Small Oscillations via Conservation of Energy

ERIC Educational Resources Information Center

Troy, Tia; Reiner, Megan; Haugen, Andrew J.; Moore, Nathan T.

2017-01-01

The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small…

Recursion, Computers and Art

ERIC Educational Resources Information Center

Kemp, Andy

2007-01-01

"Geomlab" is a functional programming language used to describe pictures that are made up of tiles. The beauty of "Geomlab" is that it introduces students to recursion, a very powerful mathematical concept, through a very simple and enticing graphical environment. Alongside the software is a series of eight worksheets which lead into producing…

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

PubMed

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

Divergence thrust loss calculations for convergent-divergent nozzles: Extensions to the classical case

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

1991-01-01

The analytical derivations of the non-axial thrust divergence losses for convergent-divergent nozzles are described as well as how these calculations are embodied in the Navy/NASA engine computer program. The convergent-divergent geometries considered are simple classic axisymmetric nozzles, two dimensional rectangular nozzles, and axisymmetric and two dimensional plug nozzles. A simple, traditional, inviscid mathematical approach is used to deduce the influence of the ineffectual non-axial thrust as a function of the nozzle exit divergence angle.

Fun with maths: exploring implications of mathematical models for malaria eradication.

PubMed

Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A

2014-12-11

Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

Graphical function mapping as a new way to explore cause-and-effect chains

USGS Publications Warehouse

Evans, Mary Anne

2016-01-01

Graphical function mapping provides a simple method for improving communication within interdisciplinary research teams and between scientists and nonscientists. This article introduces graphical function mapping using two examples and discusses its usefulness. Function mapping projects the outcome of one function into another to show the combined effect. Using this mathematical property in a simpler, even cartoon-like, graphical way allows the rapid combination of multiple information sources (models, empirical data, expert judgment, and guesses) in an intuitive visual to promote further discussion, scenario development, and clear communication.

The Identities Hidden in the Matching Laws, and Their Uses

ERIC Educational Resources Information Center

Thorne, David R.

2010-01-01

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

A Brief History of Partitions of Numbers, Partition Functions and Their Modern Applications

ERIC Educational Resources Information Center

Debnath, Lokenath

2016-01-01

This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and "k"-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's…

How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

Duan, Qi; Zhang, Huanling; Liu, Aikui; Li, Huaigu

2006-10-01

In this paper a new rational interpolation with a bi-quadratic denominator is developed to create a space surface using only values of the function being interpolated. The interpolation function has a simple and explicit rational mathematical representation. When the knots are equally spaced, the interpolating function can be expressed in matrix form, and this form has a symmetric property. The concept of integral weights coefficients of the interpolation is given, which describes the "weight" of the interpolation points in the local interpolating region.

On determining important aspects of mathematical models: Application to problems in physics and chemistry

NASA Technical Reports Server (NTRS)

Rabitz, Herschel

1987-01-01

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Falling head ponded infiltration in the nonlinear limit

NASA Astrophysics Data System (ADS)

Triadis, D.

2014-12-01

The Green and Ampt infiltration solution represents only an extreme example of behavior within a larger class of very nonlinear, delta function diffusivity soils. The mathematical analysis of these soils is greatly simplified by the existence of a sharp wetting front below the soil surface. Solutions for more realistic delta function soil models have recently been presented for infiltration under surface saturation without ponding. After general formulation of the problem, solutions for a full suite of delta function soils are derived for ponded surface water depleted by infiltration. Exact expressions for the cumulative infiltration as a function of time, or the drainage time as a function of the initial ponded depth may take implicit or parametric forms, and are supplemented by simple asymptotic expressions valid for small times, and small and large initial ponded depths. As with surface saturation without ponding, the Green-Ampt model overestimates the effect of the soil hydraulic conductivity. At the opposing extreme, a low-conductivity model is identified that also takes a very simple mathematical form and appears to be more accurate than the Green-Ampt model for larger ponded depths. Between these two, the nonlinear limit of Gardner's soil is recommended as a physically valid first approximation. Relative discrepancies between different soil models are observed to reach a maximum for intermediate values of the dimensionless initial ponded depth, and in general are smaller than for surface saturation without ponding.

Microcomputer-Assisted Mathematics: From Simple Interest to e.

ERIC Educational Resources Information Center

Kimberling, Clark

1985-01-01

The progression from simple interest to compound interest leads naturally and quickly to the number e, involving mathematical discovery learning through writing programs. Several programs are given, with suggestions for a teaching sequence. (MNS)

Segmentation-based wavelet transform for still-image compression

NASA Astrophysics Data System (ADS)

Mozelle, Gerard; Seghier, Abdellatif; Preteux, Francoise J.

1996-10-01

In order to address simultaneously the two functionalities, content-based scalability required by MPEG-4, we introduce a segmentation-based wavelet transform (SBWT). SBWT takes into account both the mathematical properties of multiresolution analysis and the flexibility of region-based approaches for image compression. The associated methodology has two stages: 1) image segmentation into convex and polygonal regions; 2) 2D-wavelet transform of the signal corresponding to each region. In this paper, we have mathematically studied a method for constructing a multiresolution analysis (VjOmega)j (epsilon) N adapted to a polygonal region which provides an adaptive region-based filtering. The explicit construction of scaling functions, pre-wavelets and orthonormal wavelets bases defined on a polygon is carried out by using scaling functions is established by using the theory of Toeplitz operators. The corresponding expression can be interpreted as a location property which allow defining interior and boundary scaling functions. Concerning orthonormal wavelets and pre-wavelets, a similar expansion is obtained by taking advantage of the properties of the orthogonal projector P(V(j(Omega )) perpendicular from the space Vj(Omega ) + 1 onto the space (Vj(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

Modeling a Neural Network as a Teaching Tool for the Learning of the Structure-Function Relationship

ERIC Educational Resources Information Center

Salinas, Dino G.; Acevedo, Cristian; Gomez, Christian R.

2010-01-01

The authors describe an activity they have created in which students can visualize a theoretical neural network whose states evolve according to a well-known simple law. This activity provided an uncomplicated approach to a paradigm commonly represented through complex mathematical formulation. From their observations, students learned many basic…

Deriving the Regression Equation without Using Calculus

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

Investigation of the blood behaviour and vascular diseases by using mathematical physic principles

NASA Astrophysics Data System (ADS)

Yardimci, Ahmet; Simsek, Buket

2017-07-01

In this paper we prepare a short survey for using of mathematical physic principles in blood flow and vascular diseases researches. The study of the behavior of blood flow in the blood vessels provides understanding on connection between flow and the development of dieseases such as atherosclerosis, thrombosis, aneurysms etc. and how the flow dynamics is changed under these conditions. Blood flow phenomena are often too complex that it would be possible to describe them entirely analytically, although simple models, such as Poiseuille model, can still provide some insight into blood flow. Blood is not an "ideal fluid" and energy is lost as flowing blood overcomes resistance. Resistance to blood flow is a function of viscosity, vessel radius, and vessel length. So, mathematical Physic principles are useful tools for blood flow research studies. Blood flow is a function of pressure gradient and resistance and resistance to flow can be estimates using Poiseuille's law. Reynold's number can be used to determine whether flow is laminar or turbulent.

An Alternative Derivation of the Energy Levels of the "Particle on a Ring" System

NASA Astrophysics Data System (ADS)

Vincent, Alan

1996-10-01

All acceptable wave functions must be continuous mathematical functions. This criterion limits the acceptable functions for a particle in a linear 1-dimensional box to sine functions. If, however, the linear box is bent round into a ring, acceptable wave functions are those which are continuous at the 'join'. On this model some acceptable linear functions become unacceptable for the ring and some unacceptable cosine functions become acceptable. This approach can be used to produce a straightforward derivation of the energy levels and wave functions of the particle on a ring. These simple wave mechanical systems can be used as models of linear and cyclic delocalised systems such as conjugated hydrocarbons or the benzene ring. The promotion energy of an electron can then be used to calculate the wavelength of absorption of uv light. The simple model gives results of the correct order of magnitude and shows that, as the chain length increases, the uv maximum moves to longer wavelengths, as found experimentally.

Simple arithmetic: not so simple for highly math anxious individuals.

PubMed

Chang, Hyesang; Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G

2017-12-01

Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low-compared to high-math anxious individuals perform better when they activate this network less-a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. © The Author (2017). Published by Oxford University Press.

Simple arithmetic: not so simple for highly math anxious individuals

PubMed Central

Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G

2017-01-01

Abstract Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. PMID:29140499

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

PubMed

Marill, Keith A

2004-01-01

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

Is the Reaction Equilibrium Composition in Non-ideal Mixtures Uniquely Determined by the Initial Composition?

NASA Astrophysics Data System (ADS)

Sefcik, Jan

1998-05-01

Reaction equilibrium can be mathematically described by the equilibrium equation and the reaction equilibrium composition can be calculated by solving this equation. It can be proved by non-elementary thermodynamic arguments that for a generic system with given initial composition, temperature and pressure there is a unique stable equilibrium state corresponding to the global minimum of the Gibbs free energy function. However, when the concept of equilibrium is introduced in undergraduate chemistry and chemical engineering courses, such arguments are generally not accessible. When there is a single reaction equilibrium among mixture components and the components form an ideal mixture, it has been demonstrated by a simple, elegant mathematical argument that there is a unique composition satisfying the equilibrium equation. It has been also suggested that this particular argument extends to non-ideal mixtures by simply incorporating activity coefficients. We show that the argument extension to non-ideal systems is not generally valid. Increasing non-ideality can result in non-monotonicity of the function crucial for the simple uniqueness argument, and only later it leads to non-uniqueness and hence phase separation. The main feature responsible for this is a composition dependence of activity coefficients in non-ideal mixtures.

Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure.

PubMed

Abdelnour, Farras; Dayan, Michael; Devinsky, Orrin; Thesen, Thomas; Raj, Ashish

2018-05-15

How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses. Copyright © 2018. Published by Elsevier Inc.

kappa-Version of Finite Element Method: A New Mathematical and Computational Framework for BVP and IVP

DTIC Science & Technology

2007-01-01

differentiability, fluid-solid interaction, error estimation, re-discretization, moving meshes 16. SECURITY CLASSIFICATION OF: 17 . LIMITATION OF 18. NUMBER...method the weight function is an indepen- dent function v = 0 6 4Ph , with v = 0 on F, if W = W0 on F1. 2. Galerkin method (GM): If Wh is an approximation...This can be demonstrated by considering a simple I-D case (like described above) in which the discretization 17 is uniform with characteristic length

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

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

Establishment of the mathematical model for diagnosing the engine valve faults by genetic programming

NASA Astrophysics Data System (ADS)

Yang, Wen-Xian

2006-05-01

Available machine fault diagnostic methods show unsatisfactory performances on both on-line and intelligent analyses because their operations involve intensive calculations and are labour intensive. Aiming at improving this situation, this paper describes the development of an intelligent approach by using the Genetic Programming (abbreviated as GP) method. Attributed to the simple calculation of the mathematical model being constructed, different kinds of machine faults may be diagnosed correctly and quickly. Moreover, human input is significantly reduced in the process of fault diagnosis. The effectiveness of the proposed strategy is validated by an illustrative example, in which three kinds of valve states inherent in a six-cylinders/four-stroke cycle diesel engine, i.e. normal condition, valve-tappet clearance and gas leakage faults, are identified. In the example, 22 mathematical functions have been specially designed and 8 easily obtained signal features are used to construct the diagnostic model. Different from existing GPs, the diagnostic tree used in the algorithm is constructed in an intelligent way by applying a power-weight coefficient to each feature. The power-weight coefficients vary adaptively between 0 and 1 during the evolutionary process. Moreover, different evolutionary strategies are employed, respectively for selecting the diagnostic features and functions, so that the mathematical functions are sufficiently utilized and in the meantime, the repeated use of signal features may be fully avoided. The experimental results are illustrated diagrammatically in the following sections.

A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

NASA Technical Reports Server (NTRS)

Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.

2009-01-01

This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.

Closed-form summations of Dowker's and related trigonometric sums

NASA Astrophysics Data System (ADS)

Cvijović, Djurdje; Srivastava, H. M.

2012-09-01

Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

Mathematical prediction of core body temperature from environment, activity, and clothing: The heat strain decision aid (HSDA).

PubMed

Potter, Adam W; Blanchard, Laurie A; Friedl, Karl E; Cadarette, Bruce S; Hoyt, Reed W

2017-02-01

Physiological models provide useful summaries of complex interrelated regulatory functions. These can often be reduced to simple input requirements and simple predictions for pragmatic applications. This paper demonstrates this modeling efficiency by tracing the development of one such simple model, the Heat Strain Decision Aid (HSDA), originally developed to address Army needs. The HSDA, which derives from the Givoni-Goldman equilibrium body core temperature prediction model, uses 16 inputs from four elements: individual characteristics, physical activity, clothing biophysics, and environmental conditions. These inputs are used to mathematically predict core temperature (T c ) rise over time and can estimate water turnover from sweat loss. Based on a history of military applications such as derivation of training and mission planning tools, we conclude that the HSDA model is a robust integration of physiological rules that can guide a variety of useful predictions. The HSDA model is limited to generalized predictions of thermal strain and does not provide individualized predictions that could be obtained from physiological sensor data-driven predictive models. This fully transparent physiological model should be improved and extended with new findings and new challenging scenarios. Published by Elsevier Ltd.

Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization.

PubMed

Das, Swagatam; Mukhopadhyay, Arpan; Roy, Anwit; Abraham, Ajith; Panigrahi, Bijaya K

2011-02-01

The theoretical analysis of evolutionary algorithms is believed to be very important for understanding their internal search mechanism and thus to develop more efficient algorithms. This paper presents a simple mathematical analysis of the explorative search behavior of a recently developed metaheuristic algorithm called harmony search (HS). HS is a derivative-free real parameter optimization algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. This paper analyzes the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. A simple but very useful modification to the classical HS has been proposed in light of the mathematical analysis undertaken here. A comparison with the most recently published variants of HS and four other state-of-the-art optimization algorithms over 15 unconstrained and five constrained benchmark functions reflects the efficiency of the modified HS in terms of final accuracy, convergence speed, and robustness.

Software Template for Instruction in Mathematics

NASA Technical Reports Server (NTRS)

Shelton, Robert O.; Moebes, Travis A.; Beall, Anna

2005-01-01

Intelligent Math Tutor (IMT) is a software system that serves as a template for creating software for teaching mathematics. IMT can be easily connected to artificial-intelligence software and other analysis software through input and output of files. IMT provides an easy-to-use interface for generating courses that include tests that contain both multiple-choice and fill-in-the-blank questions, and enables tracking of test scores. IMT makes it easy to generate software for Web-based courses or to manufacture compact disks containing executable course software. IMT also can function as a Web-based application program, with features that run quickly on the Web, while retaining the intelligence of a high-level language application program with many graphics. IMT can be used to write application programs in text, graphics, and/or sound, so that the programs can be tailored to the needs of most handicapped persons. The course software generated by IMT follows a "back to basics" approach of teaching mathematics by inducing the student to apply creative mathematical techniques in the process of learning. Students are thereby made to discover mathematical fundamentals and thereby come to understand mathematics more deeply than they could through simple memorization.

Basic Phage Mathematics.

PubMed

Abedon, Stephen T; Katsaounis, Tena I

2018-01-01

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

New Challenges in the Teaching of Mathematics.

ERIC Educational Resources Information Center

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

Making Temporal Logic Calculational: A Tool for Unification and Discovery

NASA Astrophysics Data System (ADS)

Boute, Raymond

In temporal logic, calculational proofs beyond simple cases are often seen as challenging. The situation is reversed by making temporal logic calculational, yielding shorter and clearer proofs than traditional ones, and serving as a (mental) tool for unification and discovery. A side-effect of unifying theories is easier access by practicians. The starting point is a simple generic (software tool independent) Functional Temporal Calculus (FTC). Specific temporal logics are then captured via endosemantic functions. This concept reflects tacit conventions throughout mathematics and, once identified, is general and useful. FTC also yields a reasoning style that helps discovering theorems by calculation rather than just proving given facts. This is illustrated by deriving various theorems, most related to liveness issues in TLA+, and finding strengthenings of known results. Educational issues are addressed in passing.

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

A Mathematical Diet Model

ERIC Educational Resources Information Center

Toumasis, Charalampos

2004-01-01

Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

Voltage transfer function as an optical method to characterize electrical properties of liquid crystal devices.

PubMed

Bateman, J; Proctor, M; Buchnev, O; Podoliak, N; D'Alessandro, G; Kaczmarek, M

2014-07-01

The voltage transfer function is a rapid and visually effective method to determine the electrical response of liquid crystal (LC) systems using optical measurements. This method relies on crosspolarized intensity measurements as a function of the frequency and amplitude of the voltage applied to the device. Coupled with a mathematical model of the device it can be used to determine the device time constants and electrical properties. We validate the method using photorefractive LC cells and determine the main time constants and the voltage dropped across the layers using a simple nonlinear filter model.

Air-cooling mathematical analysis as inferred from the air-temperature observation during the 1st total occultation of the Sun of the 21st century at Lusaka, Zambia

NASA Astrophysics Data System (ADS)

Peñaloza-Murillo, Marcos A.; Pasachoff, Jay M.

2015-04-01

We analyze mathematically air temperature measurements made near the ground by the Williams College expedition to observe the first total occultation of the Sun [TOS (commonly known as a total solar eclipse)] of the 21st century in Lusaka, Zambia, in the afternoon of June 21, 2001. To do so, we have revisited some earlier and contemporary methods to test their usefulness for this analysis. Two of these methods, based on a radiative scheme for solar radiation modeling and that has been originally applied to a morning occultation, have successfully been combined to obtain the delay function for an afternoon occultation, via derivation of the so-called instantaneous temperature profiles. For this purpose, we have followed the suggestion given by the third of these previously applied methods to calculate this function, although by itself it failed to do so at least for this occultation. The analysis has taken into account the limb-darkening, occultation and obscuration functions. The delay function obtained describes quite fairly the lag between the solar radiation variation and the delayed air temperature measured. Also, in this investigation, a statistical study has been carried out to get information on the convection activity produced during this event. For that purpose, the fluctuations generated by turbulence has been studied by analyzing variance and residuals. The results, indicating an irreversible steady decrease of this activity, are consistent with those published by other studies. Finally, the air temperature drop due to this event is well estimated by applying the empirical scheme given by the fourth of the previously applied methods, based on the daily temperature amplitude and the standardized middle time of the occultation. It is demonstrated then that by using a simple set of air temperature measurements obtained during solar occultations, along with some supplementary data, a simple mathematical analysis can be achieved by applying of the four methods reviewed here.

Applying a Conceptual Mini Game for Supporting Simple Mathematical Calculation Skills: Students' Perceptions and Considerations

ERIC Educational Resources Information Center

Panagiotakopoulos, Chris T.

2011-01-01

Mathematics is an area of study that particularly lacks student enthusiasm. Nevertheless, with the help of educational games, any phobias concerning mathematics can be considerably decreased and mathematics can become more appealing. In this study, an educational game addressing mathematics was designed, developed and evaluated by a sample of 33…

Simulating and mapping spatial complexity using multi-scale techniques

USGS Publications Warehouse

De Cola, L.

1994-01-01

A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields. -Author

Mathematical Gossip: Relevance and Context in the Mathematics Classroom

ERIC Educational Resources Information Center

Callingham, Rosemary

2004-01-01

Using mathematical gossip in the classroom allows teachers to expand their students' horizons, and provide pathways to improvement of understanding. The expansion of a simple idea into another mathematical context can enrich a student's learning. In particular it may help to bridge the gap between purely procedural approaches and a conceptual…

Bragg-cell receiver study

NASA Technical Reports Server (NTRS)

Wilson, Lonnie A.

1987-01-01

Bragg-cell receivers are employed in specialized Electronic Warfare (EW) applications for the measurement of frequency. Bragg-cell receiver characteristics are fully characterized for simple RF emitter signals. This receiver is early in its development cycle when compared to the IFM receiver. Functional mathematical models are derived and presented in this report for the Bragg-cell receiver. Theoretical analysis is presented and digital computer signal processing results are presented for the Bragg-cell receiver. Probability density function analysis are performed for output frequency. Probability density function distributions are observed to depart from assumed distributions for wideband and complex RF signals. This analysis is significant for high resolution and fine grain EW Bragg-cell receiver systems.

Asymptotic stability and instability of large-scale systems. [using vector Liapunov functions

NASA Technical Reports Server (NTRS)

Grujic, L. T.; Siljak, D. D.

1973-01-01

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.

Mathematical thinking and origami

NASA Astrophysics Data System (ADS)

Wares, Arsalan

2016-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.

Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

PubMed

Dinç, Erdal; Ozdemir, Abdil

2005-01-01

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

Non-symbolic arithmetic in adults and young children.

PubMed

Barth, Hilary; La Mont, Kristen; Lipton, Jennifer; Dehaene, Stanislas; Kanwisher, Nancy; Spelke, Elizabeth

2006-01-01

Five experiments investigated whether adults and preschool children can perform simple arithmetic calculations on non-symbolic numerosities. Previous research has demonstrated that human adults, human infants, and non-human animals can process numerical quantities through approximate representations of their magnitudes. Here we consider whether these non-symbolic numerical representations might serve as a building block of uniquely human, learned mathematics. Both adults and children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Success at these tasks did not depend on non-numerical continuous quantities, modality-specific quantity information, the adoption of alternative non-arithmetic strategies, or learned symbolic arithmetic knowledge. Abstract numerical quantity representations therefore are computationally functional and may provide a foundation for formal mathematics.

A general consumer-resource population model

USGS Publications Warehouse

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

2015-01-01

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

Equilibria of perceptrons for simple contingency problems.

PubMed

Dawson, Michael R W; Dupuis, Brian

2012-08-01

The contingency between cues and outcomes is fundamentally important to theories of causal reasoning and to theories of associative learning. Researchers have computed the equilibria of Rescorla-Wagner models for a variety of contingency problems, and have used these equilibria to identify situations in which the Rescorla-Wagner model is consistent, or inconsistent, with normative models of contingency. Mathematical analyses that directly compare artificial neural networks to contingency theory have not been performed, because of the assumed equivalence between the Rescorla-Wagner learning rule and the delta rule training of artificial neural networks. However, recent results indicate that this equivalence is not as straightforward as typically assumed, suggesting a strong need for mathematical accounts of how networks deal with contingency problems. One such analysis is presented here, where it is proven that the structure of the equilibrium for a simple network trained on a basic contingency problem is quite different from the structure of the equilibrium for a Rescorla-Wagner model faced with the same problem. However, these structural differences lead to functionally equivalent behavior. The implications of this result for the relationships between associative learning, contingency theory, and connectionism are discussed.

A Fast Method of Deriving the Kirchhoff Formula for Moving Surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Posey, Joe W.

2007-01-01

The Kirchhoff formula for a moving surface is very useful in many wave propagation problems, particularly in the prediction of noise from rotating machinery. Several publications in the last two decades have presented derivations of the Kirchhoff formula for moving surfaces in both time and frequency domains. Here we present a method originally developed by Farassat and Myers in time domain that is both simple and direct. It is based on generalized function theory and the useful concept of imbedding the problem in the unbounded three-dimensional space. We derive an inhomogeneous wave equation with the source terms that involve Dirac delta functions with their supports on the moving data surface. This wave equation is then solved using the simple free space Green's function of the wave equation resulting in the Kirchhoff formula. The algebraic manipulations are minimal and simple. We do not need the Green's theorem in four dimensions and there is no ambiguity in the interpretation of any terms in the final formulas. Furthermore, this method also gives the simplest derivation of the classical Kirchhoff formula which has a fairly lengthy derivation in physics and applied mathematics books. The Farassat-Myers method can be used easily in frequency domain.

Unconditionally Secure Credit/Debit Card Chip Scheme and Physical Unclonable Function

NASA Astrophysics Data System (ADS)

Kish, Laszlo B.; Entesari, Kamran; Granqvist, Claes-Göran; Kwan, Chiman

The statistical-physics-based Kirchhoff-law-Johnson-noise (KLJN) key exchange offers a new and simple unclonable system for credit/debit card chip authentication and payment. The key exchange, the authentication and the communication are unconditionally secure so that neither mathematics- nor statistics-based attacks are able to crack the scheme. The ohmic connection and the short wiring lengths between the chips in the card and the terminal constitute an ideal setting for the KLJN protocol, and even its simplest versions offer unprecedented security and privacy for credit/debit card chips and applications of physical unclonable functions (PUFs).

A survey of functional programming language principles

NASA Technical Reports Server (NTRS)

Holloway, C. M.

1986-01-01

Research in the area of functional programming languages has intensified in the 8 years since John Backus' Turing Award Lecture on the topic was published. The purpose of this paper is to present a survey of the ideas of functional programming languages. The paper assumes the reader is comfortable with mathematics and has knowledge of the basic principles of traditional programming languages, but does not assume any prior knowledge of the ideas of functional languages. A simple functional language is defined and used to illustrate the basic ideas. Topics discussed include the reasons for developing functional languages, methods of expressing concurrency, the algebra of functional programming languages, program transformation techniques, and implementations of functional languages. Existing functional languages are also mentioned. The paper concludes with the author's opinions as to the future of functional languages. An annotated bibliography on the subject is also included.

A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient.

PubMed

Biktashev, Vadim N

2014-04-01

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.

Arithmetic processing in the brain shaped by cultures

PubMed Central

Tang, Yiyuan; Zhang, Wutian; Chen, Kewei; Feng, Shigang; Ji, Ye; Shen, Junxian; Reiman, Eric M.; Liu, Yijun

2006-01-01

The universal use of Arabic numbers in mathematics raises a question whether these digits are processed the same way in people speaking various languages, such as Chinese and English, which reflect differences in Eastern and Western cultures. Using functional MRI, we demonstrated a differential cortical representation of numbers between native Chinese and English speakers. Contrasting to native English speakers, who largely employ a language process that relies on the left perisylvian cortices for mental calculation such as a simple addition task, native Chinese speakers, instead, engage a visuo-premotor association network for the same task. Whereas in both groups the inferior parietal cortex was activated by a task for numerical quantity comparison, functional MRI connectivity analyses revealed a functional distinction between Chinese and English groups among the brain networks involved in the task. Our results further indicate that the different biological encoding of numbers may be shaped by visual reading experience during language acquisition and other cultural factors such as mathematics learning strategies and education systems, which cannot be explained completely by the differences in languages per se. PMID:16815966

A Highly Similar Mathematical Model for Cerebral Blood Flow Velocity in Geriatric Patients with Suspected Cerebrovascular Disease

NASA Astrophysics Data System (ADS)

Liu, Bo; Li, Qi; Wang, Jisheng; Xiang, Hu; Ge, Hong; Wang, Hui; Xie, Peng

2015-10-01

Cerebral blood flow velocity(CBFV) is an important parameter for study of cerebral hemodynamics. However, a simple and highly similar mathematical model has not yet been established for analyzing CBFV. To alleviate this issue, through TCD examination in 100 geriatric patients with suspected cerebrovascular disease (46 males and 54 females), we established a representative eighth-order Fourier function Vx(t) that simulates the CBFV. The measured TCD waveforms were compared to those derived from Vx(t), an illustrative Kolmogorov-Smirnov test was employed to determine the validity. The results showed that the TCD waves could been reconstructed for patients with different CBFVs by implementing their variable heart rates and the formulated maximum/minimum of Vx(t). Comparisons between derived and measured TCD waveforms suggest that the two waveforms are very similar. The results confirm that CBFV can be well-modeled through an eighth-order Fourier function. This function Vx(t) can be used extensively for a prospective study of cerebral hemodynamics in geriatric patients with suspected cerebrovascular disease.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Electromagnetic density of modes for a finite-size three-dimensional structure.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Centini, Marco; Scalora, Michael; Bloemer, Mark J

2004-05-01

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

Games for Developing Mathematical Strategy.

ERIC Educational Resources Information Center

Williford, Harold

1992-01-01

The three middle school games described in this article focus on problem solving and mathematical reasoning skills. Included are Solomon's game, nine mens' morris, and nim-with-cards which all offer not only high student interest and strong mathematical value but also simple rules, ease of construction, and attractiveness for repeated play.…

Student Attrition in Mathematics E-Learning

ERIC Educational Resources Information Center

Smith, Glenn Gordon; Ferguson, David

2005-01-01

Qualitative studies indicate that mathematics does not work well in e-learning. The current study used quantitative methods to investigate more objectively the extent of problems with mathematics in e-learning. The authors used student attrition as a simple measure of student satisfaction and course viability in two studies, one investigating…

Connecting Dynamic Representations of Simple Mathematical Objects with the Construction and Exploration of Conic Sections

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Espinosa-Perez, Hugo; Reyes-Rodriguez, Aaron

2008-01-01

Different technological artefacts may offer distinct opportunities for students to develop resources and strategies to formulate, comprehend and solve mathematical problems. In particular, the use of dynamic software becomes relevant to assemble geometric configurations that may help students reconstruct and examine mathematical relationships. In…

Learning to Calculate and Learning Mathematics.

ERIC Educational Resources Information Center

Fearnley-Sander, Desmond

1980-01-01

A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

Mathematical toy model inspired by the problem of the adaptive origins of the sexual orientation continuum

NASA Astrophysics Data System (ADS)

Skinner, Brian

2016-09-01

Same-sex sexual behaviour is ubiquitous in the animal kingdom, but its adaptive origins remain a prominent puzzle. Here, I suggest the possibility that same-sex sexual behaviour arises as a consequence of the competition between an evolutionary drive for a wide diversity in traits, which improves the adaptability of a population, and a drive for sexual dichotomization of traits, which promotes opposite-sex attraction and increases the rate of reproduction. This trade-off is explored via a simple mathematical `toy model'. The model exhibits a number of interesting features and suggests a simple mathematical form for describing the sexual orientation continuum.

