Cataclysmic Variable Stars

NASA Astrophysics Data System (ADS)

Hellier, Coel

2001-01-01

Cataclysmic variable stars are the most variable stars in the night sky, fluctuating in brightness continually on timescales from seconds to hours to weeks to years. The changes can be recorded using amateur telescopes, yet are also the subject of intensive study by professional astronomers. That study has led to an understanding of cataclysmic variables as binary stars, orbiting so closely that material transfers from one star to the other. The resulting process of accretion is one of the most important in astrophysics. This book presents the first account of cataclysmic variables at an introductory level. Assuming no previous knowledge of the field, it explains the basic principles underlying the variability, while providing an extensive compilation of cataclysmic variable light curves. Aimed at amateur astronomers, undergraduates, and researchers, the main text is accessible to those with no mathematical background, while supplementary boxes present technical details and equations.

Physical Principle for Generation of Randomness

NASA Technical Reports Server (NTRS)

Zak, Michail

2009-01-01

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Brokering in Money and Mathematics.

ERIC Educational Resources Information Center

Hilgart, Faye

1996-01-01

Profiles Loy Gotham, an investment executive at PaineWebber, and how she manages stock portfolios for her clients. Distinctions are made between bonds, dividends, mutual funds, profits, and shares. Provides worksheet for tracking a stock. Describes how business was conducted in the past and how basic principles of supply and demand still apply.…

The Depletion Ratio

ERIC Educational Resources Information Center

Groetsch, Charles W.

2008-01-01

How fast does a tank drain? Of course this depends on the shape of the tank and is governed by a physical principle known as Torricelli's law. This note investigates some connections between tank shape and a mathematical function related to the time required for the tank to drain completely. The techniques employed provide some interesting…

What Spreadsheet and Database Skills Do Business Students Need?

ERIC Educational Resources Information Center

Coleman, Phillip D.; Blankenship, Ray J.

2017-01-01

The Principles of Information Systems course taught at a medium-sized Midwest University consists of Information Systems conceptual material plus Microsoft Excel and Access skills that the Information Systems faculty feel are most important to business students from all business disciplines. These skills range from using basic mathematic functions…

Measurement for Work. Teaching Guide and Sample Learning Activities.

ERIC Educational Resources Information Center

Angel, Margo; Bolton, Chris

This document is intended to help Australian technical and further education instructors in New South Wales (TAFE NSW) identify teaching principles and learning activities that they can use to help adult learners master the mathematics processes, knowledge, and skills needed to perform basic measurement tasks in today's workplace. The materials…

An Innovative Near-Peer Mentoring Model for Undergraduate and Secondary Students: STEM Focus

ERIC Educational Resources Information Center

Tenenbaum, Laura S.; Anderson, Margery K.; Jett, Marti; Yourick, Debra L.

2014-01-01

This study examined a novel mentoring model, "near-peer mentorship," that supports the development of mentee and mentor, incorporates established principles of mentoring, and offers unique opportunities to integrate research and teaching in a science, technology, engineering, and mathematics (STEM) internship. Using qualitative methods,…

6 Principles for Quantitative Reasoning and Modeling

ERIC Educational Resources Information Center

Weber, Eric; Ellis, Amy; Kulow, Torrey; Ozgur, Zekiye

2014-01-01

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

The Hardy-Weinberg Principle

ERIC Educational Resources Information Center

McMurran, Shawnee L.

2010-01-01

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

Optimization, an Important Stage of Engineering Design

ERIC Educational Resources Information Center

Kelley, Todd R.

2010-01-01

A number of leaders in technology education have indicated that a major difference between the technological design process and the engineering design process is analysis and optimization. The analysis stage of the engineering design process is when mathematical models and scientific principles are employed to help the designer predict design…

Report of the Action Committee on Agricultural Education.

ERIC Educational Resources Information Center

Taylor, Robert E.

This report is presented in four parts. Part one presents a philosophy of agricultural education. Part two describes the role of the biological sciences in agricultural education, important biological principles and concepts, and suggested programs for prospective students. Part three includes a discussion of the role of mathematics, chemistry and…

Applying the Principles of Specific Objectivity and of Generalizability to the Measurement of Change.

ERIC Educational Resources Information Center

Fischer, Gerhard H.

1987-01-01

A natural parameterization and formalization of the problem of measuring change in dichotomous data is developed. Mathematically-exact definitions of specific objectivity are presented, and the basic structures of the linear logistic test model and the linear logistic model with relaxed assumptions are clarified. (SLD)

Teaching Mass and Energy Balances by Experiment

ERIC Educational Resources Information Center

Orbey, Nese; De Jesús Vega, Marisel; Zalluhoglu, Fulya Sudur

2017-01-01

A general tank-draining problem was used as an experimental project in two undergraduate-level chemical engineering courses. The project aimed to illustrate the critical nature of experimentation in addition to use of mass and energy conservation principles in developing mathematical models that correctly describes a system. The students designed…

Evolving Agents as a Metaphor for the Developing Child

ERIC Educational Resources Information Center

Schlesinger, Matthew

2004-01-01

The emerging field of Evolutionary Computation (EC), inspired by neo-Darwinian principles (e.g. natural selection, mutation, etc.), offers developmental psychologists a wide array of mathematical tools for simulating ontogenetic processes. In this brief review, I begin by highlighting three of the approaches that EC researchers employ (Artificial…

Angular motion equations for a satellite with hinged flexible solar panel

NASA Astrophysics Data System (ADS)

Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

2016-11-01

Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

Implementing Recommendations for Introductory Biology by Writing a New Textbook

ERIC Educational Resources Information Center

Barsoum, Mark J.; Sellers, Patrick J.; Campbell, A. Malcolm; Heyer, Laurie J.; Paradise, Christopher J.

