Biology: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=187
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 21 Apr 2014 12:19:15 GMTMon, 21 Apr 2014 12:19:15 GMTNew applications in the Biology categoryhttp://www.mapleprimes.com/images/mapleapps.gifBiology: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=187
Wavelet analysis of the blood pressure and pulse frequency measurements with Maple
http://www.maplesoft.com/applications/view.aspx?SID=149420&ref=Feed
<p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p><img src="/view.aspx?si=149420/4b9024ee653d2c7be8febb717b1df52a.gif" alt="Wavelet analysis of the blood pressure and pulse frequency measurements with Maple" align="left"/><p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p>149420Sun, 14 Jul 2013 04:00:00 ZIrina A. DanishewskaIrina A. DanishewskaDispersion of arterial pulse waves
http://www.maplesoft.com/applications/view.aspx?SID=145362&ref=Feed
<p>In this paper, we are primarily focusing on the arterial pulse waves, more exactly even their dispersion. It is important because presence of this together with the non-linearity generates the conditions of existence of localized waveforms. Thus, we would like to obtain here the dispersion law for pulse waves with Maple.</p><img src="/view.aspx?si=145362/arterialpulsewaves_thumb.png" alt="Dispersion of arterial pulse waves" align="left"/><p>In this paper, we are primarily focusing on the arterial pulse waves, more exactly even their dispersion. It is important because presence of this together with the non-linearity generates the conditions of existence of localized waveforms. Thus, we would like to obtain here the dispersion law for pulse waves with Maple.</p>145362Tue, 02 Apr 2013 04:00:00 ZShiyan S.I.Shiyan S.I.Simulating the Spread of an Infection
http://www.maplesoft.com/applications/view.aspx?SID=144175&ref=Feed
<p>In the problem below I take advantage of Maple's Graph Theory package to simulate how an infection might spread throughout a small community of 15 individuals.</p>
<p>This is a computer simulation project rather than a biology project! For example, the infection may not be a biological infection at all. The 15 vertices could represent 15 different computers, and the "infection" that spreads could be interpreted as a computer virus rather than a biological virus.</p><img src="/view.aspx?si=144175/siminfection_thumb.png" alt="Simulating the Spread of an Infection" align="left"/><p>In the problem below I take advantage of Maple's Graph Theory package to simulate how an infection might spread throughout a small community of 15 individuals.</p>
<p>This is a computer simulation project rather than a biology project! For example, the infection may not be a biological infection at all. The 15 vertices could represent 15 different computers, and the "infection" that spreads could be interpreted as a computer virus rather than a biological virus.</p>144175Mon, 04 Mar 2013 05:00:00 ZDouglas LewitDouglas LewitFuzzy Sets in Examples
http://www.maplesoft.com/applications/view.aspx?SID=141714&ref=Feed
<p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p><img src="/view.aspx?si=141714/fuzzy-sets.jpg" alt="Fuzzy Sets in Examples" align="left"/><p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p>141714Sat, 22 Dec 2012 05:00:00 ZProf. Gennady P. ChuikoProf. Gennady P. ChuikoPolynomial System Solving in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132208&ref=Feed
Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.<img src="/view.aspx?si=132208/thumb.jpg" alt="Polynomial System Solving in Maple 16" align="left"/>Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.132208Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftAn Epidemic Model (for Influenza or Zombies)
http://www.maplesoft.com/applications/view.aspx?SID=127836&ref=Feed
<p>Systems of differential equations can be used to model an epidemic of influenza or of zombies. This is an interactive Maple document suitable for use in courses on mathematical biology or differential equations or calculus courses that include differential equations. No knowledge of Maple is required.</p><img src="/view.aspx?si=127836/Cholera.jpg" alt="An Epidemic Model (for Influenza or Zombies)" align="left"/><p>Systems of differential equations can be used to model an epidemic of influenza or of zombies. This is an interactive Maple document suitable for use in courses on mathematical biology or differential equations or calculus courses that include differential equations. No knowledge of Maple is required.</p>127836Thu, 17 Nov 2011 05:00:00 ZDr. Robert IsraelDr. Robert IsraelProfessional Tips & Techniques: Using Scientific Constants in Maple
http://www.maplesoft.com/applications/view.aspx?SID=1724&ref=Feed
Maple includes an extensive ScientificConstants package that provides access to the values of various constant physical quantities.