Using mathematical software to design power electronic converters

NASA Astrophysics Data System (ADS)

Hinov, Nikolay; Hranov, Tsveti

2017-12-01

In the paper is presented mathematical software, which was used for design of power electronic devices. Examined to different example, which are applied to designing electronic converters. In this way, it is possible to play different combinations of the circuit elements by simple means, thus optimizing according to certain criteria and limitations. Free software with a simple and intuitive interface is selected. No special user training is required to work with it and no further training is required. The use of mathematical software greatly facilitates the design, assists and makes it attractive and accessible to a wider range of students and specialists in power electronics training.

Mathematical toy model inspired by the problem of the adaptive origins of the sexual orientation continuum.

PubMed

Skinner, Brian

2016-09-01

Same-sex sexual behaviour is ubiquitous in the animal kingdom, but its adaptive origins remain a prominent puzzle. Here, I suggest the possibility that same-sex sexual behaviour arises as a consequence of the competition between an evolutionary drive for a wide diversity in traits, which improves the adaptability of a population, and a drive for sexual dichotomization of traits, which promotes opposite-sex attraction and increases the rate of reproduction. This trade-off is explored via a simple mathematical 'toy model'. The model exhibits a number of interesting features and suggests a simple mathematical form for describing the sexual orientation continuum.

Functional diversity through the mean trait dissimilarity: resolving shortcomings with existing paradigms and algorithms.

PubMed

de Bello, Francesco; Carmona, Carlos P; Lepš, Jan; Szava-Kovats, Robert; Pärtel, Meelis

2016-04-01

While an increasing number of indices for estimating the functional trait diversity of biological communities are being proposed, there is a growing demand by ecologists to clarify their actual implications and simplify index selection. Several key indices relate to mean trait dissimilarity between species within biological communities. Among them, the most widely used include (a) the mean species pairwise dissimilarity (MPD) and (b) the Rao quadratic entropy (and related indices). These indices are often regarded as redundant and promote the unsubstantiated yet widely held view that Rao is a form of MPD. Worryingly, existing R functions also do not always simplify the use and differentiation of these indices. In this paper, we show various distinctions between these two indices that warrant mathematical and biological consideration. We start by showing an existing form of MPD that considers species abundances and is different from Rao both mathematically and conceptually. We then show that the mathematical relationship between MPD and Rao can be presented simply as Rao = MPD × Simpson, where the Simpson diversity index is defined as 1 - dominance. We further show that this relationship is maintained for both species abundances and presence/absence. This evidence dismantles the paradigm that the Rao diversity is an abundance-weighted form of MPD and indicates that both indices can differ substantially at low species diversities. We discuss the different interpretations of trait diversity patterns in biological communities provided by Rao and MPD and then provide a simple R function, called "melodic," which avoids the unintended results that arise from existing mainstream functions.

Cognitive Enhancement or Cognitive Cost: Trait-Specific Outcomes of Brain Stimulation in the Case of Mathematics Anxiety

PubMed Central

Sarkar, Amar; Dowker, Ann

2014-01-01

The surge in noninvasive brain stimulation studies investigating cognitive enhancement has neglected the effect of interindividual differences, such as traits, on stimulation outcomes. Using the case of mathematics anxiety in a sample of healthy human participants in a placebo-controlled, double-blind, crossover experiment, we show that identical transcranial direct current stimulation (tDCS) exerts opposite behavioral and physiological effects depending on individual trait levels. Mathematics anxiety is the negative emotional response elicited by numerical tasks, impairing mathematical achievement. tDCS was applied to the dorsolateral prefrontal cortex, a frequent target for modulating emotional regulation. It improved reaction times on simple arithmetic decisions and decreased cortisol concentrations (a biomarker of stress) in high mathematics anxiety individuals. In contrast, tDCS impaired reaction times for low mathematics anxiety individuals and prevented a decrease in cortisol concentration compared with sham stimulation. Both groups showed a tDCS-induced side effect—impaired executive control in a flanker task—a cognitive function subserved by the stimulated region. These behavioral and physiological double dissociations have implications for brain stimulation research by highlighting the role of individual traits in experimental findings. Brain stimulation clearly does not produce uniform benefits, even applied in the same configuration during the same tasks, but may interact with traits to produce markedly opposed outcomes. PMID:25505313

Cognitive enhancement or cognitive cost: trait-specific outcomes of brain stimulation in the case of mathematics anxiety.

PubMed

Sarkar, Amar; Dowker, Ann; Cohen Kadosh, Roi

2014-12-10

The surge in noninvasive brain stimulation studies investigating cognitive enhancement has neglected the effect of interindividual differences, such as traits, on stimulation outcomes. Using the case of mathematics anxiety in a sample of healthy human participants in a placebo-controlled, double-blind, crossover experiment, we show that identical transcranial direct current stimulation (tDCS) exerts opposite behavioral and physiological effects depending on individual trait levels. Mathematics anxiety is the negative emotional response elicited by numerical tasks, impairing mathematical achievement. tDCS was applied to the dorsolateral prefrontal cortex, a frequent target for modulating emotional regulation. It improved reaction times on simple arithmetic decisions and decreased cortisol concentrations (a biomarker of stress) in high mathematics anxiety individuals. In contrast, tDCS impaired reaction times for low mathematics anxiety individuals and prevented a decrease in cortisol concentration compared with sham stimulation. Both groups showed a tDCS-induced side effect-impaired executive control in a flanker task-a cognitive function subserved by the stimulated region. These behavioral and physiological double dissociations have implications for brain stimulation research by highlighting the role of individual traits in experimental findings. Brain stimulation clearly does not produce uniform benefits, even applied in the same configuration during the same tasks, but may interact with traits to produce markedly opposed outcomes. Copyright © 2014 Sarkar et al.

ECOLOGICAL THEORY. A general consumer-resource population model.

PubMed

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

2015-08-21

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

A Walsh Function Module Users' Manual

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2014-01-01

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

Changing Beliefs about Teaching in Large Undergraduate Mathematics Classes

ERIC Educational Resources Information Center

Kensington-Miller, Barbara; Sneddon, Jamie; Yoon, Caroline; Stewart, Sepideh

2013-01-01

Many lecturers use teacher-centred styles of teaching in large undergraduate mathematics classes, often believing in the effectiveness of such pedagogy. Changing these beliefs about how mathematics should be taught is not a simple process and many academic staff are reluctant to change their ways of lecturing due to tradition and ease. This study…

And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

ERIC Educational Resources Information Center

Street, Garrett M.; Laubach, Timothy A.

2013-01-01

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

A Simple Model for a SARS Epidemic

ERIC Educational Resources Information Center

Ang, Keng Cheng

2004-01-01

In this paper, we examine the use of an ordinary differential equation in modelling the SARS outbreak in Singapore. The model provides an excellent example of using mathematics in a real life situation. The mathematical concepts involved are accessible to students with A level Mathematics backgrounds. Data for the SARS epidemic in Singapore are…

Math in Plain English: Literacy Strategies for the Mathematics Classroom

ERIC Educational Resources Information Center

Benjamin, Amy

2011-01-01

Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like "value" and "portion" seem to mislead them? Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak,…

The NCTM High School Curriculum Project: Why It Matters to You

ERIC Educational Resources Information Center

Martin, W. Gary

2009-01-01

This article discusses "Focus in High School Mathematics: Reasoning and Sense Making", a new (2009) publication of the National Council of Teachers of Mathematics (NCTM). Its message is simple: Reasoning and sense making provide a focus for high school mathematics that will give students a foundation for their future success. The publication…

Modeling the radiation pattern of LEDs.

PubMed

Moreno, Ivan; Sun, Ching-Cherng

2008-02-04

Light-emitting diodes (LEDs) come in many varieties and with a wide range of radiation patterns. We propose a general, simple but accurate analytic representation for the radiation pattern of the light emitted from an LED. To accurately render both the angular intensity distribution and the irradiance spatial pattern, a simple phenomenological model takes into account the emitting surfaces (chip, chip array, or phosphor surface), and the light redirected by both the reflecting cup and the encapsulating lens. Mathematically, the pattern is described as the sum of a maximum of two or three Gaussian or cosine-power functions. The resulting equation is widely applicable for any kind of LED of practical interest. We accurately model a wide variety of radiation patterns from several world-class manufacturers.

Econometric model for age- and population-dependent radiation exposures

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

Sandquist, G.M.; Slaughter, D.M.; Rogers, V.C.

1991-01-01

The economic impact associated with ionizing radiation exposures in a given human population depends on numerous factors including the individual's mean economic status as a function age, the age distribution of the population, the future life expectancy at each age, and the latency period for the occurrence of radiation-induced health effects. A simple mathematical model has been developed that provides an analytical methodology for estimating the societal econometrics associated with radiation effects are to be assessed and compared for economic evaluation.

Mathematical model of the solar radiation force and torques acting on the components of a spacecraft

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1971-01-01

General expressions for the solar radiation force and torques are derived in the vectorial form for any given reflecting surface, provided that the reflecting characteristics of the surface, as well as the value of the solar constant, are known. An appropriate choice of a spacecraft-fixed frame of reference leads to relatively simple expressions for the solar radiation forces and torques in terms of the functions of the sun-spacecraft-earth angle.

Hierarchical thinking in network biology: the unbiased modularization of biochemical networks.

PubMed

Papin, Jason A; Reed, Jennifer L; Palsson, Bernhard O

2004-12-01

As reconstructed biochemical reaction networks continue to grow in size and scope, there is a growing need to describe the functional modules within them. Such modules facilitate the study of biological processes by deconstructing complex biological networks into conceptually simple entities. The definition of network modules is often based on intuitive reasoning. As an alternative, methods are being developed for defining biochemical network modules in an unbiased fashion. These unbiased network modules are mathematically derived from the structure of the whole network under consideration.

Mathematical neuroscience: from neurons to circuits to systems.

PubMed

Gutkin, Boris; Pinto, David; Ermentrout, Bard

2003-01-01

Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.

High School Forum: Brief Introduction to the Three Laws of Thermodynamics

ERIC Educational Resources Information Center

Herron, J. Dudley

1975-01-01

Because thermodynamics is usually presented in a highly mathematical context, many students fail to comprehend even its intuitive aspects. Provides simple explanations, without complicated mathematics, for the three thermodynamics laws. (MLH)

Mechanical system diagnostics using vibration testing techniques

NASA Technical Reports Server (NTRS)

Mcleod, Catherine D.; Raju, P. K.; Crocker, M. J.

1990-01-01

The 'Cepstrum' technique of vibration-path identification allows the recovery of the transfer function of a system with little knowledge as to its excitation force, by means of a mathematical manipulation of the system output in conjunction with subtraction of part of the output and suitable signal processing. An experimental program has been conducted to evaluate the usefulness of this technique in the cases of simple, cantilever-beam and free-free plate structures as well as in that of a complex mechanical system. On the basis of the transfer functions thus recovered, it was possible to evaluate the shifts in the resonance frequencies of a structure due to the presence of defects.

A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System

NASA Technical Reports Server (NTRS)

Torres-Pomales, Wilfredo

2015-01-01

This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.

A brief history of partitions of numbers, partition functions and their modern applications

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2016-04-01

'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.

Housing decision making methods for initiation development phase process

NASA Astrophysics Data System (ADS)

Zainal, Rozlin; Kasim, Narimah; Sarpin, Norliana; Wee, Seow Ta; Shamsudin, Zarina

2017-10-01

Late delivery and sick housing project problems were attributed to poor decision making. These problems are the string of housing developer that prefers to create their own approach based on their experiences and expertise with the simplest approach by just applying the obtainable standards and rules in decision making. This paper seeks to identify the decision making methods for housing development at the initiation phase in Malaysia. The research involved Delphi method by using questionnaire survey which involved 50 numbers of developers as samples for the primary stage of collect data. However, only 34 developers contributed to the second stage of the information gathering process. At the last stage, only 12 developers were left for the final data collection process. Finding affirms that Malaysian developers prefer to make their investment decisions based on simple interpolation of historical data and using simple statistical or mathematical techniques in producing the required reports. It was suggested that they seemed to skip several important decision-making functions at the primary development stage. These shortcomings were mainly due to time and financial constraints and the lack of statistical or mathematical expertise among the professional and management groups in the developer organisations.

Haldane, Waddington and recombinant inbred lines: extension of their work to any number of genes.

PubMed

Samal, Areejit; Martin, Olivier C

2017-11-01

In the early 1930s, J. B. S. Haldane and C. H. Waddington collaborated on the consequences of genetic linkage and inbreeding. One elegant mathematical genetics problem solved by them concerns recombinant inbred lines (RILs) produced via repeated self or brother-sister mating. In this classic contribution, Haldane and Waddington derived an analytical formula for the probabilities of 2-locus and 3-locus RIL genotypes. Specifically, the Haldane-Waddington formula gives the recombination rate R in such lines as a simple function of the per generation recombination rate r. Interestingly, for more than 80 years, an extension of this result to four or more loci remained elusive. In 2015, we generalized the Haldane-Waddington self-mating result to any number of loci. Our solution used self-consistent equations of the multi-locus probabilities 'for an infinite number of generations' and solved these by simple algebraic operations. In practice, our approach provides a quantum leap in the systems that can be handled: the cases of up to six loci can be solved by hand while a computer program implementing our mathematical formalism tackles up to 20 loci on standard desktop computers.

Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

Interactions between Language and Mathematics with Deaf Students: Defining the "Language-Mathematics" Equation.

ERIC Educational Resources Information Center

Hillegeist, Eleanor; Epstein, Kenneth

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Models of Individual Trajectories in Computer-Assisted Instruction for Deaf Students. Technical Report No. 214.

ERIC Educational Resources Information Center

Suppes, P.; And Others

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability

ERIC Educational Resources Information Center

Rajagukguk, Waminton

2016-01-01

This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…

Exceptional point in a simple textbook example

NASA Astrophysics Data System (ADS)

Fernández, Francisco M.

2018-07-01

We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well-known damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.

Mathematical model for steady state, simple ampholyte isoelectric focusing: Development, computer simulation and implementation

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.

1979-01-01

The elimination of Ampholine from the system by establishing the pH gradient with simple ampholytes is proposed. A mathematical model was exercised at the level of the two-component system by using values for mobilities, diffusion coefficients, and dissociation constants representative of glutamic acid and histidine. The constants assumed in the calculations are reported. The predictions of the model and computer simulation of isoelectric focusing experiments are in direct importance to obtain Ampholine-free, stable pH gradients.

Aerodynamic coefficients in generalized unsteady thin airfoil theory

NASA Technical Reports Server (NTRS)

Williams, M. H.

1980-01-01

Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).

Endoscope shaft-rigidity control mechanism: "FORGUIDE".

PubMed

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

2012-02-01

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

A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

PubMed

Guiver, Chris; Packman, David; Townley, Stuart

2017-07-07

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

The Use of Digital Technology in Finding Multiple Paths to Solve and Extend an Equilateral Triangle Task

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2016-01-01

Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that…

Teacher and Student Use of Gesture and Access to Secondary Mathematics for Students with Learning Disabilities: An Exploratory Study

ERIC Educational Resources Information Center

Hord, Casey; Marita, Samantha; Walsh, Jennifer B.; Tomaro, Taylor-Marie; Gordon, Kiyana; Saldanha, Rene L.

2016-01-01

The researchers conducted an exploratory qualitative case study to describe the gesturing processes of tutors and students when engaging in secondary mathematics. The use of gestures ranged in complexity from simple gestures, such as pointing and moving the pointing finger in an arching motion to demonstrate mathematics relationships within…

A new diode laser acupuncture therapy apparatus

NASA Astrophysics Data System (ADS)

Li, Chengwei; Huang, Zhen; Li, Dongyu; Zhang, Xiaoyuan

2006-06-01

Since the first laser-needles acupuncture apparatus was introduced in therapy, this kind of apparatus has been well used in laser biomedicine as its non-invasive, pain- free, non-bacterium, and safetool. The laser acupuncture apparatus in this paper is based on single-chip microcomputer and associated by semiconductor laser technology. The function like traditional moxibustion including reinforcing and reducing is implemented by applying chaos method to control the duty cycle of moxibustion signal, and the traditional lifting and thrusting of acupuncture is implemented by changing power output of the diode laser. The radiator element of diode laser is made and the drive circuit is designed. And chaos mathematic model is used to produce deterministic class stochastic signal to avoid the body adaptability. This function covers the shortages of continuous irradiation or that of simple disciplinary stimulate signal, which is controlled by some simple electronic circuit and become easily adjusted by human body. The realization of reinforcing and reducing of moxibustion is technological innovation in traditional acupuncture coming true in engineering.

The promises and pitfalls of applying computational models to neurological and psychiatric disorders.

PubMed

Teufel, Christoph; Fletcher, Paul C

2016-10-01

Computational models have become an integral part of basic neuroscience and have facilitated some of the major advances in the field. More recently, such models have also been applied to the understanding of disruptions in brain function. In this review, using examples and a simple analogy, we discuss the potential for computational models to inform our understanding of brain function and dysfunction. We argue that they may provide, in unprecedented detail, an understanding of the neurobiological and mental basis of brain disorders and that such insights will be key to progress in diagnosis and treatment. However, there are also potential problems attending this approach. We highlight these and identify simple principles that should always govern the use of computational models in clinical neuroscience, noting especially the importance of a clear specification of a model's purpose and of the mapping between mathematical concepts and reality. © The Author (2016). Published by Oxford University Press on behalf of the Guarantors of Brain.

Functioning Mathematically: 1

ERIC Educational Resources Information Center

Cain, David

2007-01-01

This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…

The Semanticscience Integrated Ontology (SIO) for biomedical research and knowledge discovery

PubMed Central

2014-01-01

The Semanticscience Integrated Ontology (SIO) is an ontology to facilitate biomedical knowledge discovery. SIO features a simple upper level comprised of essential types and relations for the rich description of arbitrary (real, hypothesized, virtual, fictional) objects, processes and their attributes. SIO specifies simple design patterns to describe and associate qualities, capabilities, functions, quantities, and informational entities including textual, geometrical, and mathematical entities, and provides specific extensions in the domains of chemistry, biology, biochemistry, and bioinformatics. SIO provides an ontological foundation for the Bio2RDF linked data for the life sciences project and is used for semantic integration and discovery for SADI-based semantic web services. SIO is freely available to all users under a creative commons by attribution license. See website for further information: http://sio.semanticscience.org. PMID:24602174

Galileo's Mathematical Language of Nature.

ERIC Educational Resources Information Center

Forinash, Kyle; Rumsey, William; Lang, Chris

2000-01-01

Undergraduate students do not always make a clear distinction between physics and mathematics, particularly early in their studies. Offers a simple historical example and show how it can be used to illustrate some of the important differences and relationships between the two. (Author/SAH)

Simplification and its consequences in biological modelling: conclusions from a study of calcium oscillations in hepatocytes.

PubMed

Hetherington, James P J; Warner, Anne; Seymour, Robert M

2006-04-22

Systems Biology requires that biological modelling is scaled up from small components to system level. This can produce exceedingly complex models, which obscure understanding rather than facilitate it. The successful use of highly simplified models would resolve many of the current problems faced in Systems Biology. This paper questions whether the conclusions of simple mathematical models of biological systems are trustworthy. The simplification of a specific model of calcium oscillations in hepatocytes is examined in detail, and the conclusions drawn from this scrutiny generalized. We formalize our choice of simplification approach through the use of functional 'building blocks'. A collection of models is constructed, each a progressively more simplified version of a well-understood model. The limiting model is a piecewise linear model that can be solved analytically. We find that, as expected, in many cases the simpler models produce incorrect results. However, when we make a sensitivity analysis, examining which aspects of the behaviour of the system are controlled by which parameters, the conclusions of the simple model often agree with those of the richer model. The hypothesis that the simplified model retains no information about the real sensitivities of the unsimplified model can be very strongly ruled out by treating the simplification process as a pseudo-random perturbation on the true sensitivity data. We conclude that sensitivity analysis is, therefore, of great importance to the analysis of simple mathematical models in biology. Our comparisons reveal which results of the sensitivity analysis regarding calcium oscillations in hepatocytes are robust to the simplifications necessarily involved in mathematical modelling. For example, we find that if a treatment is observed to strongly decrease the period of the oscillations while increasing the proportion of the cycle during which cellular calcium concentrations are rising, without affecting the inter-spike or maximum calcium concentrations, then it is likely that the treatment is acting on the plasma membrane calcium pump.

Origami, geometry and art

NASA Astrophysics Data System (ADS)

Wares, Arsalan; Elstak, Iwan

2017-02-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra and geometry, like other branches of mathematics, are interrelated.

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

PubMed

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

2014-06-01

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

American Mathematics from 1940 to the Day Before Yesterday

ERIC Educational Resources Information Center

Ewing, J. H.; And Others

1976-01-01

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

Optimisation by hierarchical search

NASA Astrophysics Data System (ADS)

Zintchenko, Ilia; Hastings, Matthew; Troyer, Matthias

2015-03-01

Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields.

Wave propagation in a random medium

NASA Technical Reports Server (NTRS)

Lee, R. W.; Harp, J. C.

1969-01-01

A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.

Techniques for Accelerating Iterative Methods for the Solution of Mathematical Problems

DTIC Science & Technology

1989-07-01

m, we can find a solu ion to the problem by using generalized inverses. Hence, ;= Ih.i = GAi = G - where G is of the form (18). A simple choice for V...have understood why I was not available for many of their activities and not home many of the nights. Their love is forever. I have saved the best for...Xk) Extrapolation applied to terms xP through Xk F Operator on x G Iteration function Ik Identity matrix of rank k Solution of the problem or the limit

A new asymptotic method for jump phenomena

NASA Technical Reports Server (NTRS)

Reiss, E. L.

1980-01-01

Physical phenomena involving rapid and sudden transitions, such as snap buckling of elastic shells, explosions, and earthquakes, are characterized mathematically as a small disturbance causing a large-amplitude response. Because of this, standard asymptotic and perturbation methods are ill-suited to these problems. In the present paper, a new method of analyzing jump phenomena is proposed. The principal feature of the method is the representation of the response in terms of rational functions. For illustration, the method is applied to the snap buckling of an elastic arch and to a simple combustion problem.

Care 3, Phase 1, volume 1

NASA Technical Reports Server (NTRS)

Stiffler, J. J.; Bryant, L. A.; Guccione, L.

1979-01-01

A computer program to aid in accessing the reliability of fault tolerant avionics systems was developed. A simple mathematical expression was used to evaluate the reliability of any redundant configuration over any interval during which the failure rates and coverage parameters remained unaffected by configuration changes. Provision was made for convolving such expressions in order to evaluate the reliability of a dual mode system. A coverage model was also developed to determine the various relevant coverage coefficients as a function of the available hardware and software fault detector characteristics, and subsequent isolation and recovery delay statistics.

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2006-01-01

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

PubMed

Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

2005-05-01

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

The esophagiome: integrated anatomical, mechanical, and physiological analysis of the esophago-gastric segment.

PubMed

Zhao, Jingbo; McMahon, Barry; Fox, Mark; Gregersen, Hans

2018-06-10

Esophageal diseases are highly prevalent and carry significant socioeconomic burden. Despite the apparently simple function of the esophagus, we still struggle to better understand its physiology and pathophysiology. The assessment of large data sets and application of multiscale mathematical organ models have gained attention as part of the Physiome Project. This has long been recognized in cardiology but has only recently gained attention for the gastrointestinal(GI) tract. The term "esophagiome" implies a holistic assessment of esophageal function, from cellular and muscle physiology to the mechanical responses that transport and mix fluid contents. These anatomical, mechanical, and physiological models underlie the development of a "virtual esophagus" modeling framework to characterize and analyze function and disease. Functional models incorporate anatomical details with sensory-motor responses, especially related to biomechanical functions such as bolus transport. Our review builds on previous reviews and focuses on assessment of detailed anatomical and geometric data using advanced imaging technology for evaluation of gastro-esophageal reflux disease (GERD), and on esophageal mechanophysiology assessed using technologies that distend the esophagus. Integration of mechanics- and physiology-based analysis is a useful characteristic of the esophagiome. Experimental data on pressures and geometric characteristics are useful for the validation of mathematical and computer models of the esophagus that may provide predictions of novel endoscopic, surgical, and pharmaceutical treatment options. © 2018 New York Academy of Sciences.

The mathematical relationship between Zipf’s law and the hierarchical scaling law

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2012-06-01

The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf's distribution of cities is abstracted as a q-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf's law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2n principle and Pareto's law can be associated with one another by the hierarchical organization.

THE MATHEMATICAL ANALYSIS OF A SIMPLE DUEL

DTIC Science & Technology

The principles and techniques of simple Markov processes are used to analyze a simple duel to determine the limiting state probabilities (i.e., the...probabilities of occurrence of the various possible outcomes of the duel ). The duel is one in which A fires at B at a rate of r sub A shots per minute

Mathematics anxiety affects counting but not subitizing during visual enumeration.

PubMed

Maloney, Erin A; Risko, Evan F; Ansari, Daniel; Fugelsang, Jonathan

2010-02-01

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature. Copyright 2009 Elsevier B.V. All rights reserved.

Sharing Teaching Ideas.

ERIC Educational Resources Information Center

Tunis, Harry B., Ed.

1993-01-01

Two teaching ideas integrate mathematics and business. The first discusses consumer deception by such ploys as false bottoms on containers and simple rather than compound interest on investments. The second describes a business mathematics course in which students are motivated by contracting for certain jobs and potential bonuses. (MDH)

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

NASA Astrophysics Data System (ADS)

Ferrer, Sebastián; Lara, Martin

2010-05-01

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

Insights from mathematical modeling of renal tubular function.

PubMed

Weinstein, A M

1998-01-01

Mathematical models of proximal tubule have been developed which represent the important solute species within the constraints of known cytosolic concentrations, transport fluxes, and overall epithelial permeabilities. In general, model simulations have been used to assess the quantitative feasibility of what appear to be qualitatively plausible mechanisms, or alternatively, to identify incomplete rationalization of experimental observations. The examples considered include: (1) proximal water reabsorption, for which the lateral interspace is a locus for solute-solvent coupling; (2) ammonia secretion, for which the issue is prioritizing driving forces - transport on the Na+/H+ exchanger, on the Na,K-ATPase, or ammoniagenesis; (3) formate-stimulated NaCl reabsorption, for which simple addition of a luminal membrane chloride/formate exchanger fails to represent experimental observation, and (4) balancing luminal entry and peritubular exit, in which ATP-dependent peritubular K+ channels have been implicated, but appear unable to account for the bulk of proximal tubule cell volume homeostasis.

A novel medical information management and decision model for uncertain demand optimization.

PubMed

Bi, Ya

2015-01-01

Accurately planning the procurement volume is an effective measure for controlling the medicine inventory cost. Due to uncertain demand it is difficult to make accurate decision on procurement volume. As to the biomedicine sensitive to time and season demand, the uncertain demand fitted by the fuzzy mathematics method is obviously better than general random distribution functions. To establish a novel medical information management and decision model for uncertain demand optimization. A novel optimal management and decision model under uncertain demand has been presented based on fuzzy mathematics and a new comprehensive improved particle swarm algorithm. The optimal management and decision model can effectively reduce the medicine inventory cost. The proposed improved particle swarm optimization is a simple and effective algorithm to improve the Fuzzy interference and hence effectively reduce the calculation complexity of the optimal management and decision model. Therefore the new model can be used for accurate decision on procurement volume under uncertain demand.

A simple theoretical framework for understanding heterogeneous differentiation of CD4+ T cells

PubMed Central

2012-01-01

Background CD4+ T cells have several subsets of functional phenotypes, which play critical yet diverse roles in the immune system. Pathogen-driven differentiation of these subsets of cells is often heterogeneous in terms of the induced phenotypic diversity. In vitro recapitulation of heterogeneous differentiation under homogeneous experimental conditions indicates some highly regulated mechanisms by which multiple phenotypes of CD4+ T cells can be generated from a single population of naïve CD4+ T cells. Therefore, conceptual understanding of induced heterogeneous differentiation will shed light on the mechanisms controlling the response of populations of CD4+ T cells under physiological conditions. Results We present a simple theoretical framework to show how heterogeneous differentiation in a two-master-regulator paradigm can be governed by a signaling network motif common to all subsets of CD4+ T cells. With this motif, a population of naïve CD4+ T cells can integrate the signals from their environment to generate a functionally diverse population with robust commitment of individual cells. Notably, two positive feedback loops in this network motif govern three bistable switches, which in turn, give rise to three types of heterogeneous differentiated states, depending upon particular combinations of input signals. We provide three prototype models illustrating how to use this framework to explain experimental observations and make specific testable predictions. Conclusions The process in which several types of T helper cells are generated simultaneously to mount complex immune responses upon pathogenic challenges can be highly regulated, and a simple signaling network motif can be responsible for generating all possible types of heterogeneous populations with respect to a pair of master regulators controlling CD4+ T cell differentiation. The framework provides a mathematical basis for understanding the decision-making mechanisms of CD4+ T cells, and it can be helpful for interpreting experimental results. Mathematical models based on the framework make specific testable predictions that may improve our understanding of this differentiation system. PMID:22697466

Ancient Paradoxes Can Extend Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Active Learning Strategies for the Mathematics Classroom

ERIC Educational Resources Information Center

Kerrigan, John

2018-01-01

Active learning involves students engaging with course content beyond lecture: through writing, applets, simulations, games, and more (Prince, 2004). As mathematics is often viewed as a subject area that is taught using more traditional methods (Goldsmith & Mark, 1999), there are actually many simple ways to make undergraduate mathematics…

Sunspots and Their Simple Harmonic Motion

ERIC Educational Resources Information Center

Ribeiro, C. I.