2013-01-01

We redesigned the undergraduate introductory biology course by writing a new textbook ("Integrating Concepts in Biology" ["ICB"]) that follows first principles of learning. Our approach emphasizes primary data interpretation and the utility of mathematics in biology, while de-emphasizing memorization. This redesign divides biology into five big…

Iteration, Not Induction

ERIC Educational Resources Information Center

Dobbs, David E.

2009-01-01

The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical induction or the well-ordering principle. The method of iteration depends only on the fact that any strictly decreasing sequence of…

An Experience Teaching an Undergraduate Level Course in Biophysics

ERIC Educational Resources Information Center

Feizabadi, Mitra Shojania

2009-01-01

The importance of including concepts, examples, and techniques from mathematics and the physical and information sciences in biology courses to fulfill the need of today's undergraduates has been the principle motivation for developing interdisciplinary biology-focused courses. Although this movement started many years ago, developing and offering…

Using Physical Models to Explain a Division Algorithm.

ERIC Educational Resources Information Center

Vest, Floyd

1985-01-01

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

Rockets: Educator's Guide with Activities in Science, Technology, Engineering and Mathematics

ERIC Educational Resources Information Center

Shearer, Deborah A.; Vogt, Gregory L.

2008-01-01

This guide provides teachers and students many opportunities. Chapters within the guide present the history of rocketry, National Aeronautics and Space Administration's (NASA's) 21st Century Space Exploration Policy, rocketry principles, and practical rocketry. These topics lay the foundation for what follows--a wealth of dynamic rocket science…

Peer-Assisted Learning in Mathematics: An Observational Study of Student Success

ERIC Educational Resources Information Center

Cheng, Dorothy; Walters, Matthew

2009-01-01

The Peer-Assisted Learning (PAL) program at the University of Minnesota has drawn from the best practices of Supplemental Instruction, Peer-Led Team Learning, Structured Learning Assistance, the Emerging Scholars Program, and other successful postsecondary peer cooperative learning models to establish guiding principles for structuring learning…

Spreadsheets and Bulgarian Goats

ERIC Educational Resources Information Center

Sugden, Steve

2012-01-01

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a…

Ground Water Flow No Longer A Mystery

ERIC Educational Resources Information Center

Lehr, Jay H.; Pettyjohn, Wayne A.

1976-01-01

Examined are the physical characteristics of ground water movement. Some potential pollution problems are identified. Models are used to explain mathematical and hydraulic principles of flow toward a pumping well and an effluent stream, flow around and through lenticular beds, and effects of pumping on the water table. (Author/MR)

Cognitive Principles of Problem Solving and Instruction. Final Report.

ERIC Educational Resources Information Center

Greeno, James G.; And Others

Research in this project studied cognitive processes involved in understanding and solving problems used in instruction in the domain of mathematics, and explored implications of these cognitive analyses for the design of instruction. Three general issues were addressed: knowledge required for understanding problems, knowledge of the conditions…

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Using category theory to assess the relationship between consciousness and integrated information theory.

PubMed

Tsuchiya, Naotsugu; Taguchi, Shigeru; Saigo, Hayato

2016-06-01

One of the most mysterious phenomena in science is the nature of conscious experience. Due to its subjective nature, a reductionist approach is having a hard time in addressing some fundamental questions about consciousness. These questions are squarely and quantitatively tackled by a recently developed theoretical framework, called integrated information theory (IIT) of consciousness. In particular, IIT proposes that a maximally irreducible conceptual structure (MICS) is identical to conscious experience. However, there has been no principled way to assess the claimed identity. Here, we propose to apply a mathematical formalism, category theory, to assess the proposed identity and suggest that it is important to consider if there exists a proper translation between the domain of conscious experience and that of the MICS. If such translation exists, we postulate that questions in one domain can be answered in the other domain; very difficult questions in the domain of consciousness can be resolved in the domain of mathematics. We claim that it is possible to empirically test if such a functor exists, by using a combination of neuroscientific and computational approaches. Our general, principled and empirical framework allows us to assess the relationship between the domain of consciousness and the domain of mathematical structures, including those suggested by IIT. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Promoting students’ mathematical problem-solving skills through 7e learning cycle and hypnoteaching model

NASA Astrophysics Data System (ADS)

Saleh, H.; Suryadi, D.; Dahlan, J. A.

2018-01-01

The aim of this research was to find out whether 7E learning cycle under hypnoteaching model can enhance students’ mathematical problem-solving skill. This research was quasi-experimental study. The design of this study was pretest-posttest control group design. There were two groups of sample used in the study. The experimental group was given 7E learning cycle under hypnoteaching model, while the control group was given conventional model. The population of this study was the student of mathematics education program at one university in Tangerang. The statistical analysis used to test the hypothesis of this study were t-test and Mann-Whitney U. The result of this study show that: (1) The students’ achievement of mathematical problem solving skill who obtained 7E learning cycle under hypnoteaching model are higher than the students who obtained conventional model; (2) There are differences in the students’ enhancement of mathematical problem-solving skill based on students’ prior mathematical knowledge (PMK) category (high, middle, and low).