Such values can be used to solve equations in fields such as chemistry and physics. The ScientificConstants package also provides the units for each of the constant values, allowing for greater understanding of the equation as well as units matching for error checking of the solution.
The quantities available in the ScientificConstants package are divided into two distinct categories.
1. physical constants
2. properties of the chemical elements (and their isotopes)
This document will highlight the uses of the ScientificConstants package in Maple, and provides some examples of its use.<img src="/view.aspx?si=1724/TTMarApr.jpg" alt="Professional Tips & Techniques: Using Scientific Constants in Maple" align="left"/>Maple includes an extensive ScientificConstants package that provides access to the values of various constant physical quantities.
Such values can be used to solve equations in fields such as chemistry and physics. The ScientificConstants package also provides the units for each of the constant values, allowing for greater understanding of the equation as well as units matching for error checking of the solution.
The quantities available in the ScientificConstants package are divided into two distinct categories.
1. physical constants
2. properties of the chemical elements (and their isotopes)
This document will highlight the uses of the ScientificConstants package in Maple, and provides some examples of its use.1724Mon, 27 Mar 2006 00:00:00 ZMaplesoftMaplesoftRecognition of Leaves and General 2-D Objects
http://www.maplesoft.com/applications/view.aspx?SID=4295&ref=Feed
The shape of a complicated 2D object can be approximated by a polygon consisting of a finite number of line segments. We use Maple to compute a polygon fit to a scanned image of a maple leaf (in DXF) using a Fourier series technique.<img src="/view.aspx?si=4295/leaf.gif" alt="Recognition of Leaves and General 2-D Objects" align="left"/>The shape of a complicated 2D object can be approximated by a polygon consisting of a finite number of line segments. We use Maple to compute a polygon fit to a scanned image of a maple leaf (in DXF) using a Fourier series technique.4295Wed, 14 Aug 2002 12:00:12 ZStanislav BartonStanislav BartonAn Algorithm For Fitting Nonlinear Piecewise Functions, with an Application to Animal Growth
http://www.maplesoft.com/applications/view.aspx?SID=4294&ref=Feed
This worksheet shows how to find parameters of a piecwise nonlinear function fitting a given data set. As an example, we fit a model for the growth of a bull to actual growth data. We show an improvement in the fit of our method over the classical Gompertz function.<img src="/view.aspx?si=4294//applications/images/app_image_blank_lg.jpg" alt="An Algorithm For Fitting Nonlinear Piecewise Functions, with an Application to Animal Growth" align="left"/>This worksheet shows how to find parameters of a piecwise nonlinear function fitting a given data set. As an example, we fit a model for the growth of a bull to actual growth data. We show an improvement in the fit of our method over the classical Gompertz function.4294Wed, 14 Aug 2002 11:53:55 ZStanislav BartonStanislav BartonReconstruction of 2-D Images and CAT Scans
http://www.maplesoft.com/applications/view.aspx?SID=4273&ref=Feed
This is a Maple application centered around the article "How to resurrect a cat from its grin" that appeared in the Mathematical Recreations" section of Scientific American (Sept. 1990).<img src="/view.aspx?si=4273/cat.gif" alt="Reconstruction of 2-D Images and CAT Scans" align="left"/>This is a Maple application centered around the article "How to resurrect a cat from its grin" that appeared in the Mathematical Recreations" section of Scientific American (Sept. 1990).4273Mon, 13 May 2002 11:54:43 ZBruno GuerrieriBruno GuerrieriHIV and antiviral therapy
http://www.maplesoft.com/applications/view.aspx?SID=4205&ref=Feed
An exploration of "Mathematical Models and the design of public health policy: HIV and Antiviral therapy", by Sunetra Gupta, Roy M. Anderson, and Robert M. May, SIAM Reviw, Vol 35, No. 3, pp. 1-16, March 1993.<img src="/view.aspx?si=4205//applications/images/app_image_blank_lg.jpg" alt="HIV and antiviral therapy" align="left"/>An exploration of "Mathematical Models and the design of public health policy: HIV and Antiviral therapy", by Sunetra Gupta, Roy M. Anderson, and Robert M. May, SIAM Reviw, Vol 35, No. 3, pp. 1-16, March 1993.4205Fri, 18 Jan 2002 10:29:47 ZRobert CorlessRobert CorlessGraphical analysis of the chemostat equations