2013-01-01

In this paper an example of a simple harmonic motion, the apparent motion of sunspots due to the Sun's rotation, is described, which can be used to teach this subject to high-school students. Using real images of the Sun, students can calculate the star's rotation period with the simple harmonic motion mathematical expression.

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.

Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.

A Simple Model of Circuit Design.

DTIC Science & Technology

1980-05-01

mathematicians who discover mathematical ideas (i.cnat>, programmers who write code <Manna> <Barstow>, physicists who solve mechanics problems <de Kiecr-l...rules and shows how - they result in the design of circuits. ’l’he design rules must not only capture the purely mathematical constralints given by VICs...K VI.. *? and KCI, but also how those constraints can implement mechanism. Mathematical constraints tell us an amplifier’s input and output voltages

Number Sense Made Simple Using Number Patterns

ERIC Educational Resources Information Center

Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph

2011-01-01

This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…

Matter Gravitates, but Does Gravity Matter?

ERIC Educational Resources Information Center

Groetsch, C. W.

2011-01-01

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

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…

Deaf College Students' Mathematical Skills Relative to Morphological Knowledge, Reading Level, and Language Proficiency

ERIC Educational Resources Information Center

Kelly, Ronald R.; Gaustad, Martha G.

2007-01-01

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and…

Not Just for Computation: Basic Calculators Can Advance the Process Standards

ERIC Educational Resources Information Center

Moss, Laura J.; Grover, Barbara W.

2007-01-01

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Harmony Theory: A Mathematical Framework for Stochastic Parallel Processing.

ERIC Educational Resources Information Center

Smolensky, Paul

This paper presents preliminary results of research founded on the hypothesis that in real environments there exist regularities that can be idealized as mathematical structures that are simple enough to be analyzed. The author considered three steps in analyzing the encoding of modularity of the environment. First, a general information…

Mathematical demography of spotted owls in the Pacific Northwest

Treesearch

B.R. Noon; C.M. Biles

1990-01-01

We examined the mathematical demography of northern spotted owls (Strix occidentalis caurina) using simple deterministic population models. Our goals were to gain insights into the life history strategy, to determine demographic attributes most affecting changes in population size, and to provide guidelines for effective management of spotted owl...

Skeletal muscle contraction in protecting joints and bones by absorbing mechanical impacts

NASA Astrophysics Data System (ADS)

Rudenko, O. V.; Tsyuryupa, S.; Sarvazyan, A.

2016-09-01

We have previously hypothesized that the dissipation of mechanical energy of external impact is a fundamental function of skeletal muscle in addition to its primary function to convert chemical energy into mechanical energy. In this paper, a mathematical justification of this hypothesis is presented. First, a simple mechanical model, in which the muscle is considered as a simple Hookean spring, is considered. This analysis serves as an introduction to the consideration of a biomechanical model taking into account the molecular mechanism of muscle contraction, kinetics of myosin bridges, sarcomere dynamics, and tension of muscle fibers. It is shown that a muscle behaves like a nonlinear and adaptive spring tempering the force of impact and increasing the duration of the collision. The temporal profiles of muscle reaction to the impact as functions of the levels of muscle contraction, durations of the impact front, and the time constants of myosin bridges closing, are obtained. The absorption of mechanical shock energy is achieved due to the increased viscoelasticity of the contracting skeletal muscle. Controlling the contraction level allows for the optimization of the stiffness and viscosity of the muscle necessary for the protection of the joints and bones.

The Topographical Mapping in Drosophila Central Complex Network and Its Signal Routing

PubMed Central

Chang, Po-Yen; Su, Ta-Shun; Shih, Chi-Tin; Lo, Chung-Chuan

2017-01-01

Neural networks regulate brain functions by routing signals. Therefore, investigating the detailed organization of a neural circuit at the cellular levels is a crucial step toward understanding the neural mechanisms of brain functions. To study how a complicated neural circuit is organized, we analyzed recently published data on the neural circuit of the Drosophila central complex, a brain structure associated with a variety of functions including sensory integration and coordination of locomotion. We discovered that, except for a small number of “atypical” neuron types, the network structure formed by the identified 194 neuron types can be described by only a few simple mathematical rules. Specifically, the topological mapping formed by these neurons can be reconstructed by applying a generation matrix on a small set of initial neurons. By analyzing how information flows propagate with or without the atypical neurons, we found that while the general pattern of signal propagation in the central complex follows the simple topological mapping formed by the “typical” neurons, some atypical neurons can substantially re-route the signal pathways, implying specific roles of these neurons in sensory signal integration. The present study provides insights into the organization principle and signal integration in the central complex. PMID:28443014

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency.

PubMed

Kelly, Ronald R; Gaustad, Martha G

2007-01-01

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.

Simple Spreadsheet Models For Interpretation Of Fractured Media Tracer Tests

EPA Science Inventory

An analysis of a gas-phase partitioning tracer test conducted through fractured media is discussed within this paper. The analysis employed matching eight simple mathematical models to the experimental data to determine transport parameters. All of the models tested; two porous...

On the Mechanisms for Martensite Formation in YAG Laser Welded Austenitic NiTi

NASA Astrophysics Data System (ADS)

Oliveira, J. P.; Braz Fernandes, F. M.; Miranda, R. M.; Schell, N.

2016-03-01

Extensive work has been reported on the microstructure of laser-welded NiTi alloys either superelastic or with shape memory effect, motivated by the fact that the microstructure affects the functional properties. However, some effects of laser beam/material interaction with these alloys have not yet been discussed. This paper aims to discuss the mechanisms for the occurrence of martensite in the heat-affected zone and in the fusion zone at room temperature, while the base material is fully austenitic. For this purpose, synchrotron radiation was used together with a simple thermal analytic mathematical model. Two distinct mechanisms are proposed for the presence of martensite in different zones of a weld, which affects the mechanical and functional behavior of a welded component.

A simple technique to increase profits in wood products marketing

Treesearch

George B. Harpole

1971-01-01

Mathematical models can be used to solve quickly some simple day-to-day marketing problems. This note explains how a sawmill production manager, who has an essentially fixed-capacity mill, can solve several optimization problems by using pencil and paper, a forecast of market prices, and a simple algorithm. One such problem is to maximize profits in an operating period...

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

PubMed

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

2016-06-01

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

The Use of Modeling Approach for Teaching Exponential Functions

NASA Astrophysics Data System (ADS)

Nunes, L. F.; Prates, D. B.; da Silva, J. M.

2017-12-01

This work presents a discussion related to the teaching and learning of mathematical contents related to the study of exponential functions in a freshman students group enrolled in the first semester of the Science and Technology Bachelor’s (STB of the Federal University of Jequitinhonha and Mucuri Valleys (UFVJM). As a contextualization tool strongly mentioned in the literature, the modelling approach was used as an educational teaching tool to produce contextualization in the teaching-learning process of exponential functions to these students. In this sense, were used some simple models elaborated with the GeoGebra software and, to have a qualitative evaluation of the investigation and the results, was used Didactic Engineering as a methodology research. As a consequence of this detailed research, some interesting details about the teaching and learning process were observed, discussed and described.

Stability and chaos of Rulkov map-based neuron network with electrical synapse

NASA Astrophysics Data System (ADS)

Wang, Caixia; Cao, Hongjun

2015-02-01

In this paper, stability and chaos of a simple system consisting of two identical Rulkov map-based neurons with the bidirectional electrical synapse are investigated in detail. On the one hand, as a function of control parameters and electrical coupling strengthes, the conditions for stability of fixed points of this system are obtained by using the qualitative analysis. On the other hand, chaos in the sense of Marotto is proved by a strict mathematical way. These results could be useful for building-up large-scale neurons networks with specific dynamics and rich biophysical phenomena.

Excel VBA for Physicists; A Primer

NASA Astrophysics Data System (ADS)

Liengme, Bernard V.

2016-11-01

This book is both an introduction and a demonstration of how Visual Basic for Applications (VBA) can greatly enhance Microsoft Excel® by giving users the ability to create their own functions within a worksheet and to create subroutines to perform repetitive actions. The book is written so readers are encouraged to experiment with VBA programming with examples using fairly simple physics or non-complicated mathematics such as root finding and numerical integration. Tested Excel® workbooks are available for each chapter and there is nothing to buy or install. A tested Excel workbook for each chapter can be downloaded from Book information

Multi-Detection Events, Probability Density Functions, and Reduced Location Area

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

Eslinger, Paul W.; Schrom, Brian T.

2016-03-01

Abstract Several efforts have been made in the Comprehensive Nuclear-Test-Ban Treaty (CTBT) community to assess the benefits of combining detections of radionuclides to improve the location estimates available from atmospheric transport modeling (ATM) backtrack calculations. We present a Bayesian estimation approach rather than a simple dilution field of regard approach to allow xenon detections and non-detections to be combined mathematically. This system represents one possible probabilistic approach to radionuclide event formation. Application of this method to a recent interesting radionuclide event shows a substantial reduction in the location uncertainty of that event.

Linear Calibration of Radiographic Mineral Density Using Video-Digitizing Methods

NASA Technical Reports Server (NTRS)

Martin, R. Bruce; Papamichos, Thomas; Dannucci, Greg A.

1990-01-01

Radiographic images can provide quantitative as well as qualitative information if they are subjected to densitometric analysis. Using modem video-digitizing techniques, such densitometry can be readily accomplished using relatively inexpensive computer systems. However, such analyses are made more difficult by the fact that the density values read from the radiograph have a complex, nonlinear relationship to bone mineral content. This article derives the relationship between these variables from the nature of the intermediate physical processes, and presents a simple mathematical method for obtaining a linear calibration function using a step wedge or other standard.

Linear Calibration of Radiographic Mineral Density Using Video-Digitizing Methods

NASA Technical Reports Server (NTRS)

Martin, R. Bruce; Papamichos, Thomas; Dannucci, Greg A.

1990-01-01

Radiographic images can provide quantitative as well as qualitative information if they are subjected to densitometric analysis. Using modern video-digitizing techniques, such densitometry can be readily accomplished using relatively inexpensive computer systems. However, such analyses are made more difficult by the fact that the density values read from the radiograph have a complex, nonlinear relationship to bone mineral content. This article derives the relationship between these variables from the nature of the intermediate physical processes, and presents a simple mathematical method for obtaining a linear calibration function using a step wedge or other standard.

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

NASA Technical Reports Server (NTRS)

Pennline, James A.

2009-01-01

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research.

Incorporating spike-rate adaptation into a rate code in mathematical and biological neurons

PubMed Central

Ralston, Bridget N.; Flagg, Lucas Q.; Faggin, Eric

2016-01-01

For a slowly varying stimulus, the simplest relationship between a neuron's input and output is a rate code, in which the spike rate is a unique function of the stimulus at that instant. In the case of spike-rate adaptation, there is no unique relationship between input and output, because the spike rate at any time depends both on the instantaneous stimulus and on prior spiking (the “history”). To improve the decoding of spike trains produced by neurons that show spike-rate adaptation, we developed a simple scheme that incorporates “history” into a rate code. We utilized this rate-history code successfully to decode spike trains produced by 1) mathematical models of a neuron in which the mechanism for adaptation (IAHP) is specified, and 2) the gastropyloric receptor (GPR2), a stretch-sensitive neuron in the stomatogastric nervous system of the crab Cancer borealis, that exhibits long-lasting adaptation of unknown origin. Moreover, when we modified the spike rate either mathematically in a model system or by applying neuromodulatory agents to the experimental system, we found that changes in the rate-history code could be related to the biophysical mechanisms responsible for altering the spiking. PMID:26888106

Combinatorics of aliphatic amino acids

NASA Astrophysics Data System (ADS)

Grützmann, Konrad; Böcker, Sebastian; Schuster, Stefan

2011-01-01

This study combines biology and mathematics, showing that a relatively simple question from molecular biology can lead to complicated mathematics. The question is how to calculate the number of theoretically possible aliphatic amino acids as a function of the number of carbon atoms in the side chain. The presented calculation is based on earlier results from theoretical chemistry concerning alkyl compounds. Mathematical properties of this number series are highlighted. We discuss which of the theoretically possible structures really occur in living organisms, such as leucine and isoleucine with a chain length of four. This is done both for a strict definition of aliphatic amino acids only involving carbon and hydrogen atoms in their side chain and for a less strict definition allowing sulphur, nitrogen and oxygen atoms. While the main focus is on proteinogenic amino acids, we also give several examples of non-proteinogenic aliphatic amino acids, playing a role, for instance, in signalling. The results are in agreement with a general phenomenon found in biology: Usually, only a small number of molecules are chosen as building blocks to assemble an inconceivable number of different macromolecules as proteins. Thus, natural biological complexity arises from the multifarious combination of building blocks.

A study on nonlinear estimation of submaximal effort tolerance based on the generalized MET concept and the 6MWT in pulmonary rehabilitation

PubMed Central

Szczegielniak, Jan; Łuniewski, Jacek; Stanisławski, Rafał; Bogacz, Katarzyna; Krajczy, Marcin; Rydel, Marek

2018-01-01

Background The six-minute walk test (6MWT) is considered to be a simple and inexpensive tool for the assessment of functional tolerance of submaximal effort. The aim of this work was 1) to background the nonlinear nature of the energy expenditure process due to physical activity, 2) to compare the results/scores of the submaximal treadmill exercise test and those of 6MWT in pulmonary patients and 3) to develop nonlinear mathematical models relating the two. Methods The study group included patients with the COPD. All patients were subjected to a submaximal exercise test and a 6MWT. To develop an optimal mathematical solution and compare the results of the exercise test and the 6MWT, the least squares and genetic algorithms were employed to estimate parameters of polynomial expansion and piecewise linear models. Results Mathematical analysis enabled to construct nonlinear models for estimating the MET result of submaximal exercise test based on average walk velocity (or distance) in the 6MWT. Conclusions Submaximal effort tolerance in COPD patients can be effectively estimated from new, rehabilitation-oriented, nonlinear models based on the generalized MET concept and the 6MWT. PMID:29425213

Mathematics and complex systems.

PubMed

Foote, Richard

2007-10-19

Contemporary researchers strive to understand complex physical phenomena that involve many constituents, may be influenced by numerous forces, and may exhibit unexpected or emergent behavior. Often such "complex systems" are macroscopic manifestations of other systems that exhibit their own complex behavior and obey more elemental laws. This article proposes that areas of mathematics, even ones based on simple axiomatic foundations, have discernible layers, entirely unexpected "macroscopic" outcomes, and both mathematical and physical ramifications profoundly beyond their historical beginnings. In a larger sense, the study of mathematics itself, which is increasingly surpassing the capacity of researchers to verify "by hand," may be the ultimate complex system.

Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems

ERIC Educational Resources Information Center

Alter, Peter

2012-01-01

The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…

Finding Quality Geometry Apps: Not as Simple as a[superscript 2] + b[superscript 2] = c[superscript 2

ERIC Educational Resources Information Center

Larkin, Kevin

2016-01-01

Trying to find quality apps for use in mathematics classes can be time consuming and bewildering. This article outlines a process for evaluating apps and provides teachers with access to comprehensive qualitative evaluations of 53 geometrical apps based on pedagogical, mathematical and cognitive fidelities.

Great Lakes modeling: Are the mathematics outpacing the data and our understanding of the system?

EPA Science Inventory

Mathematical modeling in the Great Lakes has come a long way from the pioneering work done by Manhattan College in the 1970s, when the models operated on coarse computational grids (often lake-wide) and used simple eutrophication formulations. Moving forward 40 years, we are now...

Answering Junior Ant's "Why" for Pythagoras' Theorem

ERIC Educational Resources Information Center

Pask, Colin

2002-01-01

A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…

The Development from Effortful to Automatic Processing in Mathematical Cognition.

ERIC Educational Resources Information Center

Kaye, Daniel B.; And Others

This investigation capitalizes upon the information processing models that depend upon measurement of latency of response to a mathematical problem and the decomposition of reaction time (RT). Simple two term addition problems were presented with possible solutions for true-false verification, and accuracy and RT to response were recorded. Total…

"Autograph" in the KS3 Classroom

ERIC Educational Resources Information Center

Catley, Alan

2006-01-01

In this article, the author shows some simple examples of ways in which "Autograph" can enhance learning in the KS3 curriculum. He began using version 2 with A-level students to help them visualise concepts in pure mathematics. He has "Autograph" projected to the front board to keep learners focused on mathematical activity…

Modelling a Simple Mechanical System.

ERIC Educational Resources Information Center

Morland, Tim

1999-01-01

Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

Origami, Geometry and Art

ERIC Educational Resources Information Center

Wares, Arsalan; Elstak, Iwan

2017-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

The Force-Frequency Relationship: Insights from Mathematical Modeling

ERIC Educational Resources Information Center

Puglisi, Jose L.; Negroni, Jorge A.; Chen-Izu, Ye; Bers, Donald M.

2013-01-01

The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by…

Industrial Prep, Volume Four, Junior Year--Contents: Mathematics and Guidance.

ERIC Educational Resources Information Center

Hackensack Public Schools, NJ.

As part of a 3-year comprehensive interdisciplinary program in industrial preparation for vocational students, this 11th Grade teaching guide consists of units on technical mathematics and guidance. Designed as supportive material for related physics and English curriculums, the first four sections of Volume 4 on algebra, vectors, simple machines,…

SIMPLE METHOD FOR THE REPRESENTATION, QUANTIFICATION, AND COMPARISON OF THE VOLUMES AND SHAPES OF CHEMICAL COMPOUNDS

EPA Science Inventory

A conceptually and computationally simple method for the definition, display, quantification, and comparison of the shapes of three-dimensional mathematical molecular models is presented. Molecular or solvent-accessible volume and surface area can also be calculated. Algorithms, ...

Mathematics and Astronomy: Inquire Based Scientific Education at School

NASA Astrophysics Data System (ADS)

de Castro, Ana I. Gómez

2010-10-01

Mathematics is the language of science however, in secondary and high school education students are not made aware of the strong implications behind this statement. This is partially caused because mathematical training and the modelling of nature are not taught together. Astronomy provides firm scientific grounds for this joint training; the mathematics needed is simple, the data can be acquired with simple instrumentation in any place on the planet and the physics is rich with a broad range of levels. In addition, astronomy and space exploration are extremely appealing to young (14-17 years old) students helping to motivate them to study science doing science, i.e. to introduce Inquiry Based Scientific Education (IBSE). Since 1997 a global consortium is being developed to introduce IBSE techniques in secondary/high school education on a global scale: the Global Hands-On Universe association (www.globalhou.org) making use of the astronomical universe as a training lab. This contribution is a brief update on the current activities of the HOU consortium. Relevant URLS: www.globalhou.org, www.euhou.net, www.houspain.com.

Diatom-sedimentation feedback generates a self-organized geomorphic landscape on intertidal mudflats (Invited)

NASA Astrophysics Data System (ADS)

van de Koppel, J.; Weerman, E.; Herman, P.

2010-12-01

During spring, intertidal flats can exhibit strikingly regular spatial patterns of diatom-covered hummocks alternating with almost bare, water-filled hollows. We hypothesize that 1) the formation of this geomorphic landscape is caused by a strong interaction between benthic diatoms and sediment dynamics, inducing spatial self-organization, and 2) that self-organization affects ecosystem functioning by increasing the net average sedimentation on the tidal flat. We present a combined empirical and mathematical study to test the first hypothesis. We determined how the sediment erosion threshold varied with diatom cover and elevation. Our results were incorporated into a mathematical model to investigate whether the proposed mechanism could explain the formation of the observed patterns. Our mathematical model confirmed that the interaction between sedimentation, diatom growth and water redistribution could induce the formation of regular patterns on the intertidal mudflat. The model predicts that areas exhibiting spatially-self-organized patterns have increased sediment accretion and diatom biomass compared with areas lacking spatial patterns. We tested this prediction by following the sediment elevation during the season on both patterned and unpatterned parts of the mudflat. The results of our study confirmed our model prediction, as more sediment was found to accumulate in patterned parts of the mudflat, revealing how self-organization affected the functioning of mudflat ecosystems. Our study on intertidal mudflats provides a simple but clear-cut example of how the interaction between biological and geomorphological processes, through the process of self-organization, induces a self-organized geomorphic landscape.

Toward Model Building for Visual Aesthetic Perception

PubMed Central

Lughofer, Edwin; Zeng, Xianyi

2017-01-01

Several models of visual aesthetic perception have been proposed in recent years. Such models have drawn on investigations into the neural underpinnings of visual aesthetics, utilizing neurophysiological techniques and brain imaging techniques including functional magnetic resonance imaging, magnetoencephalography, and electroencephalography. The neural mechanisms underlying the aesthetic perception of the visual arts have been explained from the perspectives of neuropsychology, brain and cognitive science, informatics, and statistics. Although corresponding models have been constructed, the majority of these models contain elements that are difficult to be simulated or quantified using simple mathematical functions. In this review, we discuss the hypotheses, conceptions, and structures of six typical models for human aesthetic appreciation in the visual domain: the neuropsychological, information processing, mirror, quartet, and two hierarchical feed-forward layered models. Additionally, the neural foundation of aesthetic perception, appreciation, or judgement for each model is summarized. The development of a unified framework for the neurobiological mechanisms underlying the aesthetic perception of visual art and the validation of this framework via mathematical simulation is an interesting challenge in neuroaesthetics research. This review aims to provide information regarding the most promising proposals for bridging the gap between visual information processing and brain activity involved in aesthetic appreciation. PMID:29270194

A quasi-QSPR modelling for the photocatalytic decolourization rate constants and cellular viability (CV%) of nanoparticles by CORAL.

PubMed

Toropova, A P; Toropov, A A; Benfenati, E

2015-01-01

Most quantitative structure-property/activity relationships (QSPRs/QSARs) predict various endpoints related to organic compounds. Gradually, the variety of organic compounds has been extended to inorganic, organometallic compounds and polymers. However, the so-called molecular descriptors cannot be defined for super-complex substances such as different nanomaterials and peptides, since there is no simple and clear representation of their molecular structure. Some possible ways to define approaches for a predictive model in the case of super-complex substances are discussed. The basic idea of the approach is to change the traditionally used paradigm 'the endpoint is a mathematical function of the molecular structure' with another paradigm 'the endpoint is a mathematical function of available eclectic information'. The eclectic data can be (i) conditions of a synthesis, (ii) technological attributes, (iii) size of nanoparticles, (iv) concentration, (v) attributes related to cell membranes, and so on. Two examples of quasi-QSPR/QSAR analyses are presented and discussed. These are (i) photocatalytic decolourization rate constants (DRC) (10(-5)/s) of different nanopowders; and (ii) the cellular viability under the effect of nano-SiO(2).

A SIMPLE MODEL FOR THE UPTAKE, TRANSLOCATION, AND ACCUMULATION OF PERCHLORATE IN TOBACCO PLANTS

EPA Science Inventory

A simple mathematical model is being developed to describe the uptake, translocation, and accumulation of perchlorate in tobacco plants. The model defines a plant as a set of compartments, consisting of mass balance differential equations and plant-specific physiological paramet...

Mathematical and Numerical Analysis of Model Equations on Interactions of the HIV/AIDS Virus and the Immune System

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.

Sines and Cosines. Part 3 of 3

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1994-01-01

In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.

Check the Lambert-Beer-Bouguer law: a simple trick to boost the confidence of students toward both exponential laws and the discrete approach to experimental physics

NASA Astrophysics Data System (ADS)

Di Capua, R.; Offi, F.; Fontana, F.

2014-07-01

Exponential decay is a prototypical functional behaviour for many physical phenomena, and therefore it deserves great attention in physics courses at an academic level. The absorption of the electromagnetic radiation that propagates in a dissipative medium provides an example of the decay of light intensity, as stated by the law of Lambert-Beer-Bourguer. We devised a very simple experiment to check this law. The experimental setup, its realization, and the data analysis of the experiment are definitely simple. Our main goal was to create an experiment that is accessible to all students, including those in their first year of academic courses and those with poorly equipped laboratories. As illustrated in this paper, our proposal allowed us to develop a deep discussion about some general mathematical and numerical features of exponential decay. Furthermore, the special setup of the absorbing medium (sliced in finite thickness slabs) and the experimental outcomes allow students to understand the transition from the discrete to the continuum approach in experimental physics.

On the validity of the arithmetic-geometric mean method to locate the optimal solution in a supply chain system

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2012-08-01

Cardenas-Barron [Cardenas-Barron, L.E. (2010) 'A Simple Method to Compute Economic order Quantities: Some Observations', Applied Mathematical Modelling, 34, 1684-1688] indicates that there are several functions in which the arithmetic-geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), 'A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives', Applied Mathematical Modelling, 33, 4388-4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), 'Comment on 'Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives', International Journal of Systems Science, 40, 1095-1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), 'A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage', Production Planning and Control, 19, 601-604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic-geometric mean method of Teng et al. (2009), Teng and Goyal (2009) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.

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

ERIC Educational Resources Information Center

Gauthier, N.

2007-01-01

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

Getting to the Bottom of a Ladder Problem

ERIC Educational Resources Information Center

McCartney, Mark

2002-01-01

In this paper, the author introduces a simple problem relating to a pair of ladders. A mathematical model of the problem produces an equation which can be solved in a number of ways using mathematics appropriate to "A" level students or first year undergraduates. The author concludes that the ladder problem can be used in class to develop and…

Improving the Effectiveness of Mathematics Teaching through Active Reflection

ERIC Educational Resources Information Center

Driscoll, Kerryn

2015-01-01

A small study of active reflection was undertaken with 21 primary students in a Prep and Year 1 classroom. To provide feedback from the students on their views about their personal learning and ways they could be better supported to learn mathematics a simple survey was supplemented by one-to-one interviews. Students' perceptions of their learning…

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

ERIC Educational Resources Information Center

Higgins, Jon L., Ed.

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

Stickybear's Math Splash: Adventures in Math Fun for Ages 5-10! School Version with Lesson Plans. [CD-ROM].

ERIC Educational Resources Information Center

Highsmith, Joni Bitman

Stickybear's Math Splash is a CD-ROM-based software tool for teaching mathematics skills beyond simple number recognition to elementary students. The accompanying printed lesson plans are designed to complement mathematics skills with other methods and areas of emphasis including kinesthetic learning, listening skills, decision making skills, and…

Calling for the Development of Children's Number Sense in Primary Schools in Malaysia

ERIC Educational Resources Information Center

Kuldas, Seffetullah; Sinnakaudan, Santi; Hashim, Shahabuddin; Ghazali, Munirah

2017-01-01

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the…

Second-Degree Price Discrimination: A Graphical and Mathematical Approach

ERIC Educational Resources Information Center

Gotlibovski, Chemi; Kahana, Nava

2009-01-01

The authors use a relatively simple diagram accompanied by mathematical analysis to compare two pricing strategies: price-quantity packages and a two-part tariff. This is done both from the monopolist's point of view and from the welfare point of view. The authors show that in the case of two consumer types, the price-quantity packages strategy…

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3-5. Essential Understandings

ERIC Educational Resources Information Center

Clarke, Carne; Fisher, William; Marks, Rick; Ross, Sharon; Zbiek, Rose Mary

2010-01-01

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

Children's Criteria for Representational Adequacy in the Perception of Simple Sonic Stimuli

ERIC Educational Resources Information Center

Verschaffel, Lieven; Reybrouck, Mark; Jans, Christine; Van Dooren, Wim

2010-01-01

This study investigates children's metarepresentational competence with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2003) work on metarepresentational competence in mathematics and sciences as theoretical and empirical background, it aims to assess children's criteria for representational adequacy of graphical…

A Simple Mechanical Model for the Isotropic Harmonic Oscillator

ERIC Educational Resources Information Center

Nita, Gelu M.

2010-01-01

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

Eye Movements Reveal Students' Strategies in Simple Equation Solving

ERIC Educational Resources Information Center

Susac, Ana; Bubic, Andreja; Kaponja, Jurica; Planinic, Maja; Palmovic, Marijan

2014-01-01

Equation rearrangement is an important skill required for problem solving in mathematics and science. Eye movements of 40 university students were recorded while they were rearranging simple algebraic equations. The participants also reported on their strategies during equation solving in a separate questionnaire. The analysis of the behavioral…

Intangible heritage for sustainable future: mathematics in the paddy field

NASA Astrophysics Data System (ADS)

Dewanto, Stanley P.; Kusuma, Dianne A.; Nurani Ruchjana, Budi; Setiawan Abdullah, Atje

2017-10-01

Mathematics, as the only general language, can describe all phenomena on earth. Mathematics not only helps us to understand these phenomena, but it also can sustain human activities, consequently ensure that the future development is sustainable. Indonesia, with high cultural diversity, should aware to have its understanding, skills, and philosophies developed by certain societies, with long histories of interaction with their natural surroundings, which will provide a foundation for locally appropriate sustainable development. This paper discussed the condition and situation on certain area in Cigugur, Indonesia, and what skills, knowledge, and concept can be transmitted, regarding simple mathematics (arithmetic). Some examples are provided.

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

The molecular and mathematical basis of Waddington's epigenetic landscape: a framework for post-Darwinian biology?

PubMed

Huang, Sui

2012-02-01

The Neo-Darwinian concept of natural selection is plausible when one assumes a straightforward causation of phenotype by genotype. However, such simple 1:1 mapping must now give place to the modern concepts of gene regulatory networks and gene expression noise. Both can, in the absence of genetic mutations, jointly generate a diversity of inheritable randomly occupied phenotypic states that could also serve as a substrate for natural selection. This form of epigenetic dynamics challenges Neo-Darwinism. It needs to incorporate the non-linear, stochastic dynamics of gene networks. A first step is to consider the mathematical correspondence between gene regulatory networks and Waddington's metaphoric 'epigenetic landscape', which actually represents the quasi-potential function of global network dynamics. It explains the coexistence of multiple stable phenotypes within one genotype. The landscape's topography with its attractors is shaped by evolution through mutational re-wiring of regulatory interactions - offering a link between genetic mutation and sudden, broad evolutionary changes. Copyright © 2012 WILEY Periodicals, Inc.

Pharmacokinetic analysis of multi PEG-theophylline conjugates.

PubMed

Grassi, Mario; Bonora, Gian Maria; Drioli, Sara; Cateni, Francesca; Zacchigna, Marina

2012-10-01

In the attempt of prolonging the effect of drugs, a new branched, high-molecular weight multimeric poly(ethylene glycol) (MultiPEG), synthesized with a simple assembling procedure that devised the introduction of functional groups with divergent and selective reactivity, was employed as drug carrier. In particular, the attention was focused on the study of theophylline (THEO) and THEO-MultiPEG conjugates pharmacokinetic after oral administration in rabbit. Pharmacokinetic behavior was studied according to an ad hoc developed mathematical model accounting for THEO-MultiPEG in vivo absorption and decomposition into drug (THEO) and carrier (MultiPEG). The branched high-molecular weight MultiPEG proved to be a reliable drug delivery system able to prolong theophylline staying in the blood after oral administration of a THEO-MultiPEG solution. The analysis of experimental data by means of the developed mathematical model revealed that the prolongation of THEO effect was essentially due to the low THEO-MultiPEG permeability in comparison to that of pure THEO. Copyright © 2012 Elsevier Ltd. All rights reserved.

A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

NASA Astrophysics Data System (ADS)

Allahverdyan, A. E.; Nieuwenhuizen, Th. M.

2002-03-01

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson formulation (“cyclic changes cost energy”), applied to equilibrium. This formulation of the second law is a property akin to particle conservation (normalization of the wave function). It has been strictly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble. As the derivation does not assume time-inversion invariance, it is applicable to situations where persistent currents occur. This clear-cut derivation allows to revive the “no perpetuum mobile in equilibrium” formulation of the second law and to criticize some assumptions which are widespread in literature. The result puts recent results devoted to foundations and limitations of the second law in proper perspective, and structurizes this relatively new field of research.

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model.

PubMed

Chao, Anne; Jost, Lou; Hsieh, T C; Ma, K H; Sherwin, William B; Rollins, Lee Ann

2015-01-01

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

NASA Astrophysics Data System (ADS)

Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

2018-05-01

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

Constructing a polynomial whose nodal set is the three-twist knot 52

NASA Astrophysics Data System (ADS)

Dennis, Mark R.; Bode, Benjamin

2017-06-01

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot 52. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other simple knots and links. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.

On the nonlocal predictions of quantum optics

NASA Technical Reports Server (NTRS)

Marshall, Trevor W.; Santos, Emilio; Vidiella-Barranco, Antonio

1994-01-01

We give a definition of locality in quantum optics based upon Bell's work, and show that locality has been violated in no experiment performed up to now. We argue that the interpretation of the Wigner function as a probability density gives a very attractive local realistic picture of quantum optics provided that this function is nonnegative. We conjecture that this is the case for all states which can be realized in the laboratory. In particular, we believe that the usual representation of 'single photon states' by a Fock state of the Hilbert space is not correct and that a more physical, although less simple mathematically, representation involves density matrices. We study in some detail the experiment showing anticorrelation after a beam splitter and prove that it naturally involves a positive Wigner function. Our (quantum) predictions for this experiment disagree with the ones reported in the literature.

A Membrane Model from Implicit Elasticity Theory

PubMed Central

Freed, A. D.; Liao, J.; Einstein, D. R.

2014-01-01

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079

On imputing function to structure from the behavioural effects of brain lesions.

PubMed

Young, M P; Hilgetag, C C; Scannell, J W

2000-01-29

What is the link, if any, between the patterns of connections in the brain and the behavioural effects of localized brain lesions? We explored this question in four related ways. First, we investigated the distribution of activity decrements that followed simulated damage to elements of the thalamocortical network, using integrative mechanisms that have recently been used to successfully relate connection data to information on the spread of activation, and to account simultaneously for a variety of lesion effects. Second, we examined the consequences of the patterns of decrement seen in the simulation for each type of inference that has been employed to impute function to structure on the basis of the effects of brain lesions. Every variety of conventional inference, including double dissociation, readily misattributed function to structure. Third, we tried to derive a more reliable framework of inference for imputing function to structure, by clarifying concepts of function, and exploring a more formal framework, in which knowledge of connectivity is necessary but insufficient, based on concepts capable of mathematical specification. Fourth, we applied this framework to inferences about function relating to a simple network that reproduces intact, lesioned and paradoxically restored orientating behaviour. Lesion effects could be used to recover detailed and reliable information on which structures contributed to particular functions in this simple network. Finally, we explored how the effects of brain lesions and this formal approach could be used in conjunction with information from multiple neuroscience methodologies to develop a practical and reliable approach to inferring the functional roles of brain structures.

Complexity VIII. Ontology of closure in complex systems: The C* hypothesis and the O° notation

NASA Astrophysics Data System (ADS)

Chandler, Jerry LR

1999-03-01

Closure is a common characteristic of mathematical, natural and socio-cultural systems. Whether one is describing a graph, a molecule, a cell, a human, or a nation state, closure is implicitly understood. An objective of this paper is to continue a construction of a systematic framework for closure which is sufficient for future quantitative transdisciplinary investigations. A further objective is to extend the Birkhoff-von Neumann criterion for quantum systems to complex natural objects. The C* hypothesis is being constructed to be consistent with algebraic category theory (Ehresmann and Vanbremeersch, 1987, 1997, Chandler, 1990, 1991, Chandler, Ehresmann and Vanbremeersch, 1996). Five aspects of closure will be used to construct a framework for categories of complex systems: 1. Truth functions in mathematics and the natural sciences 2. Systematic descriptions in the mks and O° notations 3. Organizational structures in hierarchical scientific languages 4. Transitive organizational pathways in the causal structures of complex behaviors 5. Composing additive, multiplicative and exponential operations in complex systems Truth functions can be formal or objective or subjective, depending on the complexity of the system and on our capability to represent the fine structure of the system symbolically, observationally or descriptively. "Complete" material representations of the fine structure of a system may allow truth functions to be created over sets of one to one correspondences. Less complete descriptions can support less stringent truth functions based on coherence or subjective judgments. The role of human values in creating and perpetuating truth functions can be placed in context of the degree of fine structure in the system's description. The organization of complex systems are hypothesized to be categorizable into degrees relative to one another, thereby creating an ordering relationship. This ordering relationship is denoted by the symbols: O°1, O°2,O°3... For example, for material systems, an ordering relation such as particles, atoms, molecules, cells, tissues, organs, individuals and social groups might be assigned to classify observations for medical purposes. The C* hypothesis asserts that any complex system can be described in terms of four enumerable concepts: closure, conformation, concatenation and cyclicity. Mappings between objects are constructed within a notation for organization. Causality is organized within C* as pathways of relationships in time. The notation of organizational degrees is used to distinguish a directionality for causality: 1. bottom-up (energy flows) 2. top-down (control processes or dominating variables), 3. outside — inward (ecoment on organism) and 4. inside — outward (organism on ecoment). Closures are asserted to emerge from evolutionary cooperation. It is asserted that truth functions emerged from the necessity of an organism to identify ecoments where life can prosper. For example, basic truth functions of mathematics (operations of addition, multiplication and exponentiation) are made operationally consistent within the biochemical operations of sustaining exponential cellular growth. These fundamental mathematical functions can provide a logical basis (in conjunction with conservation rules) for a construction of complex material categories at higher degrees of organization. It is remarked that these simple functions suggests a biochemical origin for the intuitionistic philosophy of mathematics. The emergence and success of mathematics is conjectured to result from the need to acquire a consistent basis for communication among individuals seeking to cooperate socially. This suggests a cultural closure over a collection of individual closures.

Validation of the replica trick for simple models

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-04-01

We discuss the replica analytic continuation using several simple models in order to prove mathematically the validity of the replica analysis, which is used in a wide range of fields related to large-scale complex systems. While replica analysis consists of two analytical techniques—the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion)—we focus our study on replica analytic continuation, which is the mathematical basis of the replica trick. We apply replica analysis to solve a variety of analytical models, and examine the properties of replica analytic continuation. Based on the positive results for these models we propose that replica analytic continuation is a robust procedure in replica analysis.

The ambient dose equivalent at flight altitudes: a fit to a large set of data using a Bayesian approach.

PubMed

Wissmann, F; Reginatto, M; Möller, T

2010-09-01

The problem of finding a simple, generally applicable description of worldwide measured ambient dose equivalent rates at aviation altitudes between 8 and 12 km is difficult to solve due to the large variety of functional forms and parametrisations that are possible. We present an approach that uses Bayesian statistics and Monte Carlo methods to fit mathematical models to a large set of data and to compare the different models. About 2500 data points measured in the periods 1997-1999 and 2003-2006 were used. Since the data cover wide ranges of barometric altitude, vertical cut-off rigidity and phases in the solar cycle 23, we developed functions which depend on these three variables. Whereas the dependence on the vertical cut-off rigidity is described by an exponential, the dependences on barometric altitude and solar activity may be approximated by linear functions in the ranges under consideration. Therefore, a simple Taylor expansion was used to define different models and to investigate the relevance of the different expansion coefficients. With the method presented here, it is possible to obtain probability distributions for each expansion coefficient and thus to extract reliable uncertainties even for the dose rate evaluated. The resulting function agrees well with new measurements made at fixed geographic positions and during long haul flights covering a wide range of latitudes.

Facilitating Student Understanding of Buffering by an Integration of Mathematics and Chemical Concepts

ERIC Educational Resources Information Center

Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John

2004-01-01

We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…

Posing Complex Problems Requiring Multiplicative Thinking Prompts Students to Use Sophisticated Strategies and Build Mathematical Connections

ERIC Educational Resources Information Center

Downton, Ann; Sullivan, Peter

2017-01-01

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Issues in Combining the Use of Various Tools in Solving Mathematical Problems--Why Is Copy-Paste Often Useless

ERIC Educational Resources Information Center

Lokar, Matija; Libbrecht, Paul

2017-01-01

Mathematical formulae are information objects that can be entered in a computer, visualized, and evaluated. Thus, by the majority of (mostly occasional) users it is also expected that they are transferable through the simple copy-paste procedure. This transfer is particularly interesting when users are involved in tasks that span different…

Teaching with Technology: Exploring the Use of Robotics to Teach Mathematics

ERIC Educational Resources Information Center

Attard, Catherine

2012-01-01

In this article, the author explores the value of using simple robotics such as BeeBots and ProBots to enhance the teaching and learning of mathematics in the primary classroom. Before making the decision to use such technologies, it is important that they be evaluated in terms of their affordances and constraints. In other words, teachers need to…

Design and Use Online Platforms to Learn Mathematics and the Use of Them in Simulations of Problems in Applied Sciences

ERIC Educational Resources Information Center

Méndez-Fragoso, Ricardo; Villavicencio-Torres, Mirna; Martínez-Moreno, Josué

2017-01-01

In this contribution, we show the practical use of the computer to visualise simple computational simulations to show phenomena that occur in everyday life, or require an abstract understanding for being unintuitive phenomena. The relationship of the mathematics to different scientific disciplines motivates us to devise different treatments to…

Appreciation of Mathematics through Origami

ERIC Educational Resources Information Center

Wares, Arsalan

2013-01-01

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important mathematical concepts in geometry like surface area. This article describes how an origami box can be folded from a rectangular sheet of paper, then it goes on to describe how its surface area can be determined in terms of the…

Mathematics Curriculum Based Measurement to Predict State Test Performance: A Comparison of Measures and Methods

ERIC Educational Resources Information Center

Stevens, Olinger; Leigh, Erika

2012-01-01

Scope and Method of Study: The purpose of the study is to use an empirical approach to identify a simple, economical, efficient, and technically adequate performance measure that teachers can use to assess student growth in mathematics. The current study has been designed to expand the body of research for math CBM to further examine technical…

Science and Mathematics in Astronomy

NASA Technical Reports Server (NTRS)

Woolack, Edward

2009-01-01

A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.

A Mathematical Method to Calculate Tumor Contact Surface Area: An Effective Parameter to Predict Renal Function after Partial Nephrectomy.

PubMed

Hsieh, Po-Fan; Wang, Yu-De; Huang, Chi-Ping; Wu, Hsi-Chin; Yang, Che-Rei; Chen, Guang-Heng; Chang, Chao-Hsiang

2016-07-01

We proposed a mathematical formula to calculate contact surface area between a tumor and renal parenchyma. We examined the applicability of using contact surface area to predict renal function after partial nephrectomy. We performed this retrospective study in patients who underwent partial nephrectomy between January 2012 and December 2014. Based on abdominopelvic computerized tomography or magnetic resonance imaging, we calculated the contact surface area using the formula (2*π*radius*depth) developed by integral calculus. We then evaluated the correlation between contact surface area and perioperative parameters, and compared contact surface area and R.E.N.A.L. (Radius/Exophytic/endophytic/Nearness to collecting system/Anterior/Location) score in predicting a reduction in renal function. Overall 35, 26 and 45 patients underwent partial nephrectomy with open, laparoscopic and robotic approaches, respectively. Mean ± SD contact surface area was 30.7±26.1 cm(2) and median (IQR) R.E.N.A.L. score was 7 (2.25). Spearman correlation analysis showed that contact surface area was significantly associated with estimated blood loss (p=0.04), operative time (p=0.04) and percent change in estimated glomerular filtration rate (p <0.001). On multivariate analysis contact surface area and R.E.N.A.L. score independently affected percent change in estimated glomerular filtration rate (p <0.001 and p=0.03, respectively). On ROC curve analysis contact surface area was a better independent predictor of a greater than 10% change in estimated glomerular filtration rate compared to R.E.N.A.L. score (AUC 0.86 vs 0.69). Using this simple mathematical method, contact surface area was associated with surgical outcomes. Compared to R.E.N.A.L. score, contact surface area was a better predictor of functional change after partial nephrectomy. Copyright © 2016 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.

Quartz dissolution. I - Negative crystal experiments and a rate law. II - Theory of rough and smooth surfaces

NASA Technical Reports Server (NTRS)

Gratz, Andrew J.; Bird, Peter

1993-01-01

The range of the measured quartz dissolution rates, as a function of temperature and pOH, extent of saturation, and ionic strength, is extended to cover a wider range of solution chemistries, using the negative crystal methodology of Gratz et al. (1990) to measure the dissolution rate. A simple rate law describing the quartz dissolution kinetics above the point of zero charge of quartz is derived for ionic strengths above 0.003 m. Measurements were performed on some defective crystals, and the mathematics of step motion was developed for quartz dissolution and was compared with rough-face behavior using two different models.

Implementation of density functional theory method on object-oriented programming (C++) to calculate energy band structure using the projector augmented wave (PAW)

NASA Astrophysics Data System (ADS)

Alfianto, E.; Rusydi, F.; Aisyah, N. D.; Fadilla, R. N.; Dipojono, H. K.; Martoprawiro, M. A.

2017-05-01

This study implemented DFT method into the C++ programming language with object-oriented programming rules (expressive software). The use of expressive software results in getting a simple programming structure, which is similar to mathematical formula. This will facilitate the scientific community to develop the software. We validate our software by calculating the energy band structure of Silica, Carbon, and Germanium with FCC structure using the Projector Augmented Wave (PAW) method then compare the results to Quantum Espresso calculation’s results. This study shows that the accuracy of the software is 85% compared to Quantum Espresso.

Neutral Evolution of Duplicated DNA: An Evolutionary Stick-Breaking Process Causes Scale-Invariant Behavior

NASA Astrophysics Data System (ADS)

Massip, Florian; Arndt, Peter F.

2013-04-01

Recently, an enrichment of identical matching sequences has been found in many eukaryotic genomes. Their length distribution exhibits a power law tail raising the question of what evolutionary mechanism or functional constraints would be able to shape this distribution. Here we introduce a simple and evolutionarily neutral model, which involves only point mutations and segmental duplications, and produces the same statistical features as observed for genomic data. Further, we extend a mathematical model for random stick breaking to analytically show that the exponent of the power law tail is -3 and universal as it does not depend on the microscopic details of the model.

Boundary assessment under uncertainty: A case study

USGS Publications Warehouse

Pawlowsky, V.; Olea, R.A.; Davis, J.C.

1993-01-01

Estimating certain attributes within a geological body whose exact boundary is not known presents problems because of the lack of information. Estimation may result in values that are inadmissible from a geological point of view, especially with attributes which necessarily must be zero outside the boundary, such as the thickness of the oil column outside a reservoir. A simple but effective way to define the boundary is to use indicator kriging in two steps, the first for the purpose of extrapolating control points outside the body, the second to obtain a weighting function which expresses the uncertainty attached to estimations obtained in the boundary region. ?? 1993 International Association for Mathematical Geology.

Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?

ERIC Educational Resources Information Center

Öçal, Mehmet Fatih

2017-01-01

Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…

Simple, Flexible, Trigonometric Taper Equations

Treesearch

Charles E. Thomas; Bernard R. Parresol

1991-01-01

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

Simple Games . . . or Are They?

ERIC Educational Resources Information Center

Arn, Susan Kyle

2006-01-01

Students today begin using computers and playing video games as early as two years old. The technology behind these games is more complicated than most people can imagine. In this article, the author presents some simple number games which seem easy at the beginning, but as the games are repeated, mathematical content becomes more of the focus…

Simple Examples of the Interpretation of Changes in Kinetic and Potential Energy under Galilean Transformations

ERIC Educational Resources Information Center

Ginsberg, Edw S.

2018-01-01

The compatibility of the Newtonian formulation of mechanical energy and the transformation equations of Galilean relativity is demonstrated for three simple examples of motion treated in most introductory physics courses (free fall, a frictionless inclined plane, and a mass/spring system). Only elementary concepts and mathematics, accessible to…

Teaching the Concept of Breakdown Point in Simple Linear Regression.

ERIC Educational Resources Information Center

Chan, Wai-Sum

2001-01-01

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

Preschool Executive Functioning Abilities Predict Early Mathematics Achievement

ERIC Educational Resources Information Center

Clark, Caron A. C.; Pritchard, Verena E.; Woodward, Lianne J.

2010-01-01

Impairments in executive function have been documented in school-age children with mathematical learning difficulties. However, the utility and specificity of preschool executive function abilities in predicting later mathematical achievement are poorly understood. This study examined linkages between children's developing executive function…

Variations of anthropogenic CO2 in urban area deduced by radiocarbon concentration in modern tree rings.

PubMed

Rakowski, Andrzej Z; Nakamura, Toshio; Pazdur, Anna

2008-10-01

Radiocarbon concentration in the atmosphere is significantly lower in areas where man-made emissions of carbon dioxide occur. This phenomenon is known as Suess effect, and is caused by the contamination of clean air with non-radioactive carbon from fossil fuel combustion. The effect is more strongly observed in industrial and densely populated urban areas. Measurements of carbon isotope concentrations in a study area can be compared to those from areas of clear air in order to estimate the amount of carbon dioxide emission from fossil fuel combustion by using a simple mathematical model. This can be calculated using the simple mathematical model. The result of the mathematical model followed in this study suggests that the use of annual rings of trees to obtain the secular variations of 14C concentration of atmospheric CO2 can be useful and efficient for environmental monitoring and modeling of the carbon distribution in local scale.

Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

NASA Astrophysics Data System (ADS)

Huang, Qingdao; Qian, Hong

2009-09-01

We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells.

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels

PubMed Central

Afshar, Saeed; George, Libin; Tapson, Jonathan; van Schaik, André; Hamilton, Tara J.

2014-01-01

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively “hiding” its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research. PMID:25505378

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels.

PubMed

Afshar, Saeed; George, Libin; Tapson, Jonathan; van Schaik, André; Hamilton, Tara J

2014-01-01

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively "hiding" its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research.

The development of executive functions and early mathematics: a dynamic relationship.

PubMed

Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Boom, Jan; Leseman, Paul P M

2012-03-01

The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown. The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal development of executive functions and mathematics; and the relation between them. A total of 211 children in grade 2 (7-8 years old) from 10 schools in the Netherlands. Children were followed in grade 1 and 2 of primary education. Executive functions and mathematics were measured four times. The test battery contained multiple tasks for each executive function: Animal stroop, local global, and Simon task for inhibition; Animal Shifting, Trail Making Test in Colours, and Sorting Task for shifting; and Digit Span Backwards, Odd One Out, and Keep Track for updating. The factor structure of executive functions was assessed and relations with mathematics were investigated using growth modelling. Confirmatory factor analysis (CFA) showed that inhibition and shifting could not be distinguished from each other. Updating was a separate factor, and its development was strongly related to mathematical development while inhibition and shifting did not predict mathematics in the presence of the updating factor. The strong relationship between updating and mathematics suggest that updating skills play a key role in the maths learning process. This makes updating a promising target for future intervention studies. ©2011 The British Psychological Society.

Biodiversity patterns along ecological gradients: unifying β-diversity indices.

PubMed

Szava-Kovats, Robert C; Pärtel, Meelis

2014-01-01

Ecologists have developed an abundance of conceptions and mathematical expressions to define β-diversity, the link between local (α) and regional-scale (γ) richness, in order to characterize patterns of biodiversity along ecological (i.e., spatial and environmental) gradients. These patterns are often realized by regression of β-diversity indices against one or more ecological gradients. This practice, however, is subject to two shortcomings that can undermine the validity of the biodiversity patterns. First, many β-diversity indices are constrained to range between fixed lower and upper limits. As such, regression analysis of β-diversity indices against ecological gradients can result in regression curves that extend beyond these mathematical constraints, thus creating an interpretational dilemma. Second, despite being a function of the same measured α- and γ-diversity, the resultant biodiversity pattern depends on the choice of β-diversity index. We propose a simple logistic transformation that rids beta-diversity indices of their mathematical constraints, thus eliminating the possibility of an uninterpretable regression curve. Moreover, this transformation results in identical biodiversity patterns for three commonly used classical beta-diversity indices. As a result, this transformation eliminates the difficulties of both shortcomings, while allowing the researcher to use whichever beta-diversity index deemed most appropriate. We believe this method can help unify the study of biodiversity patterns along ecological gradients.

Biodiversity Patterns along Ecological Gradients: Unifying β-Diversity Indices

PubMed Central

Szava-Kovats, Robert C.; Pärtel, Meelis

2014-01-01

Ecologists have developed an abundance of conceptions and mathematical expressions to define β-diversity, the link between local (α) and regional-scale (γ) richness, in order to characterize patterns of biodiversity along ecological (i.e., spatial and environmental) gradients. These patterns are often realized by regression of β-diversity indices against one or more ecological gradients. This practice, however, is subject to two shortcomings that can undermine the validity of the biodiversity patterns. First, many β-diversity indices are constrained to range between fixed lower and upper limits. As such, regression analysis of β-diversity indices against ecological gradients can result in regression curves that extend beyond these mathematical constraints, thus creating an interpretational dilemma. Second, despite being a function of the same measured α- and γ-diversity, the resultant biodiversity pattern depends on the choice of β-diversity index. We propose a simple logistic transformation that rids beta-diversity indices of their mathematical constraints, thus eliminating the possibility of an uninterpretable regression curve. Moreover, this transformation results in identical biodiversity patterns for three commonly used classical beta-diversity indices. As a result, this transformation eliminates the difficulties of both shortcomings, while allowing the researcher to use whichever beta-diversity index deemed most appropriate. We believe this method can help unify the study of biodiversity patterns along ecological gradients. PMID:25330181

Blessing of dimensionality: mathematical foundations of the statistical physics of data.

PubMed

Gorban, A N; Tyukin, I Y

2018-04-28

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Blessing of dimensionality: mathematical foundations of the statistical physics of data

NASA Astrophysics Data System (ADS)

Gorban, A. N.; Tyukin, I. Y.

2018-04-01

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue `Hilbert's sixth problem'.

A complex analysis approach to the motion of uniform vortices

NASA Astrophysics Data System (ADS)

Riccardi, Giorgio

2018-02-01

A new mathematical approach to kinematics and dynamics of planar uniform vortices in an incompressible inviscid fluid is presented. It is based on an integral relation between Schwarz function of the vortex boundary and induced velocity. This relation is firstly used for investigating the kinematics of a vortex having its Schwarz function with two simple poles in a transformed plane. The vortex boundary is the image of the unit circle through the conformal map obtained by conjugating its Schwarz function. The resulting analysis is based on geometric and algebraic properties of that map. Moreover, it is shown that the steady configurations of a uniform vortex, possibly in presence of point vortices, can be also investigated by means of the integral relation. The vortex equilibria are divided in two classes, depending on the behavior of the velocity on the boundary, measured in a reference system rotating with this curve. If it vanishes, the analysis is rather simple. However, vortices having nonvanishing relative velocity are also investigated, in presence of a polygonal symmetry. In order to study the vortex dynamics, the definition of Schwarz function is then extended to a Lagrangian framework. This Lagrangian Schwarz function solves a nonlinear integrodifferential Cauchy problem, that is transformed in a singular integral equation. Its analytical solution is here approached in terms of successive approximations. The self-induced dynamics, as well as the interactions with a point vortex, or between two uniform vortices are analyzed.

Fermilab Today

Science.gov Websites

standard for special mathematical functions A new standard for mathematical special functions in C++ has the standard are frequently used in applications of high-energy physics and other mathematical

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

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

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

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

Uniform function constants of motion and their first-order perturbation

NASA Astrophysics Data System (ADS)

Prato, Domingo; Hamity, Victor H.

2005-05-01

The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

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…

Development of mathematical models of environmental physiology

NASA Technical Reports Server (NTRS)

Stolwijk, J. A. J.; Mitchell, J. W.; Nadel, E. R.

1971-01-01

Selected articles concerned with mathematical or simulation models of human thermoregulation are presented. The articles presented include: (1) development and use of simulation models in medicine, (2) model of cardio-vascular adjustments during exercise, (3) effective temperature scale based on simple model of human physiological regulatory response, (4) behavioral approach to thermoregulatory set point during exercise, and (5) importance of skin temperature in sweat regulation.

Using Blended Learning to Facilitate the Mathematical thought Processes of Primary School Learners in a Computer Laboratory: A Case Study in Calculating Simple Areas

ERIC Educational Resources Information Center

Naidoo, N.; Naidoo, R.

2007-01-01

Primary school learners' first encounters with mathematics in a traditional learning environment often create lifelong "math phobia."(Papert 1980) The situation in a country emerging from an oppressive education system designed to educationally disempower the majority of the population is much worse. The typical scenario in a previously…

Neurocognitive mechanisms of mathematical giftedness: A literature review.

PubMed

Zhang, Li; Gan, John Q; Wang, Haixian

2017-01-01

Mathematically gifted children/adolescents have demonstrated exceptional abilities and traits in logical reasoning, mental imagery, and creative thinking. In the field of cognitive neuroscience, the past studies on mathematically gifted brains have concentrated on investigating event-related brain activation regions, cerebral laterality of cognitive functions, functional specialization that is uniquely dedicated for specific cognitive purposes, and functional interactions among discrete brain regions. From structural and functional perspectives, these studies have witnessed both "general" and "unique" neural characteristics of mathematically gifted brains. In this article, the theoretical background, empirical studies, and neurocognitive mechanisms of mathematically gifted children/adolescents are reviewed. Based on the integration of the findings, some potential directions for the future research are identified and discussed.

Assessing Quantitative Learning With The Math You Need When You Need It

NASA Astrophysics Data System (ADS)

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

2008-12-01

We present new data from a pilot project using the The Math You Need, When You Need It (TMYN) web resources in conjunction with several introductory geoscience courses. TMYN is a series of NSF-supported, NAGT-sponsored, web-based modular resources designed to help students learn (or relearn) mathematical skills essential for success in introductory geoscience courses. TMYN presents mathematical topics that are relevant to introductory geoscience based on a survey of more than 75 geoscience faculty members. To date, modules include unit conversions, many aspects of graphing, density calculations, rearranging equations and other simple mathematical concepts commonly used in the geosciences. The modular nature of the resources make it simple to select the units that are appropriate for a given course. In the fall of 2008, nine TMYN modules were tested in three courses taught at Highline Community College (Geology 101) and University of Wisconsin Oshkosh (Physical and Environmental Geology). Over 300 students participated in the study by taking pre- and post-tests and completing modules relevant to their course. Feedback about the use of these modules has been mixed. Initial results confirm anecdotal evidence that students initially have difficulty applying mathematical concepts to geologic problems. Furthermore, pre- test results indicate that, although instructors assume that students can perform simple mathematical manipulations, many students arrive in courses without the skills to apply mathematical concepts in problem solving situations. TMYN resources effectively provide support for learning quantitative problem solving and a mechanism for students to engage in self-teaching. Although we have seen mixed results due to a range of instructor engagement with the material, TMYN can have significant effect on students who are math phobic or "can't do math" because they can work at their own pace to overcome affective obstacles such as fear and dislike of mathematics. TMYN is most effective when instructors make explicit connections between material in the modules and course content. Instructors who participated in the study in Fall 2008 reacted positively to the use of TMYN in introductory geoscience courses because the resources require minimal class and prep time. Furthermore, when instructors can hold students responsible for the quantitative concepts covered with TMYN, they feel more comfortable including quantitative information without significant loss of geologic content.