http://www.maplesoft.com/applications/view.aspx?SID=3850&ref=Feed
Graphical analysis of the chemostat equations for modeling population biology<img src="/view.aspx?si=3850/450.jpg" alt="Graphical analysis of the chemostat equations" align="left"/>Graphical analysis of the chemostat equations for modeling population biology3850Wed, 20 Jun 2001 00:00:00 ZMatt MillerMatt MillerDensity dependent natural selection
http://www.maplesoft.com/applications/view.aspx?SID=3895&ref=Feed
This worksheet is explores the paper Jonathan Roughgarden, 1971, Density dependent natural selection , Ecology 52 : 453-468, in which Roughgarden merges population genetics with population ecology.<img src="/view.aspx?si=3895//applications/images/app_image_blank_lg.jpg" alt="Density dependent natural selection" align="left"/>This worksheet is explores the paper Jonathan Roughgarden, 1971, Density dependent natural selection , Ecology 52 : 453-468, in which Roughgarden merges population genetics with population ecology.3895Wed, 20 Jun 2001 00:00:00 ZMatt MillerMatt MillerMcConnell equations in biochemistry
http://www.maplesoft.com/applications/view.aspx?SID=3848&ref=Feed
This worksheet shows how the McConnell equations, a linear inhomogeneous system of differential equations with constant coefficients, can be solved elegantly by using symbolic matrix algebra only, in particular by using matrix exponentials<img src="/view.aspx?si=3848/448.jpg" alt="McConnell equations in biochemistry" align="left"/>This worksheet shows how the McConnell equations, a linear inhomogeneous system of differential equations with constant coefficients, can be solved elegantly by using symbolic matrix algebra only, in particular by using matrix exponentials3848Wed, 20 Jun 2001 00:00:00 ZJohannes GrotendorstJohannes Grotendorst3-D surface models of seashells
http://www.maplesoft.com/applications/view.aspx?SID=3851&ref=Feed
Seashells can be modeled by surfaces in 3D. Their self-similar shape can be generated by a simple formula with a certain number of free parameters. This worksheet implements these models and displays the results as stunning Maple graphics<img src="/view.aspx?si=3851/shell.gif" alt="3-D surface models of seashells" align="left"/>Seashells can be modeled by surfaces in 3D. Their self-similar shape can be generated by a simple formula with a certain number of free parameters. This worksheet implements these models and displays the results as stunning Maple graphics3851Wed, 20 Jun 2001 00:00:00 ZAlain GorielyAlain GorielyOptimal control problem in fertilizer economics
http://www.maplesoft.com/applications/view.aspx?SID=3798&ref=Feed
Optimal fertiliser application involves trading off between the costs of buying and spreading fertiliser and the benefits of increased production. This is complicated because fertiliser nutrients carry over in the soil from one year to the next, so that investment in fertiliser in the present contributes a stream of benefit through future years. We are developing a commercial decision support computer application, named Outlook(TM), to assist New Zealand farmers in planning their fertiliser expenditure on a 10-year time horizon. The biological basis for this software is a dynamic nutrient carryover model which predicts the changes in soil nutrient status from year to year under a given application of fertiliser. The original model considered only phosphate dynamics (Metherell et al 1995) and the economic optimisation of that model is described in Woodward (in press). This model is currently being updated to consider the coupled dynamics of both phosphorus and sulphur, the two most important nutrients in New Zealand pastoral farming.