Preservice Mathematics Teachers' Experiences about Function and Equation Concepts

ERIC Educational Resources Information Center

Dede, Yuksel; Soybas, Danyal

2011-01-01

The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were…

The Functions of Function Discourse--University Mathematics Teaching from a Commognitive Standpoint

ERIC Educational Resources Information Center

Viirman, Olov

2014-01-01

This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the…

A novel method for calculating relative free energy of similar molecules in two environments

NASA Astrophysics Data System (ADS)

Farhi, Asaf; Singh, Bipin

2017-03-01

Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy, simple implementation, robustness and efficiency, which prevent the calculations from being automated and limit their use. Here we present an exact and complete decoupling analysis in which the partition functions of the compared systems decompose into the partition functions of the common and different subsystems. This decoupling analysis is applicable to submolecules with coupled degrees of freedom such as the methyl group and to any potential function (including the typical dihedral potentials), enabling to remove less terms in the transformation which results in a more efficient calculation. Then we show mathematically, in the context of partition function decoupling, that the two compared systems can be simulated separately, eliminating the need to design a composite system. We demonstrate the decoupling analysis and the separate transformations in a relative free energy calculation using MD simulations for a general force field and compare to another calculation and to experimental results. We present a unified soft-core technique that ensures the monotonicity of the numerically integrated function (analytical proof) which is important for the selection of intermediates. We show mathematically that in this soft-core technique the numerically integrated function can be non-steep only when we transform the systems separately, which can simplify the numerical integration. Finally, we show that when the systems have rugged energy landscape they can be equilibrated without introducing another sampling dimension which can also enable to use the simulation results for other free energy calculations.

Advances and Computational Tools towards Predictable Design in Biological Engineering

PubMed Central

2014-01-01

The design process of complex systems in all the fields of engineering requires a set of quantitatively characterized components and a method to predict the output of systems composed by such elements. This strategy relies on the modularity of the used components or the prediction of their context-dependent behaviour, when parts functioning depends on the specific context. Mathematical models usually support the whole process by guiding the selection of parts and by predicting the output of interconnected systems. Such bottom-up design process cannot be trivially adopted for biological systems engineering, since parts function is hard to predict when components are reused in different contexts. This issue and the intrinsic complexity of living systems limit the capability of synthetic biologists to predict the quantitative behaviour of biological systems. The high potential of synthetic biology strongly depends on the capability of mastering this issue. This review discusses the predictability issues of basic biological parts (promoters, ribosome binding sites, coding sequences, transcriptional terminators, and plasmids) when used to engineer simple and complex gene expression systems in Escherichia coli. A comparison between bottom-up and trial-and-error approaches is performed for all the discussed elements and mathematical models supporting the prediction of parts behaviour are illustrated. PMID:25161694

On the Prony series representation of stretched exponential relaxation

NASA Astrophysics Data System (ADS)

Mauro, John C.; Mauro, Yihong Z.

2018-09-01

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

Exploring Measurement Error with Cookies: A Real and Virtual Approach via Interactive Excel

ERIC Educational Resources Information Center

Sinex, Scott A; Gage, Barbara A.; Beck, Peggy J.

2007-01-01

A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive…

Grass Grows, the Cow Eats: A Simple Grazing Systems Model with Emergent Properties

ERIC Educational Resources Information Center

Ungar, Eugene David; Seligman, Noam G.; Noy-Meir, Imanuel

2004-01-01

We describe a simple, yet intellectually challenging model of grazing systems that introduces basic concepts in ecology and systems analysis. The practical is suitable for high-school and university curricula with a quantitative orientation, and requires only basic skills in mathematics and spreadsheet use. The model is based on Noy-Meir's (1975)…

Cooperative Team Networks

DTIC Science & Technology

2016-06-01

team processes, such as identifying motifs of dynamic communication exchanges which goes well beyond simple dyadic and triadic configurations; as well...new metrics and ways to formulate team processes, such as identifying motifs of dynamic communication exchanges which goes well beyond simple dyadic ...sensing, communication , information, and decision networks - Darryl Ahner (AFIT: Air Force Inst Tech) Panel Session: Mathematical Models of

Turning Points of the Spherical Pendulum and the Golden Ratio

ERIC Educational Resources Information Center

Essen, Hanno; Apazidis, Nicholas

2009-01-01

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…

Dynamic Boolean Mathematics

ERIC Educational Resources Information Center

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

2016-01-01

Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

Learning Abstract Physical Concepts from Experience: Design and Use of an RC Circuit

NASA Astrophysics Data System (ADS)

Parra, Alfredo; Ordenes, Jorge; de la Fuente, Milton

2018-05-01

Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a simple experimental model in this work that allows students to easily design, build, and analyze RC circuits, thus providing an opportunity to test personal ideas, build graphical descriptions, and explore the meaning of the respective mathematical models, ultimately gaining a better grasp of the concepts involved. The result suggests that the simple setup indeed helps untrained students to visualize the essential points of this kind of circuit.

The correlation structure of several popular pseudorandom number generators

NASA Technical Reports Server (NTRS)

Neuman, F.; Merrick, R.; Martin, C. F.

1973-01-01

One of the desirable properties of a pseudorandom number generator is that the sequence of numbers it generates should have very low autocorrelation for all shifts except for zero shift and those that are multiples of its cycle length. Due to the simple methods of constructing random numbers, the ideal is often not quite fulfilled. A simple method of examining any random generator for previously unsuspected regularities is discussed. Once they are discovered it is often easy to derive the mathematical relationships, which describe the mathematical relationships, which describe the regular behavior. As examples, it is shown that high correlation exists in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle lengths.

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

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

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

Temperature extrapolation of multicomponent grand canonical free energy landscapes

NASA Astrophysics Data System (ADS)

Mahynski, Nathan A.; Errington, Jeffrey R.; Shen, Vincent K.

2017-08-01

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.

Shape Control in Multivariate Barycentric Rational Interpolation

NASA Astrophysics Data System (ADS)

Nguyen, Hoa Thang; Cuyt, Annie; Celis, Oliver Salazar

2010-09-01

The most stable formula for a rational interpolant for use on a finite interval is the barycentric form [1, 2]. A simple choice of the barycentric weights ensures the absence of (unwanted) poles on the real line [3]. In [4] we indicate that a more refined choice of the weights in barycentric rational interpolation can guarantee comonotonicity and coconvexity of the rational interpolant in addition to a polefree region of interest. In this presentation we generalize the above to the multivariate case. We use a product-like form of univariate barycentric rational interpolants and indicate how the location of the poles and the shape of the function can be controlled. This functionality is of importance in the construction of mathematical models that need to express a certain trend, such as in probability distributions, economics, population dynamics, tumor growth models etc.

Verification of floating-point software

NASA Technical Reports Server (NTRS)

Hoover, Doug N.

1990-01-01

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

The contribution of executive functions to emergent mathematic skills in preschool children.

PubMed

Espy, Kimberly Andrews; McDiarmid, Melanie M; Cwik, Mary F; Stalets, Melissa Meade; Hamby, Arlena; Senn, Theresa E

2004-01-01

Mathematical ability is related to both activation of the prefrontal cortex in neuroimaging studies of adults and to executive functions in school-age children. The purpose of this study was to determine whether executive functions were related to emergent mathematical proficiency in preschool children. Preschool children (N = 96) were administered an executive function battery that was reduced empirically to working memory (WM), inhibitory control (IC), and shifting abilities by calculating composite scores derived from principal component analysis. Both WM and IC predicted early arithmetic competency, with the observed relations robust after controlling statistically for child age, maternal education, and child vocabulary. Only IC accounted for unique variance in mathematical skills, after the contribution of other executive functions were controlled statistically as well. Specific executive functions are related to emergent mathematical proficiency in this age range. Longitudinal studies using structural equation modeling are necessary to better characterize these ontogenetic relations.

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

ERIC Educational Resources Information Center

Ko, Yi-Yin; Knuth, Eric

2009-01-01

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

Mathematical Astronomy in India

NASA Astrophysics Data System (ADS)

Plofker, Kim

Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.

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

ERIC Educational Resources Information Center

Newton, Lawrence R.

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

Exploring Mathematics Teachers' Pedagogical Content Knowledge in the Context of Knowledge of Students

ERIC Educational Resources Information Center

Aksu, Zeki; Kul, Ümit

2016-01-01

Functions are one of the basic topics taught in mathematics curriculum at Secondary school level requiring knowledge from the students' past, and uniting mathematical topics. Mathematics teachers have both their own learning experience of functions, as well as their own teaching experience, leading to the question of what level of student…

Executive functioning as a predictor of children's mathematics ability: inhibition, switching, and working memory.

PubMed

Bull, R; Scerif, G

2001-01-01

Children's mathematical skills were considered in relation to executive functions. Using multiple measures--including the Wisconsin Card Sorting Task (WCST), dual-task performance, Stroop task, and counting span-it was found that mathematical ability was significantly correlated with all measures of executive functioning, with the exception of dual-task performance. Furthermore, regression analyses revealed that each executive function measure predicted unique variance in mathematics ability. These results are discussed in terms of a central executive with diverse functions (Shallice & Burgess, 1996) and with recent evidence from Miyake, et al. (2000) showing the unity and diversity among executive functions. It is proposed that the particular difficulties for children of lower mathematical ability are lack of inhibition and poor working memory, which result in problems with switching and evaluation of new strategies for dealing with a particular task. The practical and theoretical implications of these results are discussed, along with suggestions for task changes and longitudinal studies that would clarify theoretical and developmental issues related to executive functioning.

The art of spacecraft design: A multidisciplinary challenge

NASA Technical Reports Server (NTRS)

Abdi, F.; Ide, H.; Levine, M.; Austel, L.

1989-01-01

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition.

Determination of point of incidence for the case of reflection or refraction at spherical surface knowing two points lying on the ray.

PubMed

Mikš, Antonín; Novák, Pavel

2017-09-01

The paper is focused on the problem of determination of the point of incidence of a light ray for the case of reflection or refraction at the spherical optical surface, assuming that two fixed points in space that the sought light ray should go through are given. The requirement is that one of these points lies on the incident ray and the other point on the reflected/refracted ray. Although at first glance it seems to be a simple problem, it will be shown that it has no simple analytical solution. The basic idea of the solution is given, and it is shown that the problem leads to a nonlinear equation in one variable. The roots of the resulting nonlinear equation can be found by numerical methods of mathematical optimization. The proposed methods were implemented in MATLAB, and the proper function of these algorithms was verified on several examples.

A statistical method for measuring activation of gene regulatory networks.

PubMed

Esteves, Gustavo H; Reis, Luiz F L

2018-06-13

Gene expression data analysis is of great importance for modern molecular biology, given our ability to measure the expression profiles of thousands of genes and enabling studies rooted in systems biology. In this work, we propose a simple statistical model for the activation measuring of gene regulatory networks, instead of the traditional gene co-expression networks. We present the mathematical construction of a statistical procedure for testing hypothesis regarding gene regulatory network activation. The real probability distribution for the test statistic is evaluated by a permutation based study. To illustrate the functionality of the proposed methodology, we also present a simple example based on a small hypothetical network and the activation measuring of two KEGG networks, both based on gene expression data collected from gastric and esophageal samples. The two KEGG networks were also analyzed for a public database, available through NCBI-GEO, presented as Supplementary Material. This method was implemented in an R package that is available at the BioConductor project website under the name maigesPack.

Greener corona discharge for enhanced wind generation with a simple dip-coated carbon nanotube decoration

NASA Astrophysics Data System (ADS)

Wu, Yishan; Li, Jun; Ye, Jianchun; Chen, Xiaohong; Li, Huili; Huang, Sumei; Zhao, Ran; Ou-Yang, Wei

2017-10-01

Corona discharge-induced wind (CDIW) has been widely utilized in production lines in the food and semiconductor industries and in indoor devices such as electrostatic precipitators. Some ozone is inevitably emitted, posing serious health risks to respiratory system and lung function of a human being. In this work, a greener corona discharge with enhanced wind generation for a needle-to-cylinder discharge structure is demonstrated using a simple dip-coating method to attach carbon nanotubes (CNTs) to the discharge electrode of a stainless steel needle. Compared with a conventional discharge electrode without CNT decoration, the velocity of the CDIW is greatly enhanced, the onset voltage is lowered, the energy conversion efficiency is greatly improved and the concentration of generated ozone is much reduced, making this easy method of CNT decoration a promising candidate for greener corona discharge systems. In addition, several impact factors for improved performance are discussed mathematically and phenomenologically, providing an insight into the corona discharge and wind generation.

Kepler Observations of Rapid Optical Variability in the BL Lac Object W2r192+42

NASA Technical Reports Server (NTRS)

R.Edelson; Mushotzky, R.; Vaughn, S.; Scargle, J.; Gandhi, P.; Malkan, M.; Baumgartner, W.

2013-01-01

We present the first Kepler monitoring of a strongly variable BL Lac, W2R1926+42. The light curve covers 181 days with approx. 0.2% errors, 30 minute sampling and >90% duty cycle, showing numerous delta-I/I > 25% flares over timescales as short as a day. The flux distribution is highly skewed and non-Gaussian. The variability shows a strong rms-flux correlation with the clearest evidence to date for non-linearity in this relation. We introduce a method to measure periodograms from the discrete autocorrelation function, an approach that may be well-suited to a wide range of Kepler data. The periodogram is not consistent with a simple power-law, but shows a flattening at frequencies below 7x10(exp -5) Hz. Simple models of the power spectrum, such as a broken power law, do not produce acceptable fits, indicating that the Kepler blazar light curve requires more sophisticated mathematical and physical descriptions than currently in use.

Phase properties of elastic waves in systems constituted of adsorbed diatomic molecules on the (001) surface of a simple cubic crystal

NASA Astrophysics Data System (ADS)

Deymier, P. A.; Runge, K.

2018-03-01

A Green's function-based numerical method is developed to calculate the phase of scattered elastic waves in a harmonic model of diatomic molecules adsorbed on the (001) surface of a simple cubic crystal. The phase properties of scattered waves depend on the configuration of the molecules. The configurations of adsorbed molecules on the crystal surface such as parallel chain-like arrays coupled via kinks are used to demonstrate not only linear but also non-linear dependency of the phase on the number of kinks along the chains. Non-linear behavior arises for scattered waves with frequencies in the vicinity of a diatomic molecule resonance. In the non-linear regime, the variation in phase with the number of kinks is formulated mathematically as unitary matrix operations leading to an analogy between phase-based elastic unitary operations and quantum gates. The advantage of elastic based unitary operations is that they are easily realizable physically and measurable.

The Eye of a Mathematical Physicist

NASA Astrophysics Data System (ADS)

Hepp, Klaus

2009-03-01

In this essay we are searching for neural correlates of `doing mathematical physics'. We introduce a toy model of a mathematical physicist, a brain connected with the outside world only by vision and saccadic eye movements and interacting with a computer screen. First, we describe the neuroanatomy of the visuo-saccadic system and Listing's law, which binds saccades and the optics of the eye. Then we explain space-time transformations in the superior colliculus, the performance of a canonical cortical circuit in the frontal eye field and finally the recurrent interaction of both areas, which leads to a coherent percept of space in spite of saccades. This sets the stage in the brain for doing mathematical physics, which is analyzed in simple examples.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

The Relative Importance of Children's Criteria for Representational Adequacy in the Perception of Simple Sonic Stimuli

ERIC Educational Resources Information Center

Verschaffel, Lieven; Reybrouck, Mark; Degraeuwe, Goedele; Van Dooren, Wim

2013-01-01

This study investigates children's metarepresentational competence (MRC) with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2002) seminal work on MRC in mathematics and sciences as background, it aims to assess the relative importance children attribute to several criteria for representational adequacy…

Pizza Again? On the Division of Polygons into Sections with a Common Origin

ERIC Educational Resources Information Center

Sinitsky, Ilya; Stupel, Moshe; Sinitsky, Marina

2018-01-01

The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to…

Projectiles, pendula, and special relativity

NASA Astrophysics Data System (ADS)

Price, Richard H.

2005-05-01

The kind of flat-earth gravity used in introductory physics appears in an accelerated reference system in special relativity. From this viewpoint, we work out the special relativistic description of a ballistic projectile and a simple pendulum, two examples of simple motion driven by earth-surface gravity. The analysis uses only the basic mathematical tools of special relativity typical of a first-year university course.

Functions in the Secondary School Mathematics Curriculum

ERIC Educational Resources Information Center

Denbel, Dejene Girma

2015-01-01

Functions are used in every branch of mathematics, as algebraic operations on numbers, transformations on points in the plane or in space, intersection and union of pairs of sets, and so forth. Function is a unifying concept in all mathematics. Relationships among phenomena in everyday life, such as the relationship between the speed of a car and…

Simple analytical model reveals the functional role of embodied sensorimotor interaction in hexapod gaits

PubMed Central

Aoi, Shinya; Nachstedt, Timo; Manoonpong, Poramate; Wörgötter, Florentin; Matsuno, Fumitoshi

2018-01-01

Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect’s neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory feedback contributes to generation of insect-like ipsilateral interlimb coordination during hexapod locomotion. PMID:29489831

Convoluted Quasi Sturmian basis for the two-electron continuum

NASA Astrophysics Data System (ADS)

Ancarani, Lorenzo Ugo; Zaytsev, A. S.; Zaytsev, S. A.

2016-09-01

In the construction of solutions for the Coulomb three-body scattering problem one encounters a series of mathematical and numerical difficulties, one of which are the cumbersome boundary conditions the wave function should obey. We propose to describe a Coulomb three-body system continuum with a set of two-particle functions, named Convoluted Quasi Sturmian (CQS) in. They are built using recently introduced Quasi Sturmian (QS) functions which have the merit of possessing a closed form. Unlike a simple product of two one-particle functions, by construction, the CQS functions look asymptotically like a six-dimensional outgoing spherical wave. The proposed CQS basis is tested through the study of the double ionization of helium by high-energy electron impact in the framework of the Temkin-Poet model. An adequate logarithmic-like phase factor is further included in order to take into account the Coulomb interelectronic interaction and formally build the correct asymptotic behavior when all interparticle distances are large. With such a phase-factor (that can be easily extended to take into account higher partial waves) rapid convergence of the expansion can be obtained.

Optimal control of LQR for discrete time-varying systems with input delays

NASA Astrophysics Data System (ADS)

Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

2018-04-01

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study.

PubMed

Mercader, Jessica; Miranda, Ana; Presentación, M Jesús; Siegenthaler, Rebeca; Rosel, Jesús F

2017-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

PubMed Central

Mercader, Jessica; Miranda, Ana; Presentación, M. Jesús; Siegenthaler, Rebeca; Rosel, Jesús F.

2018-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5–6 and 7–8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed. PMID:29379462

Computing with scale-invariant neural representations

NASA Astrophysics Data System (ADS)

Howard, Marc; Shankar, Karthik

The Weber-Fechner law is perhaps the oldest quantitative relationship in psychology. Consider the problem of the brain representing a function f (x) . Different neurons have receptive fields that support different parts of the range, such that the ith neuron has a receptive field at xi. Weber-Fechner scaling refers to the finding that the width of the receptive field scales with xi as does the difference between the centers of adjacent receptive fields. Weber-Fechner scaling is exponentially resource-conserving. Neurophysiological evidence suggests that neural representations obey Weber-Fechner scaling in the visual system and perhaps other systems as well. We describe an optimality constraint that is solved by Weber-Fechner scaling, providing an information-theoretic rationale for this principle of neural coding. Weber-Fechner scaling can be generated within a mathematical framework using the Laplace transform. Within this framework, simple computations such as translation, correlation and cross-correlation can be accomplished. This framework can in principle be extended to provide a general computational language for brain-inspired cognitive computation on scale-invariant representations. Supported by NSF PHY 1444389 and the BU Initiative for the Physics and Mathematics of Neural Systems,.

New approaches for calculating Moran's index of spatial autocorrelation.

PubMed

Chen, Yanguang

2013-01-01

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran's index. Moran's scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran's index and Geary's coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran's index and Geary's coefficient will be clarified and defined. One of theoretical findings is that Moran's index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

A Simple Colorimeter.

ERIC Educational Resources Information Center

Martinez-Anton, J. C.; And Others

1995-01-01

Describes a system that demonstrates how a color may be generated and specified in mathematical terms. Illustrates the mixing of primary colors as well as the concepts of saturation, luminance, and illumination. (JRH)

Dynamic Characteristics of Simple Cylindrical Hydraulic Engine Mount Utilizing Air Compressibility

NASA Astrophysics Data System (ADS)

Nakahara, Kazunari; Nakagawa, Noritoshi; Ohta, Katsutoshi

A cylindrical hydraulic engine mount with simple construction has been developed. This engine mount has a sub chamber formed by utilizing air compressibility without a diaphragm. A mathematical model of the mount is presented to predict non-linear dynamic characteristics in consideration of the effect of the excitation amplitude on the storage stiffness and loss factor. The mathematical model predicts experimental results well for the frequency responses of the storage stiffness and loss factor over the frequency range of 5 Hz to 60Hz. The effect of air volume and internal pressure on the dynamic characteristics is clarified by the analysis and dynamic characterization testing. The effectiveness of the cylindrical hydraulic engine mount on the reduction of engine shake is demonstrated for riding comfort through on-vehicle testing with a chassis dynamometer.

Data-driven outbreak forecasting with a simple nonlinear growth model

PubMed Central

Lega, Joceline; Brown, Heidi E.

2016-01-01

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. PMID:27770752

Causality

NASA Astrophysics Data System (ADS)

Pearl, Judea

2000-03-01

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

Helping parents to motivate adolescents in mathematics and science: an experimental test of a utility-value intervention.

PubMed

Harackiewicz, Judith M; Rozek, Christopher S; Hulleman, Chris S; Hyde, Janet S

2012-08-01

The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem.

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

PISA Functional Literacy as Represented in Taiwanese Mathematics Textbooks

ERIC Educational Resources Information Center

Lee, Suiv

2013-01-01

PISA is a large international educational assessment activity coordinated by the "Organization for Economic Co-operation and Development" (OECD). PISA's "Functional Literacy" emphasizes the theoretical concept of mathematics as a human activity. From this pedagogical point of view, PISA's "mathematization cycle"…

Visual Perceptual Difficulties and Under-Achievement at School in a Large Community-Based Sample of Children

PubMed Central

Williams, Cathy; Northstone, Kate; Sabates, Ricardo; Feinstein, Leon; Emond, Alan; Dutton, Gordon N.

2011-01-01

Introduction Difficulties with visual perception (VP) are often described in children with neurological or developmental problems. However, there are few data regarding the range of visual perceptual abilities in populations of normal children, or on the impact of these abilities on children's day-to-day functioning. Methods Data were obtained for 4512 participants in an ongoing birth cohort study (Avon Longitudinal Study of Parents and Children; ALSPAC). The children's mothers responded to questions designed to elicit indications of visual perceptual difficulties or immaturity, when their children were aged 13 years. We examined associations with standardised school test results in reading and in mathematics at age 13–14 years (SATS-KS3), accounting for potential confounders including IQ. Results Three underlying factors explained half the variance in the VP question responses. These correlated best with questions on interpreting cluttered scenes; guidance of movement and face recognition. The adjusted parameter estimates (95% CI) for the cluttered-scenes factor (0.05; 0.02 to 0.08; p<0.001) suggested positive associations with the reading test results whilst that for the guidance-of-movement factor (0.03; 0.00 to 0.06; p = 0.026) suggested positive association with the mathematics results. The raw scores were associated with both test results. Discussion VP abilities were widely distributed in this sample of 13-year old children. Lower levels of VP function were associated with under-achievement in reading and in mathematics. Simple interventions can help children with VP difficulties, so research is needed into practicable, cost-effective strategies for identification and assessment, so that support can be targeted appropriately. PMID:21445286

Kinematic analysis of asymmetric folds in competent layers using mathematical modelling

NASA Astrophysics Data System (ADS)

Aller, J.; Bobillo-Ares, N. C.; Bastida, F.; Lisle, R. J.; Menéndez, C. O.

2010-08-01

Mathematical 2D modelling of asymmetric folds is carried out by applying a combination of different kinematic folding mechanisms: tangential longitudinal strain, flexural flow and homogeneous deformation. The main source of fold asymmetry is discovered to be due to the superimposition of a general homogeneous deformation on buckle folds that typically produces a migration of the hinge point. Forward modelling is performed mathematically using the software 'FoldModeler', by the superimposition of simple shear or a combination of simple shear and irrotational strain on initial buckle folds. The resulting folds are Ramsay class 1C folds, comparable to those formed by symmetric flattening, but with different length of limbs and layer thickness asymmetry. Inverse modelling is made by fitting the natural fold to a computer-simulated fold. A problem of this modelling is the search for the most appropriate homogeneous deformation to be superimposed on the initial fold. A comparative analysis of the irrotational and rotational deformations is made in order to find the deformation which best simulates the shapes and attitudes of natural folds. Modelling of recumbent folds suggests that optimal conditions for their development are: a) buckling in a simple shear regime with a sub-horizontal shear direction and layering gently dipping towards this direction; b) kinematic amplification due to superimposition of a combination of simple shear and irrotational strain with a sub-vertical maximum shortening direction for the latter component. The modelling shows that the amount of homogeneous strain necessary for the development of recumbent folds is much less when an irrotational strain component is superimposed at this stage that when the superimposed strain is only simple shear. In nature, the amount of the irrotational strain component probably increases during the development of the fold as a consequence of the increasing influence of the gravity due to the tectonic superimposition of rocks.

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

Analysis of the moments of the sensitivity function for resistivity over a homogeneous half-space: Rules of thumb for pseudoposition, offline sensitivity and resolution

NASA Astrophysics Data System (ADS)

Butler, S. L.

2017-08-01

It is instructive to consider the sensitivity function for a homogeneous half space for resistivity since it has a simple mathematical formula and it does not require a priori knowledge of the resistivity of the ground. Past analyses of this function have allowed visualization of the regions that contribute most to apparent resistivity measurements with given array configurations. The horizontally integrated form of this equation gives the sensitivity function for an infinitesimally thick horizontal slab with a small resistivity contrast and analysis of this function has admitted estimates of the depth of investigation for a given electrode array. Recently, it has been shown that the average of the vertical coordinate over this function yields a simple formula that can be used to estimate the depth of investigation. The sensitivity function for a vertical inline slab has also been previously calculated. In this contribution, I show that the sensitivity function for a homogeneous half-space can also be integrated so as to give sensitivity functions to semi-infinite vertical slabs that are perpendicular to the array axis. These horizontal sensitivity functions can, in turn, be integrated over the spatial coordinates to give the mean horizontal positions of the sensitivity functions. The mean horizontal positions give estimates for the centres of the regions that affect apparent resistivity measurements for arbitrary array configuration and can be used as horizontal positions when plotting pseudosections even for non-collinear arrays. The mean of the horizontal coordinate that is perpendicular to a collinear array also gives a simple formula for estimating the distance over which offline resistivity anomalies will have a significant effect. The root mean square (rms) widths of the sensitivity functions are also calculated in each of the coordinate directions as an estimate of the inverse of the resolution of a given array. For depth and in the direction perpendicular to the array, the rms thickness is shown to be very similar to the mean distance. For the direction parallel to the array, the rms thickness is shown to be proportional to the array length and similar to the array length divided by 2 for many arrays. I expect that these formulas will provide useful rules of thumb for estimating the centres and extents of regions influencing apparent resistivity measurements for survey planning and for education.

The Science of Sex Differences in Science and Mathematics

PubMed Central

Halpern, Diane F.; Benbow, Camilla P.; Geary, David C.; Gur, Ruben C.; Hyde, Janet Shibley; Gernsbacher, Morton Ann

2014-01-01

Summary Amid ongoing public speculation about the reasons for sex differences in careers in science and mathematics, we present a consensus statement that is based on the best available scientific evidence. Sex differences in science and math achievement and ability are smaller for the mid-range of the abilities distribution than they are for those with the highest levels of achievement and ability. Males are more variable on most measures of quantitative and visuospatial ability, which necessarily results in more males at both high- and low-ability extremes; the reasons why males are often more variable remain elusive. Successful careers in math and science require many types of cognitive abilities. Females tend to excel in verbal abilities, with large differences between females and males found when assessments include writing samples. High-level achievement in science and math requires the ability to communicate effectively and comprehend abstract ideas, so the female advantage in writing should be helpful in all academic domains. Males outperform females on most measures of visuospatial abilities, which have been implicated as contributing to sex differences on standardized exams in mathematics and science. An evolutionary account of sex differences in mathematics and science supports the conclusion that, although sex differences in math and science performance have not directly evolved, they could be indirectly related to differences in interests and specific brain and cognitive systems. We review the brain basis for sex differences in science and mathematics, describe consistent effects, and identify numerous possible correlates. Experience alters brain structures and functioning, so causal statements about brain differences and success in math and science are circular. A wide range of sociocultural forces contribute to sex differences in mathematics and science achievement and ability—including the effects of family, neighborhood, peer, and school influences; training and experience; and cultural practices. We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math and that these effects add and interact in complex ways. There are no single or simple answers to the complex questions about sex differences in science and mathematics. PMID:25530726

pyomocontrib_simplemodel v. 1.0

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

Hart, William

2017-03-02

Pyomo supports the formulation and analysis of mathematical models for complex optimization applications. This library extends the API of Pyomo to include a simple modeling representation: a list of objectives and constraints.

Working memory, math performance, and math anxiety.

PubMed

Ashcraft, Mark H; Krause, Jeremy A

2007-04-01

The cognitive literature now shows how critically math performance depends on working memory, for any form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric literature is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious avoid math: They avoid elective coursework in math, both in high school and college, they avoid college majors that emphasize math, and they avoid career paths that involve math. We go beyond these psychometric relationships to examine the cognitive consequences of math anxiety. We show how performance on a standardized math achievement test varies as a function of math anxiety, and that math anxiety compromises the functioning of working memory. High math anxiety works much like a dual task setting: Preoccupation with one's math fears and anxieties functions like a resource-demanding secondary task. We comment on developmental and educational factors related to math and working memory, and on factors that may contribute to the development of math anxiety.

A multi-objective genetic algorithm for a mixed-model assembly U-line balancing type-I problem considering human-related issues, training, and learning

NASA Astrophysics Data System (ADS)

Rabbani, Masoud; Montazeri, Mona; Farrokhi-Asl, Hamed; Rafiei, Hamed

2016-12-01

Mixed-model assembly lines are increasingly accepted in many industrial environments to meet the growing trend of greater product variability, diversification of customer demands, and shorter life cycles. In this research, a new mathematical model is presented considering balancing a mixed-model U-line and human-related issues, simultaneously. The objective function consists of two separate components. The first part of the objective function is related to balance problem. In this part, objective functions are minimizing the cycle time, minimizing the number of workstations, and maximizing the line efficiencies. The second part is related to human issues and consists of hiring cost, firing cost, training cost, and salary. To solve the presented model, two well-known multi-objective evolutionary algorithms, namely non-dominated sorting genetic algorithm and multi-objective particle swarm optimization, have been used. A simple solution representation is provided in this paper to encode the solutions. Finally, the computational results are compared and analyzed.

Fate of ethanol during cooking of liquid foods prepared with alcoholic beverages: Theory and experimental studies.

PubMed

Snitkjær, Pia; Ryapushkina, Julia; Skovenborg, Erik; Astrup, Arne; Bech, Lene Mølskov; Jensen, Morten Georg; Risbo, Jens

2017-09-01

To obtain an understanding of the ethanol loss during cooking of liquid foods containing alcoholic beverages, ethanol concentration was measured as a function of time and remaining volume in meat stocks prepared with wine and beer. A mathematical model describing the decline in volatile compounds during heating of simple liquid foods was derived. The experimental results and the model show that concentration of ethanol at any given time is determined by the initial concentration and a power law function of the remaining volume fraction. The power law function is found to be independent of factors like pot dimensions and temperature. When using a lid to cover the pot during cooking, the model was still valid but the ethanol concentrations decreased more steeply, corresponding to a higher exponent. The results provide a theoretical and empirical guideline for predicting the ethanol concentration in cooked liquid foods. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Membrane Model from Implicit Elasticity Theory. Application to Visceral Pleura

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

Freed, Alan D.; Liao, Jun; Einstein, Daniel R.

2013-11-27

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal energy function. The theory utilizes Biot’s (Lond Edinb Dublin Philos Mag J Sci 27:468–489, 1939) definitions for stress and strain that, in one-dimension, are the stress/strain measures adopted by Fung (Am J Physiol 28:1532–1544, 1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from amore » porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly nonlinear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model.« less

Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.

Mathematics Anxiety in Young Children: Concurrent and Longitudinal Associations with Mathematical Performance

ERIC Educational Resources Information Center

Vukovic, Rose K.; Kieffer, Michael J.; Bailey, Sean P.; Harari, Rachel R.

2013-01-01

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of…

Mathematical study on robust tissue pattern formation in growing epididymal tubule.

PubMed

Hirashima, Tsuyoshi

2016-10-21

Tissue pattern formation during development is a reproducible morphogenetic process organized by a series of kinetic cellular activities, leading to the building of functional and stable organs. Recent studies focusing on mechanical aspects have revealed physical mechanisms on how the cellular activities contribute to the formation of reproducible tissue patterns; however, the understanding for what factors achieve the reproducibility of such patterning and how it occurs is far from complete. Here, I focus on a tube pattern formation during murine epididymal development, and show that two factors influencing physical design for the patterning, the proliferative zone within the tubule and the viscosity of tissues surrounding to the tubule, control the reproducibility of epididymal tubule pattern, using a mathematical model based on experimental data. Extensive numerical simulation of the simple mathematical model revealed that a spatially localized proliferative zone within the tubule, observed in experiments, results in more reproducible tubule pattern. Moreover, I found that the viscosity of tissues surrounding to the tubule imposes a trade-off regarding pattern reproducibility and spatial accuracy relating to the region where the tubule pattern is formed. This indicates an existence of optimality in material properties of tissues for the robust patterning of epididymal tubule. The results obtained by numerical analysis based on experimental observations provide a general insight on how physical design realizes robust tissue pattern formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and fluency.

PubMed

Kellman, Philip J; Massey, Christine M; Son, Ji Y

2010-04-01

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning. Copyright © 2009 Cognitive Science Society, Inc.

Understanding synergy.

PubMed

Geary, Nori

2013-02-01

Analysis of the interactive effects of combinations of hormones or other manipulations with qualitatively similar individual effects is an important topic in basic and clinical endocrinology as well as other branches of basic and clinical research related to integrative physiology. Functional, as opposed to mechanistic, analyses of interactions rely on the concept of synergy, which can be defined qualitatively as a cooperative action or quantitatively as a supra-additive effect according to some metric for the addition of different dose-effect curves. Unfortunately, dose-effect curve addition is far from straightforward; rather, it requires the development of an axiomatic mathematical theory. I review the mathematical soundness, face validity, and utility of the most frequently used approaches to supra-additive synergy. These criteria highlight serious problems in the two most common synergy approaches, response additivity and Loewe additivity, which is the basis of the isobole and related response surface approaches. I conclude that there is no adequate, generally applicable, supra-additive synergy metric appropriate for endocrinology or any other field of basic and clinical integrative physiology. I recommend that these metrics be abandoned in favor of the simpler definition of synergy as a cooperative, i.e., nonantagonistic, effect. This simple definition avoids mathematical difficulties, is easily applicable, meets regulatory requirements for combination therapy development, and suffices to advance phenomenological basic research to mechanistic studies of interactions and clinical combination therapy research.

Mathematics deficits in adolescents with bipolar I disorder.

PubMed

Lagace, Diane C; Kutcher, Stanley P; Robertson, Heather A

2003-01-01

This study examined mathematical ability in adolescents with bipolar I disorder, compared to adolescents with major depressive disorder and psychiatrically healthy comparison subjects. Participants (N=119) included adolescents in remission from bipolar disorder (N=44) or major depressive disorder (N=30), as well as comparison subjects (N=45) with no psychiatric history. Participants were assessed with the following measures: the Wide-Range Achievement Test, Revised 2 (WRAT-R2), Peabody Individual Achievement Test, Bay Area Functional Performance Evaluation Task-Oriented Assessment (functional mathematics subtest), Test of Nonverbal Intellegence-2, and a self-report of mathematics performance. WRAT-R2 and Peabody Individual Achievement Test scores for spelling, mathematics, and reading revealed that adolescents with bipolar disorder had significantly lower achievement in mathematics, compared to subjects with major depressive disorder and comparison subjects. Results for the Test of Nonverbal Intellegence-2 were not significantly different between groups. Adolescents with bipolar disorder took significantly longer to complete the Bay Area Functional Performance Evaluation mathematics task. Significantly fewer adolescents with bipolar disorder (9%) reported above-average mathematics performance, compared with the other groups. Adolescents with remitted bipolar disorder have a specific profile of mathematics difficulties that differentiates them from both adolescents with unipolar depression and psychiatrically healthy comparison subjects. These mathematics deficits may not derive simply from more global deficits in nonverbal intelligence or executive functioning, but may be associated with neuroanatomical abnormalities that result in cognitive deficits, including a slowed response time. These deficits suggest the need for specialized assessment of mathematics as part of a comprehensive clinical follow-up treatment plan.

Optimal quality control of bakers' yeast fed-batch culture using population dynamics.

PubMed

Dairaku, K; Izumoto, E; Morikawa, H; Shioya, S; Takamatsu, T

1982-12-01

An optimal quality control policy for the overall specific growth rate of bakers' yeast, which maximizes the fermentative activity in the making of bread, was obtained by direct searching based on the mathematical model proposed previously. The mathematical model had described the age distribution of bakers' yeast which had an essential relationship to the ability of fermentation in the making of bread. The mathematical model is a simple aging model with two periods: Nonbudding and budding. Based on the result obtained by direct searching, the quality control of bakers' yeast fed-batch culture was performed and confirmed to be experimentally valid.

A simple mathematical model of society collapse applied to Easter Island

NASA Astrophysics Data System (ADS)

Bologna, M.; Flores, J. C.

2008-02-01

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.

Impact of the Equation of State in Models for Surfactant Spreading Experiments

NASA Astrophysics Data System (ADS)

Levy, Rachel

2014-11-01

Pulmonary surfactant spreading models often rely on an equation of state relating surfactant concentration to surface tension. Mathematically, these models have been analyzed with simple functional relationships. However, to model an experiment with a given fluid and surfactant, a physically meaningful equation of state can be derived from experimentally obtained isotherms. We discuss the comparison between model and experiment for NBD-PC lipid (surfactant) spreading on glycerol for an empirically-determined equation of state, and compare those results to simulations with traditionally employed functional forms. In particular we compare the timescales by tracking the leading edge of surfactant, the central fluid height and dynamics of the Marangoni ridge. We consider both outward spreading of a disk-shaped region of surfactant and the hole-closure problem in which a disk-shaped surfactant-free region self-heals. Support from NSF-DMS-FRG 0968154, RCSA-CCS-19788, and HHMI.

Extended probit mortality model for zooplankton against transient change of PCO(2).

PubMed

Sato, Toru; Watanabe, Yuji; Toyota, Koji; Ishizaka, Joji

2005-09-01

The direct injection of CO(2) in the deep ocean is a promising way to mitigate global warming. One of the uncertainties in this method, however, is its impact on marine organisms in the near field. Since the concentration of CO(2), which organisms experience in the ocean, changes with time, it is required to develop a biological impact model for the organisms against the unsteady change of CO(2) concentration. In general, the LC(50) concept is widely applied for testing a toxic agent for the acute mortality. Here, we regard the probit-transformed mortality as a linear function not only of the concentration of CO(2) but also of exposure time. A simple mathematical transform of the function gives a damage-accumulation mortality model for zooplankton. In this article, this model was validated by the mortality test of Metamphiascopsis hirsutus against the transient change of CO(2) concentration.

A solution to the surface intersection problem. [Boolean functions in geometric modeling

NASA Technical Reports Server (NTRS)

Timer, H. G.

1977-01-01

An application-independent geometric model within a data base framework should support the use of Boolean operators which allow the user to construct a complex model by appropriately combining a series of simple models. The use of these operators leads to the concept of implicitly and explicitly defined surfaces. With an explicitly defined model, the surface area may be computed by simply summing the surface areas of the bounding surfaces. For an implicitly defined model, the surface area computation must deal with active and inactive regions. Because the surface intersection problem involves four unknowns and its solution is a space curve, the parametric coordinates of each surface must be determined as a function of the arc length. Various subproblems involved in the general intersection problem are discussed, and the mathematical basis for their solution is presented along with a program written in FORTRAN IV for implementation on the IBM 370 TSO system.

Feedback Error Learning Controller for Functional Electrical Stimulation Assistance in a Hybrid Robotic System for Reaching Rehabilitation

PubMed Central

Resquín, Francisco; Gonzalez-Vargas, Jose; Ibáñez, Jaime; Brunetti, Fernando; Pons, José Luis

2016-01-01

Hybrid robotic systems represent a novel research field, where functional electrical stimulation (FES) is combined with a robotic device for rehabilitation of motor impairment. Under this approach, the design of robust FES controllers still remains an open challenge. In this work, we aimed at developing a learning FES controller to assist in the performance of reaching movements in a simple hybrid robotic system setting. We implemented a Feedback Error Learning (FEL) control strategy consisting of a feedback PID controller and a feedforward controller based on a neural network. A passive exoskeleton complemented the FES controller by compensating the effects of gravity. We carried out experiments with healthy subjects to validate the performance of the system. Results show that the FEL control strategy is able to adjust the FES intensity to track the desired trajectory accurately without the need of a previous mathematical model. PMID:27990245

Introduction to Solar Motion Geometry on the Basis of a Simple Model

ERIC Educational Resources Information Center

Khavrus, Vyacheslav; Shelevytsky, Ihor

2010-01-01

By means of a simple mathematical model developed by the authors, the apparent movement of the Sun can be studied for arbitrary latitudes. Using this model, it is easy to gain insight into various phenomena, such as the passage of the seasons, dependences of position and time of sunrise or sunset on a specific day of year, day duration for…

A Domain-Specific Language for Discrete Mathematics

NASA Astrophysics Data System (ADS)

Jha, Rohit; Samuel, Alfy; Pawar, Ashmee; Kiruthika, M.

2013-05-01

This paper discusses a Domain Specific Language (DSL) that has been developed to enable implementation of concepts of discrete mathematics. A library of data types and functions provides functionality which is frequently required by users. Covering the areas of Mathematical Logic, Set Theory, Functions, Graph Theory, Number Theory, Linear Algebra and Combinatorics, the language's syntax is close to the actual notation used in the specific fields.

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-05-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-03-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

The S-Matrix and Acoustic Signal Structure in Simple and Compound Waveguides.

DTIC Science & Technology

1982-12-01

RD-A125 583 THE S-MATRIX AND ACOUSTIC SIGNAL STRUCTURE IN SIMPLE- L/1 AND COMPOUND WAVEGUIDES(U) UTAH UNIV SALT LAKE CITY DEPT OF MATHEMATICS C H...WILCOX DEC 82 TSR-45 UNCLASSIFIED N6@8i4-76-C-8276 F/G 12/1 NL IEINEIIIIIIEIhllhlllllllIflllllflflflflflEN L-- U5-12 III,2,0 III.J --IL.,5 MICROCOP ...RESLUIO TETCHRNATIONA BUREA OF 20NADS16 THE S-MATRIX AND ACOUSTIC SIGNAL STRUCTURE IN SIMPLE AND COMPOUND WAVEGUIDES C. H. Wilcox Technical Simmary Report

Computer Classification of Triangles and Quadrilaterals--A Challenging Application

ERIC Educational Resources Information Center

Dennis, J. Richard

1978-01-01

Two computer exercises involving the classification of geometric figures are given. The mathematics required is relatively simple but comes from several areas--synthetic geometry, analytic geometry, and linear algebra. (MN)

A Simple Optical Waveguide Experiment.

ERIC Educational Resources Information Center

Phelps, J.; Sambles, J. R.

1989-01-01

Describes a thin film rectangular dielectric waveguide and its laboratory use. Discusses the theory of uniaxial thin film waveguides with mathematical expressions and the laboratory procedures for a classroom experiment with diagrams. (Author/YP)

Factors involved in making post-performance judgments in mathematics problem-solving.

PubMed

García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A

2015-01-01

This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.

Integration of CAI into a Freshmen Liberal Arts Math Course in the Community College.

ERIC Educational Resources Information Center

McCall, Michael B.; Holton, Jean L.

1982-01-01

Discusses four computer-assisted-instruction programs used in a college-level mathematics course to introduce computer literacy and improve mathematical skills. The BASIC programs include polynomial functions, trigonometric functions, matrix algebra, and differential calculus. Each program discusses mathematics theory and introduces programming…

Is There a Role for Executive Functions in the Development of Mathematics Ability?

ERIC Educational Resources Information Center

Blair, Clancy; Knipe, Hilary; Gamson, David

2008-01-01

This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based…

Phonological Storage and Executive Function Deficits in Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Peng, Peng; Congying, Sun; Beilei, Li; Sha, Tao

2012-01-01

Children with mathematics difficulties suffer from working memory deficits. This study investigated the deficit profile of phonological storage and executive functions in working memory among children with mathematics difficulties. Based on multiple instruments and two assessment points, 68 children were screened out of 805 fifth graders. Of these…

A simple method to evaluate the number of bradyrhizobia on soybean seeds and its implication on inoculant quality control

PubMed Central

2011-01-01

Soybean seeds are non-sterile and their bacterial population interferes with the enumeration of beneficial bacteria, making it difficult to assess survival under different conditions. Within this context, the principal aims of this work were: (1) to improve a selective media for the enumeration of B. japonicum recovered from inoculated soybean seeds; (2) to establish the most representative mathematical function for B. japonicum mortality on soybean seeds after inoculation; (3) to evaluate if environmental or physiological conditions modify B. japonicum mortality on soybean seeds; and (4) to create a new protocol for quality control of soybean inoculants. We successfully evaluated the combination of pentachloronitrobenzene and vancomycin added to the yeast-mannitol medium to inhibit most fungi and Gram-positive soybean microbiota, thus producing reliable counts of B. japonicum from inoculated soybean seeds. Percentages of recovery and survival factors were obtained and used to construct a two-phase exponential decay non-linear regression function. High temperature and desiccation decreased these parameters, while the optimization of temperature and the use of osmoprotective compounds with inoculants increased them. The use of this protocol minimized heterogeneity between experiments and may be considered more reliable than the simple expression of direct colony count of bacteria recovered from seeds. PMID:21906377

Implementing digital holograms to create and measure complex-plane optical fields

NASA Astrophysics Data System (ADS)

Dudley, Angela; Majola, Nombuso; Chetty, Naven; Forbes, Andrew

2016-02-01

The coherent superposition of a Gaussian beam with an optical vortex can be mathematically described to occupy the complex plane. We provide a simple analogy between the mathematics, in the form of the complex plane, and the visual representation of these two superimposed optical fields. We provide detailed instructions as to how one can experimentally produce, measure, and control these fields with the use of digital holograms encoded on a spatial light modulator.

Domain decomposition: A bridge between nature and parallel computers

NASA Technical Reports Server (NTRS)

Keyes, David E.

1992-01-01

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Novel design solutions for fishing reel mechanisms

NASA Astrophysics Data System (ADS)

Lovasz, Erwin-Christian; Modler, Karl-Heinz; Neumann, Rudolf; Gruescu, Corina Mihaela; Perju, Dan; Ciupe, Valentin; Maniu, Inocentiu

2015-07-01

Currently, there are various reels on the market regarding the type of mechanism, which achieves the winding and unwinding of the line. The designers have the purpose of obtaining a linear transmission function, by means of a simple and small-sized mechanism. However, the present solutions are not satisfactory because of large deviations from linearity of the transmission function and complexity of mechanical schema. A novel solution for the reel spool mechanism is proposed. Its kinematic schema and synthesis method are described. The kinematic schema of the chosen mechanism is based on a noncircular gear in series with a scotch-yoke mechanism. The yoke is driven by a stud fixed on the driving noncircular gear. The drawbacks of other models regarding the effects occurring at the ends of the spool are eliminated through achieving an appropriate transmission function of the spool. The linear function approximation with curved end-arches appropriately computed to ensure mathematical continuity is very good. The experimental results on the mechanism model validate the theoretical approach. The developed mechanism solution is recorded under a reel spool mechanism patent.

Quantum mechanics over sets

NASA Astrophysics Data System (ADS)

Ellerman, David

2014-03-01

In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

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

NASA Astrophysics Data System (ADS)

Arney, Dale Curtis

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

[Mathematical abilities and executive function in children with attention deficit hyperactivity disorder and learning disabilities in mathematics].

PubMed

Miranda Casas, Ana; Meliá de Alba, Amanda; Marco Taverner, Rafaela

2009-02-01

Mathematical abilities and executive function in children with attention deficit hyperactivity disorder and learning disabilities in mathematics. Even though 26% of children with attention deficit hyperactivity disorder (ADHD) show a specific mathematic learning difficulty (MLD), the studies have been scarce. The present study had the following goals: 1) to study the profile related to cognitive and metacognitive skills implied in calculation and problem-solving in children with ADHD+MLD, and to compare them in children with ADHD, children with MLD, and children without problems; 2) to study the severity of the deficit in executive function (EF) in children with ADHD+MLD. Comparing the groups MLD, ADHD, ADHD+MLD, and children without problems, the results highlighted that children with ADHD+MLD showed a cognitive and metacognitive deficit in mathematic achievement. Furthermore, results showed a more severe deficit in the EF in children with ADHD+MLD.

Synthetic analog computation in living cells.

PubMed

Daniel, Ramiz; Rubens, Jacob R; Sarpeshkar, Rahul; Lu, Timothy K

2013-05-30

A central goal of synthetic biology is to achieve multi-signal integration and processing in living cells for diagnostic, therapeutic and biotechnology applications. Digital logic has been used to build small-scale circuits, but other frameworks may be needed for efficient computation in the resource-limited environments of cells. Here we demonstrate that synthetic analog gene circuits can be engineered to execute sophisticated computational functions in living cells using just three transcription factors. Such synthetic analog gene circuits exploit feedback to implement logarithmically linear sensing, addition, ratiometric and power-law computations. The circuits exhibit Weber's law behaviour as in natural biological systems, operate over a wide dynamic range of up to four orders of magnitude and can be designed to have tunable transfer functions. Our circuits can be composed to implement higher-order functions that are well described by both intricate biochemical models and simple mathematical functions. By exploiting analog building-block functions that are already naturally present in cells, this approach efficiently implements arithmetic operations and complex functions in the logarithmic domain. Such circuits may lead to new applications for synthetic biology and biotechnology that require complex computations with limited parts, need wide-dynamic-range biosensing or would benefit from the fine control of gene expression.

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

USGS Publications Warehouse

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

2014-01-01

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

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

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

Tutorial on Fourier space coverage for scattering experiments, with application to SAR

NASA Astrophysics Data System (ADS)

Deming, Ross W.

2010-04-01

The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.

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.

The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.

2018-03-01

Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

Semantic Processing of Mathematical Gestures

ERIC Educational Resources Information Center

Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

2009-01-01

Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…

Functions in Contemporary Secondary Mathematics Textbook Series in the United States

ERIC Educational Resources Information Center

Ross, Daniel J.

2011-01-01

Textbooks play a central role in US mathematics classrooms (Stein, Remillard, & Smith, 2007) and functions are a key topic in secondary mathematics (Carlson, Jacobs, Coe, Larsen, & Hsu, 2002). This study presents results from an analysis of this essential topic in the latest editions of three textbook series: the Glencoe Mathematics…

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…

Mathematics Performance of the Primary School Students: Attention and Shifting

ERIC Educational Resources Information Center

Poorghorban, Maryam; Jabbari, Susan; Chamandar, Fatemah

2018-01-01

The purpose of this study was to understand the relationship between executive functions and mathematical abilities to determine the contribution of these functions to math performance. In this study, 30 students were selected from among 4th graders of elementary school, in two groups with low achievement in mathematics (poor) and high achievement…

Mathematics forBioMathics.

PubMed

Hoffman, William C

2013-09-01

The essence of biological phenomena appears in form and function: "Form follows function." Mathematically, G × M → M, where G contains the parameters of the action and M is the form. The Mathematics for this purpose is largely available and is well described in a recent book (Felix et al., 2008). Copyright © 2013. Published by Elsevier Ltd.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

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

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

Theory of the fundamental laser linewidth

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

Goldberg, P.; Milonni, P.W.; Sundaram, B.

1991-08-01

The theory of the laser linewidth is formulated to account for arbitrarily large output couplings and spatial hole burning. We show explicitly that the linewidth can be interpreted in terms of either spontaneous-emission noise or the amplification of vacuum field modes leaking into the cavity, depending on the ordering of operators in the correlation function determining the laser spectrum. This allows us to derive the Petermann {ital K} factor associated with excess spontaneous-emission noise'' in a physically transparent and mathematically simple way, without the need to introduce adjoint modes of the resonator. It also allows us to straightforwardly include spatial-hole-burningmore » effects, which are found to increase the {ital K} factor and the linewidth in high-gain systems appreciably.« less

Elastic Waves: Mental Models and Teaching/Learning Sequences

NASA Astrophysics Data System (ADS)

Tarantino, Giovanni

In last years many research studies have pointed out relevant student diff- culties in understanding the physics of mechanical waves. Moreover, it has been reported that these diffculties deal with some fundamental concepts as the role of the medium in wave propagation, the superposition principle and the mathematical description of waves involving the use of functions of two variables. In the context of pre-service courses for teacher preparation a teaching/learning (T/L) sequence based on using simple RTL experiments and interactive simulation environments aimed to show the effect of medium properties on the propagation speed of a wave pulse, has been experimented. Here, preliminary results of investigations carried out with a 120 traineeteacher (TT) group are reported and discussed.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Applications of Dirac's Delta Function in Statistics

ERIC Educational Resources Information Center

Khuri, Andre

2004-01-01

The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Mechanics of train collision

DOT National Transportation Integrated Search

1976-04-30

A simple and a more detailed mathematical model for the simulation of train collisions are presented. The study presents considerable insight as to the causes and consequences of train motions on impact. Comparison of model predictions with two full ...

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

NASA Technical Reports Server (NTRS)

Thompson, David E.

2005-01-01

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Exponential growth kinetics for Polyporus versicolor and Pleurotus ostreatus in submerged culture

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

Carroad, P.A.; Wilke, C.R.

1977-04-01

Simple mathematical models for a batch culture of pellet-forming fungi in submerged culture were tested on growth data for Polyporus versicolor (ATCC 12679) and Pleurotus ostreatus (ATCC 9415). A kinetic model based on a growth rate proportional to the two-thirds power of the cell mass was shown to be satisfactory. A model based on a growth rate directly proportional to the cell mass fitted the data equally well, however, and may be preferable because of mathematical simplicity.

Pyroelectric effect in tryglicyne sulphate single crystals - Differential measurement method

NASA Astrophysics Data System (ADS)

Trybus, M.

2018-06-01

A simple mathematical model of the pyroelectric phenomenon was used to explain the electric response of the TGS (triglycine sulphate) samples in the linear heating process in ferroelectric and paraelectric phases. Experimental verification of mathematical model was realized. TGS single crystals were grown and four electrode samples were fabricated. Differential measurements of the pyroelectric response of two different regions of the samples were performed and the results were compared with data obtained from the model. Experimental results are in good agreement with model calculations.

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

NASA Astrophysics Data System (ADS)

Akbulut, Arzu; Taşcan, Filiz

2018-04-01

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

Gravitational orientation of the orbital complex, Salyut-6--Soyuz

NASA Technical Reports Server (NTRS)

Grecho, G. M.; Sarychev, V. A.; Legostayev, V. P.; Sazonov, V. V.; Gansvind, I. N.

1983-01-01

A simple mathematical model is proposed for the Salyut-6-Soyuz orbital complex motion with respect to the center of mass under the one-axis gravity-gradient orientation regime. This model was used for processing the measurements of the orbital complex motion parameters when the above orientation region was implemented. Some actual satellite motions are simulated and the satellite's aerodynamic parameters are determined. Estimates are obtained for the accuracy of measurements as well as that of the mathematical model.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

ERIC Educational Resources Information Center

Powell, Sarah R.; Nelson, Gena

2017-01-01

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

The Relationship between Mathematical Induction, Proposition Functions, and Implication Functions

ERIC Educational Resources Information Center

Andrew, Lane

2010-01-01

In this study, I explored the relationship between mathematical induction ability and proposition and implication functions through a mixed methods approach. Students from three universities (N = 78) and 6 classrooms completed a written assessment testing their conceptual and procedural capabilities with induction and functions. In addition, I…

Adaptive behaviour and multiple equilibrium states in a predator-prey model.

PubMed

Pimenov, Alexander; Kelly, Thomas C; Korobeinikov, Andrei; O'Callaghan, Michael J A; Rachinskii, Dmitrii

2015-05-01

There is evidence that multiple stable equilibrium states are possible in real-life ecological systems. Phenomenological mathematical models which exhibit such properties can be constructed rather straightforwardly. For instance, for a predator-prey system this result can be achieved through the use of non-monotonic functional response for the predator. However, while formal formulation of such a model is not a problem, the biological justification for such functional responses and models is usually inconclusive. In this note, we explore a conjecture that a multitude of equilibrium states can be caused by an adaptation of animal behaviour to changes of environmental conditions. In order to verify this hypothesis, we consider a simple predator-prey model, which is a straightforward extension of the classic Lotka-Volterra predator-prey model. In this model, we made an intuitively transparent assumption that the prey can change a mode of behaviour in response to the pressure of predation, choosing either "safe" of "risky" (or "business as usual") behaviour. In order to avoid a situation where one of the modes gives an absolute advantage, we introduce the concept of the "cost of a policy" into the model. A simple conceptual two-dimensional predator-prey model, which is minimal with this property, and is not relying on odd functional responses, higher dimensionality or behaviour change for the predator, exhibits two stable co-existing equilibrium states with basins of attraction separated by a separatrix of a saddle point. Copyright © 2015 Elsevier Inc. All rights reserved.