<img src="/view.aspx?si=3798//applications/images/app_image_blank_lg.jpg" alt="Optimal control problem in fertilizer economics" align="left"/>Optimal fertiliser application involves trading off between the costs of buying and spreading fertiliser and the benefits of increased production. This is complicated because fertiliser nutrients carry over in the soil from one year to the next, so that investment in fertiliser in the present contributes a stream of benefit through future years. We are developing a commercial decision support computer application, named Outlook(TM), to assist New Zealand farmers in planning their fertiliser expenditure on a 10-year time horizon. The biological basis for this software is a dynamic nutrient carryover model which predicts the changes in soil nutrient status from year to year under a given application of fertiliser. The original model considered only phosphate dynamics (Metherell et al 1995) and the economic optimisation of that model is described in Woodward (in press). This model is currently being updated to consider the coupled dynamics of both phosphorus and sulphur, the two most important nutrients in New Zealand pastoral farming.3798Tue, 19 Jun 2001 00:00:00 ZSimon WoodwardSimon WoodwardGame of Life and Cellular Automata
http://www.maplesoft.com/applications/view.aspx?SID=3790&ref=Feed
This worksheet demonstrates the use of Maple for matrix manipulations and the capabilites of Maple as a programming language. In this particular worksheet the well-known Game Of Life has been implemented using the matrixplot-command for graphical output. Hope you like it!<img src="/view.aspx?si=3790/life.gif" alt="Game of Life and Cellular Automata" align="left"/>This worksheet demonstrates the use of Maple for matrix manipulations and the capabilites of Maple as a programming language. In this particular worksheet the well-known Game Of Life has been implemented using the matrixplot-command for graphical output. Hope you like it!3790Tue, 19 Jun 2001 00:00:00 ZBjörn SchäferBjörn SchäferPopulation growth and the earth's human carrying capacity
http://www.maplesoft.com/applications/view.aspx?SID=3550&ref=Feed
Population growth and the earth's human carrying capacity is the focus of this application. The annual rate of increase of the earth's population was 0.04% per year from AD 1 to 1650, rose to a peak of 2.1% per year around 1965-1970, and is now 1.6%. What are the consequences of these differences in rates? <img src="/view.aspx?si=3550//applications/images/app_image_blank_lg.jpg" alt="Population growth and the earth's human carrying capacity " align="left"/>Population growth and the earth's human carrying capacity is the focus of this application. The annual rate of increase of the earth's population was 0.04% per year from AD 1 to 1650, rose to a peak of 2.1% per year around 1965-1970, and is now 1.6%. What are the consequences of these differences in rates? 3550Mon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerMathematical treatment of competition theory
http://www.maplesoft.com/applications/view.aspx?SID=3546&ref=Feed
This application describes Volterra's proposal of two logistically growing species having rates of increase that were determined by their own as well as their competitors' abundance<img src="/view.aspx?si=3546//applications/images/app_image_blank_lg.jpg" alt="Mathematical treatment of competition theory" align="left"/>This application describes Volterra's proposal of two logistically growing species having rates of increase that were determined by their own as well as their competitors' abundance3546Mon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerDemography of the vegetable ivory palm Pytelephas seemanii in Colombia, and the impact of seed harvesting
http://www.maplesoft.com/applications/view.aspx?SID=3626&ref=Feed
This paper is an analysis of a stage-based model of the dynamics of a palm tree species, using, a modification of the Leslie model. In this case, the assumption is that the stage of an organism (size class) is a better indicator of reproductive performance and survival than age is. This assumption works well for many plants, and any organism in which size is correlated with survival and fecundity. <img src="/view.aspx?si=3626//applications/images/app_image_blank_lg.jpg" alt="Demography of the vegetable ivory palm Pytelephas seemanii in Colombia, and the impact of seed harvesting " align="left"/>This paper is an analysis of a stage-based model of the dynamics of a palm tree species, using, a modification of the Leslie model. In this case, the assumption is that the stage of an organism (size class) is a better indicator of reproductive performance and survival than age is. This assumption works well for many plants, and any organism in which size is correlated with survival and fecundity. 3626Mon, 18 Jun 2001 00:00:00 ZMatt MillerMatt Miller