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

PubMed

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

2017-09-01

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

Exploring Crossing Differential Item Functioning by Gender in Mathematics Assessment

ERIC Educational Resources Information Center

Ong, Yoke Mooi; Williams, Julian; Lamprianou, Iasonas

2015-01-01

The purpose of this article is to explore crossing differential item functioning (DIF) in a test drawn from a national examination of mathematics for 11-year-old pupils in England. An empirical dataset was analyzed to explore DIF by gender in a mathematics assessment. A two-step process involving the logistic regression (LR) procedure for…

Biomedical Mathematics, Unit I: Measurement, Linear Functions and Dimensional Algebra. Student Text. Revised Version, 1975.

ERIC Educational Resources Information Center

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…

Using a Functional Model to Develop a Mathematical Formula

ERIC Educational Resources Information Center

Otto, Charlotte A.; Everett, Susan A.; Luera, Gail R.

2008-01-01

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

Independent component model for cognitive functions of multiple subjects using [15O]H2O PET images.

PubMed

Park, Hae-Jeong; Kim, Jae-Jin; Youn, Tak; Lee, Dong Soo; Lee, Myung Chul; Kwon, Jun Soo

2003-04-01

An independent component model of multiple subjects' positron emission tomography (PET) images is proposed to explore the overall functional components involved in a task and to explain subject specific variations of metabolic activities under altered experimental conditions utilizing the Independent component analysis (ICA) concept. As PET images represent time-compressed activities of several cognitive components, we derived a mathematical model to decompose functional components from cross-sectional images based on two fundamental hypotheses: (1) all subjects share basic functional components that are common to subjects and spatially independent of each other in relation to the given experimental task, and (2) all subjects share common functional components throughout tasks which are also spatially independent. The variations of hemodynamic activities according to subjects or tasks can be explained by the variations in the usage weight of the functional components. We investigated the plausibility of the model using serial cognitive experiments of simple object perception, object recognition, two-back working memory, and divided attention of a syntactic process. We found that the independent component model satisfactorily explained the functional components involved in the task and discuss here the application of ICA in multiple subjects' PET images to explore the functional association of brain activations. Copyright 2003 Wiley-Liss, Inc.

Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments

NASA Astrophysics Data System (ADS)

Zia, R. K. P.; Dong, J. J.; Schmittmann, B.

2011-07-01

The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes.

Analytical determination of space station response to crew motion and design of suspension system for microgravity experiments

NASA Technical Reports Server (NTRS)

Liu, F. C.

1986-01-01

The objective of this investigation is to make analytical determination of the acceleration produced by crew motion in an orbiting space station and define design parameters for the suspension system of microgravity experiments. A simple structural model for simulation of the IOC space station is proposed. Mathematical formulation of this model provides the engineers a simple and direct tool for designing an effective suspension system.

Simple Examples of the Interpretation of Changes in Kinetic and Potential Energy Under Galilean Transformations

NASA Astrophysics Data System (ADS)

Ginsberg, Edw. S.

2018-02-01

The compatibility of the Newtonian formulation of mechanical energy and the transformation equations of Galilean relativity is demonstrated for three simple examples of motion treated in most introductory physics courses (free fall, a frictionless inclined plane, and a mass/spring system). Only elementary concepts and mathematics, accessible to students at that level, are used. Emphasis is on pedagogy and concepts related to the transformation properties of potential energy.

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

Luminance, Colour, Viewpoint and Border Enhanced Disparity Energy Model

PubMed Central

Martins, Jaime A.; Rodrigues, João M. F.; du Buf, Hans

2015-01-01

The visual cortex is able to extract disparity information through the use of binocular cells. This process is reflected by the Disparity Energy Model, which describes the role and functioning of simple and complex binocular neuron populations, and how they are able to extract disparity. This model uses explicit cell parameters to mathematically determine preferred cell disparities, like spatial frequencies, orientations, binocular phases and receptive field positions. However, the brain cannot access such explicit cell parameters; it must rely on cell responses. In this article, we implemented a trained binocular neuronal population, which encodes disparity information implicitly. This allows the population to learn how to decode disparities, in a similar way to how our visual system could have developed this ability during evolution. At the same time, responses of monocular simple and complex cells can also encode line and edge information, which is useful for refining disparities at object borders. The brain should then be able, starting from a low-level disparity draft, to integrate all information, including colour and viewpoint perspective, in order to propagate better estimates to higher cortical areas. PMID:26107954

Steady-state groundwater recharge in trapezoidal-shaped aquifers: A semi-analytical approach based on variational calculus

NASA Astrophysics Data System (ADS)

Mahdavi, Ali; Seyyedian, Hamid

2014-05-01

This study presents a semi-analytical solution for steady groundwater flow in trapezoidal-shaped aquifers in response to an areal diffusive recharge. The aquifer is homogeneous, anisotropic and interacts with four surrounding streams of constant-head. Flow field in this laterally bounded aquifer-system is efficiently constructed by means of variational calculus. This is accomplished by minimizing a properly defined penalty function for the associated boundary value problem. Simple yet demonstrative scenarios are defined to investigate anisotropy effects on the water table variation. Qualitative examination of the resulting equipotential contour maps and velocity vector field illustrates the validity of the method, especially in the vicinity of boundary lines. Extension to the case of triangular-shaped aquifer with or without an impervious boundary line is also demonstrated through a hypothetical example problem. The present solution benefits from an extremely simple mathematical expression and exhibits strictly close agreement with the numerical results obtained from Modflow. Overall, the solution may be used to conduct sensitivity analysis on various hydrogeological parameters that affect water table variation in aquifers defined in trapezoidal or triangular-shaped domains.

Finite element meshing approached as a global minimization process

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

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within amore » charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.« less

Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance.

PubMed

Mazzocco, Michèle M M; Chan, Jenny Yun-Chen; Bock, Allison M

2017-01-01

In this chapter, we address one potentially overlooked component of the relation between executive function (EF) skills and early mathematics, a relation for which there is widespread empirical support. Evidence for this relation has, thus far, been largely correlational. Here we emphasize that because positive correlations do not guarantee concordance among all members of a sample or population, a small but meaningful number of children may either fare well in mathematics despite poor EF skills, or may have strong EF skills despite weak mathematics skills. We propose that attention to different profiles of discordance for EF and mathematics may help identify individualized learning needs for students at risk for mathematics difficulties and disabilities. © 2017 Elsevier Inc. All rights reserved.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

NASA Astrophysics Data System (ADS)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Development of Energy Concepts in Introductory Physics Courses.

ERIC Educational Resources Information Center

Arons, Arnold B.

1999-01-01

Believes that a student's understanding of energy concepts can be enhanced by introducing and using the concept of internal energy by articulating the first law of thermodynamics in a simple, phenomenological form without mathematical encumbrances. (Author/CCM)

A Simple Method to Determine the Refractive Index of Glass.

ERIC Educational Resources Information Center

Mak, Se-yuen

1988-01-01

Describes an experiment for determining the refractive index. Discusses the experiment procedure and mathematical expression for calculating the index. Provides two geometrical diagrams and a graph for determining the index with a typical data. (YP)

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)

A study of stiffness, residual strength and fatigue life relationships for composite laminates

NASA Technical Reports Server (NTRS)

Ryder, J. T.; Crossman, F. W.

1983-01-01

Qualitative and quantitative exploration of the relationship between stiffness, strength, fatigue life, residual strength, and damage of unnotched, graphite/epoxy laminates subjected to tension loading. Clarification of the mechanics of the tension loading is intended to explain previous contradictory observations and hypotheses; to develop a simple procedure to anticipate strength, fatigue life, and stiffness changes; and to provide reasons for the study of more complex cases of compression, notches, and spectrum fatigue loading. Mathematical models are developed based upon analysis of the damage states. Mathematical models were based on laminate analysis, free body type modeling or a strain energy release rate. Enough understanding of the tension loaded case is developed to allow development of a proposed, simple procedure for calculating strain to failure, stiffness, strength, data scatter, and shape of the stress-life curve for unnotched laminates subjected to tension load.

Data-driven outbreak forecasting with a simple nonlinear growth model.

PubMed

Lega, Joceline; Brown, Heidi E

2016-12-01

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Receptors as a master key for synchronization of rhythms

NASA Astrophysics Data System (ADS)

Nagano, Seido

2004-03-01

A simple, but general scheme to achieve synchronization of rhythms was derived. The scheme has been inductively generalized from the modelling study of cellular slime mold. It was clarified that biological receptors work as apparatuses that can convert external stimulus to the form of nonlinear interaction within individual oscillators. Namely, the mathematical model receptor works as a nonlinear coupling apparatus between nonlinear oscillators. Thus, synchronization is achieved as a result of competition between two kinds of non-linearities, and to achieve synchronization, even a small external stimulation via model receptors can change the characteristics of individual oscillators significantly. The derived scheme is very simple mathematically, but it is a very powerful scheme as numerically demonstrated. The biological receptor scheme should significantly help understanding of synchronization phenomena in biology since groups of limit cycle oscillators and receptors are ubiquitous in biological systems. Reference: S. Nagano, Phys Rev. E67, 056215(2003)

The Mathematics of Dispatchability, Revisited

NASA Technical Reports Server (NTRS)

Morris, Paul

2016-01-01

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently, it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, dispatchability has considerable theoretical as well as practical significance. One thing that hampers further work in this area is the underdeveloped theory. Moreover, the existing foundation is inadequate in certain respects. In this paper, we develop a new mathematical theory of dispatchability and its relationship to execution. We also provide several characterizations of dispatchability, including characterizations in terms of the structural properties of the STN graph. This facilitates the potential application of the theory to other areas.

The Mathematics of Dispatchability Revisited

NASA Technical Reports Server (NTRS)

Morris, Paul

2016-01-01

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, the dispatchability property has both theoretical and practical interest. One thing that hampers further work in this area is the underdeveloped theory. The existing definitions are expressed in terms of algorithms, and are less suitable for mathematical proofs. In this paper, we develop a new formal theory of dispatchability in terms of execution sequences. We exploit this to prove a characterization of dispatchability involving the structural properties of the STN graph. This facilitates the potential application of the theory to uncertainty reasoning.

Road simulation for four-wheel vehicle whole input power spectral density

NASA Astrophysics Data System (ADS)

Wang, Jiangbo; Qiang, Baomin

2017-05-01

As the vibration of running vehicle mainly comes from road and influence vehicle ride performance. So the road roughness power spectral density simulation has great significance to analyze automobile suspension vibration system parameters and evaluate ride comfort. Firstly, this paper based on the mathematical model of road roughness power spectral density, established the integral white noise road random method. Then in the MATLAB/Simulink environment, according to the research method of automobile suspension frame from simple two degree of freedom single-wheel vehicle model to complex multiple degrees of freedom vehicle model, this paper built the simple single incentive input simulation model. Finally the spectrum matrix was used to build whole vehicle incentive input simulation model. This simulation method based on reliable and accurate mathematical theory and can be applied to the random road simulation of any specified spectral which provides pavement incentive model and foundation to vehicle ride performance research and vibration simulation.

Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

PubMed Central

Gilmore, Camilla; Cragg, Lucy

2014-01-01

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers. PMID:25674156

Teachers' Understanding of the Role of Executive Functions in Mathematics Learning.

PubMed

Gilmore, Camilla; Cragg, Lucy

2014-09-01

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term "executive functions." This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers.

Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

ERIC Educational Resources Information Center

Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

2017-01-01

Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…

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

ERIC Educational Resources Information Center

Chesler, Joshua

2012-01-01

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

Students' Conceptions of Function Transformation in a Dynamic Mathematical Environment

ERIC Educational Resources Information Center

Daher, Wajeeh; Anabousy, Ahlam

2015-01-01

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

Brain Activity Associated with Translation between Graphical and Symbolic Representations of Functions in Generally Gifted and Excelling in Mathematics Adolescents

ERIC Educational Resources Information Center

Waisman, Ilana; Leikin, Mark; Shaul, Shelley; Leikin, Roza

2014-01-01

In this study, we examine the impact and the interplay of general giftedness (G) and excellence in mathematics (EM) on high school students' mathematical performance associated with translations from graphical to symbolic representations of functions, as reflected in cortical electrical activity (by means of ERP--event-related…

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

2018-03-01

Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

The mass-luminosity relation in an introductory astronomy lab

NASA Astrophysics Data System (ADS)

LoPresto, Michael C.

2016-11-01

Exposing students in general education science courses of lower mathematical levels to experiments that make use of quantitative skills such as collecting and analyzing data is very important because they provide examples of how science is actually done. Experiments with relatively simple procedures that are also interesting and engaging which serve this purpose can be hard to find. This can especially be true for introductory college astronomy courses; however, courses of this type often do still have a laboratory component because most students, regardless of major, are required to take at least one laboratory science course. When required to work with data in a quantitative fashion, the difficulty students with lower mathematical skills often have is that any actual physical meaning of an experiment can become completely lost in a procedure that, to them, seems to be purely an exercise in complex mathematics and for which they have resorted to simply following by rote, from which, perhaps needless to say, they are likely to learn little or nothing. I have seen this happen numerous times and it has inspired me to focus on attempting to develop meaningful laboratory experiences for students of lower mathematical level courses, such as introductory astronomy and conceptual physics, that involve both the gathering and analysis of numerical data. What follows is a simple experiment of this type on the mass-luminosity relation for stars on the main sequence of the Hertzsprung-Russell diagram that has proven useful for an introductory astronomy laboratory course.

Sampling and sensitivity analyses tools (SaSAT) for computational modelling

PubMed Central

Hoare, Alexander; Regan, David G; Wilson, David P

2008-01-01

SaSAT (Sampling and Sensitivity Analysis Tools) is a user-friendly software package for applying uncertainty and sensitivity analyses to mathematical and computational models of arbitrary complexity and context. The toolbox is built in Matlab®, a numerical mathematical software package, and utilises algorithms contained in the Matlab® Statistics Toolbox. However, Matlab® is not required to use SaSAT as the software package is provided as an executable file with all the necessary supplementary files. The SaSAT package is also designed to work seamlessly with Microsoft Excel but no functionality is forfeited if that software is not available. A comprehensive suite of tools is provided to enable the following tasks to be easily performed: efficient and equitable sampling of parameter space by various methodologies; calculation of correlation coefficients; regression analysis; factor prioritisation; and graphical output of results, including response surfaces, tornado plots, and scatterplots. Use of SaSAT is exemplified by application to a simple epidemic model. To our knowledge, a number of the methods available in SaSAT for performing sensitivity analyses have not previously been used in epidemiological modelling and their usefulness in this context is demonstrated. PMID:18304361

Mathematics and morphogenesis of cities: A geometrical approach

NASA Astrophysics Data System (ADS)

Courtat, Thomas; Gloaguen, Catherine; Douady, Stephane

2011-03-01

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

Theoretical ecology without species

NASA Astrophysics Data System (ADS)

Tikhonov, Mikhail

The sequencing-driven revolution in microbial ecology demonstrated that discrete ``species'' are an inadequate description of the vast majority of life on our planet. Developing a novel theoretical language that, unlike classical ecology, would not require postulating the existence of species, is a challenge of tremendous medical and environmental significance, and an exciting direction for theoretical physics. Here, it is proposed that community dynamics can be described in a naturally hierarchical way in terms of population fluctuation eigenmodes. The approach is applied to a simple model of division of labor in a multi-species community. In one regime, effective species with a core and accessory genome are shown to naturally appear as emergent concepts. However, the same model allows a transition into a regime where the species formalism becomes inadequate, but the eigenmode description remains well-defined. Treating a community as a black box that expresses enzymes in response to resources reveals mathematically exact parallels between a community and a single coherent organism with its own fitness function. This coherence is a generic consequence of division of labor, requires no cooperative interactions, and can be expected to be widespread in microbial ecosystems. Harvard Center of Mathematical Sciences and Applications;John A. Paulson School of Engineering and Applied Sciences.

New Approaches for Calculating Moran’s Index of Spatial Autocorrelation

PubMed Central

Chen, Yanguang

2013-01-01

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation. PMID:23874592

Modeling and simulation for fewer-axis grinding of complex surface

NASA Astrophysics Data System (ADS)

Li, Zhengjian; Peng, Xiaoqiang; Song, Ci

2017-10-01

As the basis of fewer-axis grinding of complex surface, the grinding mathematical model is of great importance. A mathematical model of the grinding wheel was established, and then coordinate and normal vector of the wheel profile could be calculated. Through normal vector matching at the cutter contact point and the coordinate system transformation, the grinding mathematical model was established to work out the coordinate of the cutter location point. Based on the model, interference analysis was simulated to find out the right position and posture of workpiece for grinding. Then positioning errors of the workpiece including the translation positioning error and the rotation positioning error were analyzed respectively, and the main locating datum was obtained. According to the analysis results, the grinding tool path was planned and generated to grind the complex surface, and good form accuracy was obtained. The grinding mathematical model is simple, feasible and can be widely applied.

Mathematical Modeling for Scrub Typhus and Its Implications for Disease Control.

PubMed

Min, Kyung Duk; Cho, Sung Il

2018-03-19

The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease. We developed mathematical models of ordinary differential equations including human, rodent and mite groups. Two models, including simple and complex models, were developed, and all parameters employed in the models were adopted from previous articles that represent epidemiological situations in the Republic of Korea. The simulation results showed that the force of infection at the equilibrium state under the simple model was 0.236 (per 100,000 person-months), and that in the complex model was 26.796 (per 100,000 person-months). Sensitivity analyses indicated that the most influential parameters were rodent and mite populations and contact rate between them for the simple model, and trans-ovarian transmission for the complex model. In both models, contact rate between humans and mites is more influential than morality rate of rodent and mite group. The results indicate that the effect of controlling either rodents or mites could be limited, and reducing the contact rate between humans and mites is more practical and effective strategy. However, the current level of control would be insufficient relative to the growing mite population. © 2018 The Korean Academy of Medical Sciences.

Simulated Three-Point Problems.

ERIC Educational Resources Information Center

Leyden, Michael B.

1979-01-01

The concept of sloping bedrock strata is portrayed by simple construction of a cardboard model. By use of wires and graph paper, students simulate the drilling of wells and use standard mathematical operations to determine strike and dip of the model stratum. (RE)

Foxes and Rabbits - and a Spreadsheet.

ERIC Educational Resources Information Center

Carson, S. R.

1996-01-01

Presents a numerical simulation of a simple food chain together with a set of mathematical rules generalizing the model to a food web of any complexity. Discusses some of the model's interesting features and its use by students. (Author/JRH)

Mastery of Simple Probability Ideas Among G.C.E. Ordinary Level Mathematics Candidates

ERIC Educational Resources Information Center

Wood, R.; Brown, M.

1976-01-01

Questions concerning probability which appeared on the General Certificate of Education test are analyzed in terms of the processes required to answer them. The relationships between these processes and cognitive development are discussed. (SD)

Implementing the "Curriculum and Evaluation Standards."

ERIC Educational Resources Information Center

Pacyga, Robert

1994-01-01

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invite students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MDH)

Science, Technology, Engineering, Mathematics Poster

NASA Technical Reports Server (NTRS)

Kozusko, Timothy J.

2016-01-01

This is a simple poster for Community Day at the Visitor Center. It describes, as an overview, an example of the use of GPS and LiDAR data to determine the loss of scrubjay habitat due to a change in water table.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Understanding space weather with new physical, mathematical and philosophical approaches

NASA Astrophysics Data System (ADS)

Mateev, Lachezar; Velinov, Peter; Tassev, Yordan

2016-07-01

The actual problems of solar-terrestrial physics, in particular of space weather are related to the prediction of the space environment state and are solved by means of different analyses and models. The development of these investigations can be considered also from another side. This is the philosophical and mathematical approach towards this physical reality. What does it constitute? We have a set of physical processes which occur in the Sun and interplanetary space. All these processes interact with each other and simultaneously participate in the general process which forms the space weather. Let us now consider the Leibniz's monads (G.W. von Leibniz, 1714, Monadologie, Wien; Id., 1710, Théodicée, Amsterdam) and use some of their properties. There are total 90 theses for monads in the Leibniz's work (1714), f.e. "(1) The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts'. (Theod. 10.); … (56) Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.); (59) … this universal harmony, according to which every substance exactly expresses all others through the relations it has with them. (63) … every Monad is, in its own way, a mirror of the universe, and the universe is ruled according to a perfect order. (Theod. 403.)", etc. Let us introduce in the properties of monads instead of the word "monad" the word "process". We obtain the following statement: Each process reflects all other processes and all other processes reflect this process. This analogy is not formal at all, it reflects accurately the relation between the physical processes and their unity. The category monad which in the Leibniz's Monadology reflects generally the philosophical sense is fully identical with the physical one, in our case. The corresponding mathematical relations are needed for the application of this analogy in the solar-terrestrial physics and space weather. For this purpose in the contemporary categories theory in the algebra a whole field for it exists - the theory of monads (M. Barr, Ch. Wells, 1985, Toposes, Triples and Theories, Springer-Verlag, 278, p. 82). This theory is generated by analogous elements as in the Leibniz's Monadology. As it is known the categories theory and in particular the monad theory (also named triple or triad theory) tends to make axioms in mathematics. This approach would be very useful for such complex systems and processes as these in the solar-terrestrial physics and space weather. Here some methods for algebraic data structures could be introduced. Or some imperative programs can be embedded in a purely functional program for modeling, respectively. All these problems are principally considered in the proposed report.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Domain General Mediators of the Relation between Kindergarten Number Sense and First-Grade Mathematics Achievement

PubMed Central

Hassinger-Das, Brenna; Jordan, Nancy C.; Glutting, Joseph; Irwin, Casey; Dyson, Nancy

2013-01-01

Domain general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that attention problems and executive functioning both were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance while executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense. PMID:24237789

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement.

PubMed

Hassinger-Das, Brenna; Jordan, Nancy C; Glutting, Joseph; Irwin, Casey; Dyson, Nancy

2014-02-01

Domain-general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense. Copyright © 2013 Elsevier Inc. All rights reserved.

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

Bastian, Mark; Trigueros, Jose V.

Phoenix is a Java Virtual Machine (JVM) based library for performing mathematical and astrodynamics calculations. It consists of two primary sub-modules, phoenix-math and phoenix-astrodynamics. The mathematics package has a variety of mathematical classes for performing 3D transformations, geometric reasoning, and numerical analysis. The astrodynamics package has various classes and methods for computing locations, attitudes, accesses, and other values useful for general satellite modeling and simulation. Methods for computing celestial locations, such as the location of the Sun and Moon, are also included. Phoenix is meant to be used as a library within the context of a larger application. For example,more » it could be used for a web service, desktop client, or to compute simple values in a scripting environment.« less

Concentrator optical characterization using computer mathematical modelling and point source testing

NASA Technical Reports Server (NTRS)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

Approximate method for calculating convective heat flux on the surface of bodies of simple geometric shapes

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.

2017-02-01

The paper formulated engineering and physical mathematical model for aerothermodynamics hypersonic flight vehicle (HFV) in laminar and turbulent boundary layers (model designed for an approximate estimate of the convective heat flow in the range of speeds M = 6-28, and height H = 20-80 km). 2D versions of calculations of convective heat flows for bodies of simple geometric forms (individual elements of the design HFV) are presented.

Classification of quantum groups and Belavin–Drinfeld cohomologies for orthogonal and symplectic Lie algebras

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

Kadets, Boris; Karolinsky, Eugene; Pop, Iulia

2016-05-15

In this paper we continue to study Belavin–Drinfeld cohomology introduced in Kadets et al., Commun. Math. Phys. 344(1), 1-24 (2016) and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra #Mathematical Fraktur Small G#. Here we compute Belavin–Drinfeld cohomology for all non-skewsymmetric r-matrices on the Belavin–Drinfeld list for simple Lie algebras of type B, C, and D.

Comparison of Virginia's College and Career Ready Mathematics Performance Expectations with the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Virginia Department of Education, 2010

2010-01-01

This paper presents a comparison of Virginia's mathematics performance expectations with the common core state standards for mathematics. The comparison focuses on number and quantity, algebra, functions, geometry, and statistics and probability. (Contains 1 footnote.)

Software Quality Metrics Enhancements. Volume 1

DTIC Science & Technology

1980-04-01

the mathematical relationships which relate metrics to ratings of the various quality factors) for factors which were not validated previously were...function, provides a mathematical relationship between the metrics and the quality factors. (3) Validation of these normalization functions was performed by...samples, further research is needed before a high degree of confidence can be placed on the mathematical relationships established to date l (3.3.3) 6

Can gender priming eliminate the effects of stereotype threat? The case of simple dynamic systems.

PubMed

Lungwitz, Vivien; Sedlmeier, Peter; Schwarz, Marcus

2018-05-31

Mathematics and mental rotation are classic fields where it has been shown that priming women with their gender identity impedes performance. Whereas past research focused mainly on stereotype threat effects in women in a narrowly defined context, this study broadened the research focus: We primed 264 women and men equally with a male, a neutral, or a female prime before they had to solve a simple dynamic system task. As expected, female-primed women subsequently performed worst of all six groups. Solution rates were almost 14% higher for the women in the male-primed condition. Men performed better than women in all three priming conditions. However, this difference was reduced in the male-primed condition as women's performance had increased as anticipated. Unexpected was a decline in the male performance in the same condition. The study showed that gender priming had a significant effect on women in tasks involving simple dynamic systems. However, mathematical knowledge and area of occupation clearly were stronger predictors for both men and women. Priming alone cannot eliminate the effects of stereotype threat. Copyright © 2018. Published by Elsevier B.V.

Experiment and mathematical model for the heat transfer in water around 4 °C

NASA Astrophysics Data System (ADS)

Ogawa, Naohisa; Kaneko, Fumitoshi

2017-03-01

Water, which is the habitat for a variety of living creatures, has a maximum density at 4.0 °C. This crucial property is considered to play a very important role in the biology of a lake and also has a close relationship with the areas of environmentology and geoscience. It would be desirable for students to confirm this important property of water themselves by carrying out simple experiments. However, it is not easy to detect the maximum density at 4.0 °C because the temperature dependence of the water density is very small close to its freezing point. For example, the density of water is 0.999 975 g cm-3 at 4.0 °C and 0.999 850 g cm-3 at 0.1 °C. The aim in this manuscript is to demonstrate a simple experiment to detect 4.0 °C as the temperature of maximum density, in which the time dependence of the water temperature is measured at several different depths by chilling the water surface. This is a simple experiment that can also be performed by high school students. We also present a mathematical model that can explain the results of this experiment.

Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function

ERIC Educational Resources Information Center

Steele, Michael D.; Hillen, Amy F.; Smith, Margaret S.

2013-01-01

This study describes teacher learning in a teaching experiment consisting of a content-focused methods course involving the mathematical knowledge for teaching function. Prospective and practicing teachers in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the…

Surface-Height Determination of Crevassed Glaciers-Mathematical Principles of an Autoadaptive Density-Dimension Algorithm and Validation Using ICESat-2 Simulator (SIMPL) Data

NASA Technical Reports Server (NTRS)

Herzfeld, Ute C.; Trantow, Thomas M.; Harding, David; Dabney, Philip W.

2017-01-01

Glacial acceleration is a main source of uncertainty in sea-level-change assessment. Measurement of ice-surface heights with a spatial and temporal resolution that not only allows elevation-change calculation, but also captures ice-surface morphology and its changes is required to aid in investigations of the geophysical processes associated with glacial acceleration.The Advanced Topographic Laser Altimeter System aboard NASAs future ICESat-2 Mission (launch 2017) will implement multibeam micropulse photon-counting lidar altimetry aimed at measuring ice-surface heights at 0.7-m along-track spacing. The instrument is designed to resolve spatial and temporal variability of rapidly changing glaciers and ice sheets and the Arctic sea ice. The new technology requires the development of a new mathematical algorithm for the retrieval of height information.We introduce the density-dimension algorithm (DDA) that utilizes the radial basis function to calculate a weighted density as a form of data aggregation in the photon cloud and considers density an additional dimension as an aid in auto-adaptive threshold determination. The auto-adaptive capability of the algorithm is necessary to separate returns from noise and signal photons under changing environmental conditions. The algorithm is evaluated using data collected with an ICESat-2 simulator instrument, the Slope Imaging Multi-polarization Photon-counting Lidar, over the heavily crevassed Giesecke Braer in Northwestern Greenland in summer 2015. Results demonstrate that ICESat-2 may be expected to provide ice-surface height measurements over crevassed glaciers and other complex ice surfaces. The DDA is generally applicable for the analysis of airborne and spaceborne micropulse photon-counting lidar data over complex and simple surfaces.

The Mechanisms of Water Exchange: The Regulatory Roles of Multiple Interactions in Social Wasps.

PubMed

Agrawal, Devanshu; Karsai, Istvan

2016-01-01

Evolutionary benefits of task fidelity and improving information acquisition via multiple transfers of materials between individuals in a task partitioned system have been shown before, but in this paper we provide a mechanistic explanation of these phenomena. Using a simple mathematical model describing the individual interactions of the wasps, we explain the functioning of the common stomach, an information center, which governs construction behavior and task change. Our central hypothesis is a symmetry between foragers who deposit water and foragers who withdraw water into and out of the common stomach. We combine this with a trade-off between acceptance and resistance to water transfer. We ultimately derive a mathematical function that relates the number of interactions that foragers complete with common stomach wasps during a foraging cycle. We use field data and additional model assumptions to calculate values of our model parameters, and we use these to explain why the fullness of the common stomach stabilizes just below 50 percent, why the average number of successful interactions between foragers and the wasps forming the common stomach is between 5 and 7, and why there is a variation in this number of interactions over time. Our explanation is that our proposed water exchange mechanism places natural bounds on the number of successful interactions possible, water exchange is set to optimize mediation of water through the common stomach, and the chance that foragers abort their task prematurely is very low.

The Mechanisms of Water Exchange: The Regulatory Roles of Multiple Interactions in Social Wasps

PubMed Central

Agrawal, Devanshu; Karsai, Istvan

2016-01-01

Evolutionary benefits of task fidelity and improving information acquisition via multiple transfers of materials between individuals in a task partitioned system have been shown before, but in this paper we provide a mechanistic explanation of these phenomena. Using a simple mathematical model describing the individual interactions of the wasps, we explain the functioning of the common stomach, an information center, which governs construction behavior and task change. Our central hypothesis is a symmetry between foragers who deposit water and foragers who withdraw water into and out of the common stomach. We combine this with a trade-off between acceptance and resistance to water transfer. We ultimately derive a mathematical function that relates the number of interactions that foragers complete with common stomach wasps during a foraging cycle. We use field data and additional model assumptions to calculate values of our model parameters, and we use these to explain why the fullness of the common stomach stabilizes just below 50 percent, why the average number of successful interactions between foragers and the wasps forming the common stomach is between 5 and 7, and why there is a variation in this number of interactions over time. Our explanation is that our proposed water exchange mechanism places natural bounds on the number of successful interactions possible, water exchange is set to optimize mediation of water through the common stomach, and the chance that foragers abort their task prematurely is very low. PMID:26751076

Upper-Division Student Difficulties with the Dirac Delta Function

ERIC Educational Resources Information Center

Wilcox, Bethany R.; Pollock, Steven J.

2015-01-01

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

The Development of Executive Functions and Early Mathematics: A Dynamic Relationship

ERIC Educational Resources Information Center

Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Boom, Jan; Leseman, Paul P. M.

2012-01-01

Background: The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown. Aim: The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal…

Use of the transect method in satellite survey missions with application to the infrared astronomical satellite /IRAS/

NASA Technical Reports Server (NTRS)

Mclaughlin, W. I.; Lundy, S. A.; Ling, H. Y.; Stroberg, M. W.

1980-01-01

The coverage of the celestial sphere or the surface of the earth with a narrow-field instrument onboard a satellite can be described by a set of swaths on the sphere. A transect is a curve on this sphere constructed to sample the coverage. At each point on the transect the number of times that the field-of-view of the instrument has passed over the point is recorded. This information is conveniently displayed as an integer-valued histogram over the length of the transect. The effectiveness of the transect method for a particular observing plan and the best placement of the transects depends upon the structure of the set of observations. Survey missions are usually characterized by a somewhat parallel alignment of the instrument swaths. Using autocorrelation and cross-correlation functions among the histograms the structure of a survey has been analyzed into two components, and each is illustrated by a simple mathematical model. The complex, all-sky survey to be performed by the Infrared Astronomical Satellite (IRAS) is synthesized in some detail utilizing the objectives and constraints of that mission. It is seen that this survey possesses the components predicted by the simple models and this information is useful in characterizing the properties of the IRAS survey and the placement of the transects as a function of celestial latitude and certain structural properties of the coverage.

Dynamical systems, attractors, and neural circuits.

PubMed

Miller, Paul

2016-01-01

Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic-they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.

Predicting haemodynamic networks using electrophysiology: The role of non-linear and cross-frequency interactions

PubMed Central

Tewarie, P.; Bright, M.G.; Hillebrand, A.; Robson, S.E.; Gascoyne, L.E.; Morris, P.G.; Meier, J.; Van Mieghem, P.; Brookes, M.J.

2016-01-01

Understanding the electrophysiological basis of resting state networks (RSNs) in the human brain is a critical step towards elucidating how inter-areal connectivity supports healthy brain function. In recent years, the relationship between RSNs (typically measured using haemodynamic signals) and electrophysiology has been explored using functional Magnetic Resonance Imaging (fMRI) and magnetoencephalography (MEG). Significant progress has been made, with similar spatial structure observable in both modalities. However, there is a pressing need to understand this relationship beyond simple visual similarity of RSN patterns. Here, we introduce a mathematical model to predict fMRI-based RSNs using MEG. Our unique model, based upon a multivariate Taylor series, incorporates both phase and amplitude based MEG connectivity metrics, as well as linear and non-linear interactions within and between neural oscillations measured in multiple frequency bands. We show that including non-linear interactions, multiple frequency bands and cross-frequency terms significantly improves fMRI network prediction. This shows that fMRI connectivity is not only the result of direct electrophysiological connections, but is also driven by the overlap of connectivity profiles between separate regions. Our results indicate that a complete understanding of the electrophysiological basis of RSNs goes beyond simple frequency-specific analysis, and further exploration of non-linear and cross-frequency interactions will shed new light on distributed network connectivity, and its perturbation in pathology. PMID:26827811

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

A Preservice Mathematics Teacher's Beliefs about Teaching Mathematics with Technology

ERIC Educational Resources Information Center

Belbase, Shashidhar

2015-01-01

This paper analyzed a preservice mathematics teacher's beliefs about teaching mathematics with technology. The researcher used five semi-structured task-based interviews in the problematic contexts of teaching fraction multiplications with JavaBars, functions and limits, and geometric transformations with Geometer's Sketchpad, and statistical data…

Bilingual Teaching Research and Practice of Complex Function Theory

ERIC Educational Resources Information Center

Ma, Lixin

2011-01-01

Mathematics bilingual teaching is assisted in Chinese with English teaching, and gradually enables students to independently use English to learn, study, reflect and exchange Mathematics. In order to better carry out mathematics teaching, department of mathematics in Dezhou University forms discussion groups and launches bilingual teaching…

Computer simulation of two electrophoretic columns coupled for isoelectric focusing in simple buffers

NASA Technical Reports Server (NTRS)

Tsai, Amos; Mosher, Richard A.; Bier, Milan

1986-01-01

Computer simulation is used to analyze a system of two electrophoretic columns coupled by mixing the anolyte of one with the catholyte of the other. A mathematical model is presented which is used to predict the pH gradients formed by monovalent buffers in this system, when the currents in the columns are unequal. In the column with the higher current a pH gradient is created which increases from anode to cathode and is potentially useful for isoelectric focusing. The breadth of this gradient is dependent upon the ratio of the currents. The function of the second column is the compensation of buffer migration which occurs in the first column, thereby maintaining constant electrolyte composition. The effects of buffer pKs and mobilities are evaluated.

Search times and probability of detection in time-limited search

NASA Astrophysics Data System (ADS)

Wilson, David; Devitt, Nicole; Maurer, Tana

2005-05-01

When modeling the search and target acquisition process, probability of detection as a function of time is important to war games and physical entity simulations. Recent US Army RDECOM CERDEC Night Vision and Electronics Sensor Directorate modeling of search and detection has focused on time-limited search. Developing the relationship between detection probability and time of search as a differential equation is explored. One of the parameters in the current formula for probability of detection in time-limited search corresponds to the mean time to detect in time-unlimited search. However, the mean time to detect in time-limited search is shorter than the mean time to detect in time-unlimited search and the relationship between them is a mathematical relationship between these two mean times. This simple relationship is derived.

All two-loop maximally helicity-violating amplitudes in multi-Regge kinematics from applied symbology

NASA Astrophysics Data System (ADS)

Prygarin, Alexander; Spradlin, Marcus; Vergu, Cristian; Volovich, Anastasia

2012-04-01

Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multiloop computations. The symbol for all two-loop maximally helicity violating amplitudes in planar supersymmetric Yang-Mills theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multi-Regge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct Balitsky-Fadin-Kuraev-Lipatov computation carried out in a parallel publication.

An efficient algorithm for automatic phase correction of NMR spectra based on entropy minimization

NASA Astrophysics Data System (ADS)

Chen, Li; Weng, Zhiqiang; Goh, LaiYoong; Garland, Marc

2002-09-01

A new algorithm for automatic phase correction of NMR spectra based on entropy minimization is proposed. The optimal zero-order and first-order phase corrections for a NMR spectrum are determined by minimizing entropy. The objective function is constructed using a Shannon-type information entropy measure. Entropy is defined as the normalized derivative of the NMR spectral data. The algorithm has been successfully applied to experimental 1H NMR spectra. The results of automatic phase correction are found to be comparable to, or perhaps better than, manual phase correction. The advantages of this automatic phase correction algorithm include its simple mathematical basis and the straightforward, reproducible, and efficient optimization procedure. The algorithm is implemented in the Matlab program ACME—Automated phase Correction based on Minimization of Entropy.

Optimal design of reverse osmosis module networks

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

Maskan, F.; Wiley, D.E.; Johnston, L.P.M.

2000-05-01

The structure of individual reverse osmosis modules, the configuration of the module network, and the operating conditions were optimized for seawater and brackish water desalination. The system model included simple mathematical equations to predict the performance of the reverse osmosis modules. The optimization problem was formulated as a constrained multivariable nonlinear optimization. The objective function was the annual profit for the system, consisting of the profit obtained from the permeate, capital cost for the process units, and operating costs associated with energy consumption and maintenance. Optimization of several dual-stage reverse osmosis systems were investigated and compared. It was found thatmore » optimal network designs are the ones that produce the most permeate. It may be possible to achieve economic improvements by refining current membrane module designs and their operating pressures.« less

Scattering measurements on natural and model trees

NASA Technical Reports Server (NTRS)

Rogers, James C.; Lee, Sung M.

1990-01-01

The acoustical back scattering from a simple scale model of a tree has been experimentally measured. The model consisted of a trunk and six limbs, each with 4 branches; no foliage or twigs were included. The data from the anechoic chamber measurements were then mathematically combined to construct the effective back scattering from groups of trees. Also, initial measurements have been conducted out-of-doors on a single tree in an open field in order to characterize its acoustic scattering as a function of azimuth angle. These measurements were performed in the spring, prior to leaf development. The data support a statistical model of forest scattering; the scattered signal spectrum is highly irregular but with a remarkable general resemblance to the incident signal spectrum. Also, the scattered signal's spectra showed little dependence upon scattering angle.

Insertion device calculations with mathematica

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

Carr, R.; Lidia, S.

1995-02-01

The design of accelerator insertion devices such as wigglers and undulators has usually been aided by numerical modeling on digital computers, using code in high level languages like Fortran. In the present era, there are higher level programming environments like IDL{reg_sign}, MatLab{reg_sign}, and Mathematica{reg_sign} in which these calculations may be performed by writing much less code, and in which standard mathematical techniques are very easily used. The authors present a suite of standard insertion device modeling routines in Mathematica to illustrate the new techniques. These routines include a simple way to generate magnetic fields using blocks of CSEM materials, trajectorymore » solutions from the Lorentz force equations for given magnetic fields, Bessel function calculations of radiation for wigglers and undulators and general radiation calculations for undulators.« less

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

PubMed

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

2014-08-28

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

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

NASA Astrophysics Data System (ADS)

Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Basic mathematical function libraries for scientific computation

NASA Technical Reports Server (NTRS)

Galant, David C.

1989-01-01

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

The Functional Use of a Mathematical Sign

ERIC Educational Resources Information Center

Berger, Margot

2004-01-01

The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both…

Friend Influence and Susceptibility to Influence: Changes in Mathematical Reasoning as a Function of Relative Peer Acceptance and Interest in Mathematics

ERIC Educational Resources Information Center

DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa

2016-01-01

This study investigated friend influence over mathematics achievement in 202 same-sex friendship dyads (106 girl dyads). Participants were in the third grade (around age 9) at the outset. Each friend completed a questionnaire describing interest in mathematics and a standardized mathematical reasoning assessment. Peer nominations provided a…

Making Connections by Using Molecular Models in Geometry.

ERIC Educational Resources Information Center

Pacyga, Robert

1995-01-01

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invites students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MKR)

Lemon-Lime Science Time.

ERIC Educational Resources Information Center

Brown, Helen

1995-01-01

Presents a unit to investigate lemons and experience the real taste of a lemon that includes simple, enjoyable, and inexpensive activities that develop students' observation, prediction, measurement, and inference skills. Students also developed creative arts projects, explored mathematical concepts, and wrote stories about fruit. (NB)

Colour by Numbers

ERIC Educational Resources Information Center

Wetherell, Chris

2017-01-01

This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Hitchin functionals are related to measures of entanglement

NASA Astrophysics Data System (ADS)

Lévay, Péter; Sárosi, Gábor

2012-11-01

According to the black hole/qubit correspondence (BHQC) certain black hole entropy formulas in supergravity can be related to multipartite entanglement measures of quantum information. Here we show that the origin of this correspondence is a connection between Hitchin functionals used as action functionals for form theories of gravity related to topological strings and entanglement measures for systems with a small number of constituents. The basic idea acting as a unifying agent in these seemingly unrelated fields is stability connected to the mathematical notion of special prehomogeneous vector spaces associated to Freudenthal systems coming from simple Jordan algebras. It is shown that the nonlinear function featuring these functionals and defining Calabi-Yau and generalized Calabi-Yau structures is the Freudenthal dual, a concept introduced recently in connection with the BHQC. We propose to use the Hitchin invariant for three-forms in seven dimensions as an entanglement measure playing a basic role in classifying three-fermion systems with seven modes. The representative of the class of maximal tripartite entanglement is the three-form used as a calibration for compactification on manifolds with G2 holonomy. The idea that entanglement measures are related to action functionals from which the usual correspondence of the BHQC follows at the tree level suggests that one can use the BHQC in a more general context.

Aerodynamic interference effects on tilting proprotor aircraft. [using the Green function method

NASA Technical Reports Server (NTRS)

Soohoo, P.; Morino, L.; Noll, R. B.; Ham, N. D.

1977-01-01

The Green's function method was used to study tilting proprotor aircraft aerodynamics with particular application to the problem of the mutual interference of the wing-fuselage-tail-rotor wake configuration. While the formulation is valid for fully unsteady rotor aerodynamics, attention was directed to steady state aerodynamics, which was achieved by replacing the rotor with the actuator disk approximation. The use of an actuator disk analysis introduced a mathematical singularity into the formulation; this problem was studied and resolved. The pressure distribution, lift, and pitching moment were obtained for an XV-15 wing-fuselage-tail rotor configuration at various flight conditions. For the flight configurations explored, the effects of the rotor wake interference on the XV-15 tilt rotor aircraft yielded a reduction in the total lift and an increase in the nose-down pitching moment. This method provides an analytical capability that is simple to apply and can be used to investigate fuselage-tail rotor wake interference as well as to explore other rotor design problem areas.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Low-order modelling of a drop on a highly-hydrophobic substrate: statics and dynamics

NASA Astrophysics Data System (ADS)

Wray, Alexander W.; Matar, Omar K.; Davis, Stephen H.

2017-11-01

We analyse the behaviour of droplets resting on highly-hydrophobic substrates. This problem is of practical interest due to its appearance in many physical contexts involving the spreading, wetting, and dewetting of fluids on solid substrates. In mathematical terms, it exhibits an interesting challenge as the interface is multi-valued as a function of the natural Cartesian co-ordinates, presenting a stumbling block to typical low-order modelling techniques. Nonetheless, we show that in the static case, the interfacial shape is governed by the Young-Laplace equation, which may be solved explicitly in terms of elliptic functions. We present simple low-order expressions that faithfully reproduce the shapes. We then consider the dynamic case, showing that the predictions of our low-order model compare favourably with those obtained from direct numerical simulations. We also examine the characteristic flow regimes of interest. EPSRC, UK, MEMPHIS program Grant (EP/K003976/1), RAEng Research Chair (OKM).

The skewed weak lensing likelihood: why biases arise, despite data and theory being sound

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim

2018-07-01

We derive the essentials of the skewed weak lensing likelihood via a simple hierarchical forward model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of Lambda cold dark matter. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from cosmic microwave background analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30 per cent of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.

Terasaki Ramps in the Endoplasmic Reticulum: Structure, Function and Formation

NASA Astrophysics Data System (ADS)

Huber, Greg; Guven, Jemal; Valencia, Dulce-Maria

2015-03-01

The endoplasmic reticulum (ER) has long been considered an exceedingly important and complex cellular organelle in eukaryotes (like you). It is a membrane structure, part folded lamellae, part tubular network, that both envelopes the nucleus and threads its way outward, all the way to the cell's periphery. Despite the elegant mechanics of bilayer membranes offered by the work of Helfrich and Canham, as far as the ER is concerned, theory has mostly sat on the sidelines. However, refined imaging of the ER has recently revealed beautiful and subtle geometrical forms - simple geometries, from the mathematical point of view - which some have called a ``parking garage for ribosomes.'' I'll review the discovery and physics of Terasaki ramps and discuss their relation to cell-biological questions, such as ER and nuclear-membrane re-organization during mitosis. Rather than being a footnote in a textbook on differential geometry, these structures suggest answers to a number of the ER's structure-function problems.

Real-time digital signal recovery for a multi-pole low-pass transfer function system.

PubMed

Lee, Jhinhwan

2017-08-01

In order to solve the problems of waveform distortion and signal delay by many physical and electrical systems with multi-pole linear low-pass transfer characteristics, a simple digital-signal-processing (DSP)-based method of real-time recovery of the original source waveform from the distorted output waveform is proposed. A mathematical analysis on the convolution kernel representation of the single-pole low-pass transfer function shows that the original source waveform can be accurately recovered in real time using a particular moving average algorithm applied on the input stream of the distorted waveform, which can also significantly reduce the overall delay time constant. This method is generalized for multi-pole low-pass systems and has noise characteristics of the inverse of the low-pass filter characteristics. This method can be applied to most sensors and amplifiers operating close to their frequency response limits to improve the overall performance of data acquisition systems and digital feedback control systems.

The skewed weak lensing likelihood: why biases arise, despite data and theory being sound.

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim

2018-04-01

We derive the essentials of the skewed weak lensing likelihood via a simple Hierarchical Forward Model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of ΛCDM. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from CMB analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30% of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.

Funny Face Contest: A Formative Assessment

ERIC Educational Resources Information Center

Colen, Yong S.

2010-01-01

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

ERIC Educational Resources Information Center

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-01-01

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

Core-Plus Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…

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)…

Bridging History of the Concept of Function with Learning of Mathematics: Students' Meta-Discursive Rules, Concept Formation and Historical Awareness

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid

2014-01-01

In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a…

An Empirical Fitting Method for Type Ia Supernova Light Curves: A Case Study of SN 2011fe

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

Zheng, WeiKang; Filippenko, Alexei V., E-mail: zwk@astro.berkeley.edu

We present a new empirical fitting method for the optical light curves of Type Ia supernovae (SNe Ia). We find that a variant broken-power-law function provides a good fit, with the simple assumption that the optical emission is approximately the blackbody emission of the expanding fireball. This function is mathematically analytic and is derived directly from the photospheric velocity evolution. When deriving the function, we assume that both the blackbody temperature and photospheric velocity are constant, but the final function is able to accommodate these changes during the fitting procedure. Applying it to the case study of SN 2011fe givesmore » a surprisingly good fit that can describe the light curves from the first-light time to a few weeks after peak brightness, as well as over a large range of fluxes (∼5 mag, and even ∼7 mag in the g band). Since SNe Ia share similar light-curve shapes, this fitting method has the potential to fit most other SNe Ia and characterize their properties in large statistical samples such as those already gathered and in the near future as new facilities become available.« less

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

Moore, J. A. M.; Jiang, J.; Post, W. M.

Carbon cycle models often lack explicit belowground organism activity, yet belowground organisms regulate carbon storage and release in soil. Ectomycorrhizal fungi are important players in the carbon cycle because they are a conduit into soil for carbon assimilated by the plant. It is hypothesized that ectomycorrhizal fungi can also be active decomposers when plant carbon allocation to fungi is low. Here, we reviewed the literature on ectomycorrhizal decomposition and we developed a simulation model of the plant-mycorrhizae interaction where a reduction in plant productivity stimulates ectomycorrhizal fungi to decompose soil organic matter. Our review highlights evidence demonstrating the potential formore » ectomycorrhizal fungi to decompose soil organic matter. Our model output suggests that ectomycorrhizal activity accounts for a portion of carbon decomposed in soil, but this portion varied with plant productivity and the mycorrhizal carbon uptake strategy simulated. Lower organic matter inputs to soil were largely responsible for reduced soil carbon storage. Using mathematical theory, we demonstrated that biotic interactions affect predictions of ecosystem functions. Specifically, we developed a simple function to model the mycorrhizal switch in function from plant symbiont to decomposer. In conclusion, we show that including mycorrhizal fungi with the flexibility of mutualistic and saprotrophic lifestyles alters predictions of ecosystem function.« less

Entropy of spatial network ensembles

NASA Astrophysics Data System (ADS)

Coon, Justin P.; Dettmann, Carl P.; Georgiou, Orestis

2018-04-01

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are indicative of nearly maximally entropic ensembles.

Teaching Mathematical Functions Using Geometric Functions Approach and Its Effect on Ninth Grade Students' Motivation

ERIC Educational Resources Information Center

Akçakin, Veysel

2018-01-01

The purpose of this study is to investigate the effects of using geometric functions approach on 9th grade students' motivation levels toward mathematics in functions unit. Participants of this study were 87 students who were ongoing in the first year of high school in Turkey. In this research, pretest and posttest control group quasiexperimental…

Rethinking the Discovery Function of Proof within the Context of Proofs and Refutations

ERIC Educational Resources Information Center

Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta

2014-01-01

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor.

PubMed

Masić, Alma; Bengtsson, Jessica; Christensson, Magnus

2010-09-01

In this paper we determine the oxygen profile in a biofilm on suspended carriers in two ways: firstly by microelectrode measurements and secondly by a simple mathematical model. The Moving Bed Biofilm Reactor is well-established for wastewater treatment where bacteria grow as a biofilm on the protective surfaces of suspended carriers. The flat shaped BiofilmChip P was developed to allow good conditions for transport of substrates into the biofilm. The oxygen profile was measured in situ the nitrifying biofilm with a microelectrode and it was simulated with a one-dimensional mathematical model. We extended the model by adding a CSTR equation, to connect the reactor to the biofilm through the boundary conditions. We showed the dependence of the thickness of the mass transfer boundary layer on the bulk flow rate. Finally, we estimated the erosion parameter lambda to increase the concordance between the measured and simulated profiles. This lead to a simple empirical relationship between lambda and the flow rate. The data gathered by in situ microelectrode measurements can, together with the mathematical model, be used in predictive modeling and give more insight in the design of new carriers, with the ambition of making process operation more energy efficient. Copyright 2010 Elsevier Inc. All rights reserved.

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

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

NASA Astrophysics Data System (ADS)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice.

PubMed

Whitcomb, David C; Ermentrout, G Bard

2004-08-01

To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation. A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT. This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion. A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.

PubMed

Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

2015-07-22

A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.

Evolutionary game theory using agent-based methods.

PubMed

Adami, Christoph; Schossau, Jory; Hintze, Arend

2016-12-01

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright © 2016 Elsevier B.V. All rights reserved.

BOOK REVIEW: Symmetry and the Monster: One of the Greatest Quests of Mathematics

NASA Astrophysics Data System (ADS)

Szabo, R. J.

2007-04-01

The book Symmetry and the Monster: One of the Greatest Quests of Mathematics describes historical events leading up to the discovery of the Monster sporadic group, the largest simple sporadic group. It also expounds the significance and deep relationships between this group and other areas of mathematics and theoretical physics. It begins, in the prologue, with a nice overview of some of the mathematical drama surrounding the discovery of the Monster and its subsequent relationship to number theory (the so-called Moonshine conjectures). From a historical perspective, the book traces back to the roots of group theory, Galois theory, and steadily runs through time through the many famous mathematicians who contributed to group theory, including Lie, Killing and Cartan. Throughout, the author has provided a very nice and deep insight into the sociological and scientific problems at the time, and gives the reader a very prominent inside view of the real people behind the mathematics. The book should be an enjoyable read to anyone with an interest in the history of mathematics. For the non-mathematician the book makes a good, and mostly successful, attempt at being non-technical. Technical mathematical jargon is replaced with more heuristic, intuitive terminology, making the mathematical descriptions in the book fairly easy going. A glossary\\hspace{0.25pc} of\\hspace{0.25pc} terminology for noindent the more scientifically inclined is included in various footnotes throughout the book and in a comprehensive listing at the end of the book. Some more technical material is also included in the form of appendices at the end of the book. Some aspects of physics are also explained in a simple, intuitive way. The author further attempts at various places to give the non-specialist a glimpse into what mathematical proof is all about, and explains the difficulties and technicalities involved in this very nicely (for instance, he mentions the various 100+ page articles that appeared in the hey-day of finite group theory, indicating the enormous technical nature of the subject). The book nicely paints a dramatic landscape leading up to the discovery of the Monster group, and the problems that remain to this day in trying to understand its significance. One can really take from this book a feel of the mathematics leading up to its appearance, and the importance of the classification problem which was responsible for this. One also really gets an appreciation of the efforts and commitments of the mathematicians who contributed to the subject. All in all, this book achieves a nice balance between providing a beautiful historical account of group theory, and explaining the classification problem for finite groups in a way that is accessible to non-scientists. This should prove to be a good read for both the layperson interested in mathematics or mathematical physics, and also both mathematicians and physicists alike.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

DTIC Science & Technology

2009-05-01

free Internet Myth The story recounted below of the scale-free nature of the Internet seems convincing, sound, and al- most too good to be true ...models. In fact, much of the initial excitement in the nascent field of network science can be attributed to an ear- ly and appealingly simple class...this new class of networks, com- monly referred to as scale-free networks. The term scale-free derives from the simple observation that power-law node

The analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference

NASA Astrophysics Data System (ADS)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

The aim of this study was to describe the analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference. The purpose of this study is to describe the analysis of mathematics teacher's learning on limit algebraic functions in terms of the differences of teaching experience. Learning analysis focused on Pedagogical Content Knowledge (PCK) of teachers in mathematics on limit algebraic functions related to the knowledge of pedagogy. PCK of teachers on limit algebraic function is a type of specialized knowledge for teachers on how to teach limit algebraic function that can be understood by students. Subjects are two high school mathematics teacher who has difference of teaching experience they are one Novice Teacher (NP) and one Experienced Teacher (ET). Data are collected through observation of learning in the class, videos of learning, and then analyzed using qualitative analysis. Teacher's knowledge of Pedagogic defined as a knowledge and understanding of teacher about planning and organizing of learning, and application of learning strategy. The research results showed that the Knowledge of Pedagogy on subject NT in mathematics learning on the material of limit function algebra showed that the subject NT tended to describe procedurally, without explaining the reasons why such steps were used, asking questions which tended to be monotonous not be guiding and digging deeper, and less varied in the use of learning strategies while subject ET gave limited guidance and opportunities to the students to find their own answers, exploit the potential of students to answer questions, provide an opportunity for students to interact and work in groups, and subject ET tended to combine conceptual and procedural explanation.

A Naturalistic Study of Executive Function and Mathematical Problem-Solving

ERIC Educational Resources Information Center

Kotsopoulos, Donna; Lee, Joanne

2012-01-01

Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…

Algebraic Functions, Computer Programming, and the Challenge of Transfer

ERIC Educational Resources Information Center

Schanzer, Emmanuel Tanenbaum

2015-01-01

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

ERIC Educational Resources Information Center

Hatisaru, Vesife; Erbas, Ayhan Kursat

2017-01-01

The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers…

Detection of Gender-Based Differential Item Functioning in a Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Wang, Ning; Lane, Suzanne

This study used three different differential item functioning (DIF) procedures to examine the extent to which items in a mathematics performance assessment functioned differently for matched gender groups. In addition to examining the appropriateness of individual items in terms of DIF with respect to gender, an attempt was made to identify…

Neurovascular Network Explorer 2.0: A Simple Tool for Exploring and Sharing a Database of Optogenetically-evoked Vasomotion in Mouse Cortex In Vivo.

PubMed

Uhlirova, Hana; Tian, Peifang; Kılıç, Kıvılcım; Thunemann, Martin; Sridhar, Vishnu B; Chmelik, Radim; Bartsch, Hauke; Dale, Anders M; Devor, Anna; Saisan, Payam A

2018-05-04

The importance of sharing experimental data in neuroscience grows with the amount and complexity of data acquired and various techniques used to obtain and process these data. However, the majority of experimental data, especially from individual studies of regular-sized laboratories never reach wider research community. A graphical user interface (GUI) engine called Neurovascular Network Explorer 2.0 (NNE 2.0) has been created as a tool for simple and low-cost sharing and exploring of vascular imaging data. NNE 2.0 interacts with a database containing optogenetically-evoked dilation/constriction time-courses of individual vessels measured in mice somatosensory cortex in vivo by 2-photon microscopy. NNE 2.0 enables selection and display of the time-courses based on different criteria (subject, branching order, cortical depth, vessel diameter, arteriolar tree) as well as simple mathematical manipulation (e.g. averaging, peak-normalization) and data export. It supports visualization of the vascular network in 3D and enables localization of the individual functional vessel diameter measurements within vascular trees. NNE 2.0, its source code, and the corresponding database are freely downloadable from UCSD Neurovascular Imaging Laboratory website 1 . The source code can be utilized by the users to explore the associated database or as a template for databasing and sharing their own experimental results provided the appropriate format.