Applications, Examples and Libraries

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Recently I was skimming on the Internet for algorithms for alignment of biological sequences (e.g. DNA sequences, protein sequences). The usual purpose of such comparisons is to determine the evolutionary genetic history of two sequences, which in the case of DNA you can think of as strings over the alphabet {A,G,C,T} (the nucleobases). Differences between sequences can arise though substitutions (A → G, G → A, C → T, or T → C), insertions, or deletions. In the last two cases, the resulting string differs in length from the original, and dealing with these size differences is the chief problem that alignment algorithms face. The Needleman-Wunsch algorithm is a very straightforward global sequence alignment algorithm, first proposed in 1970. It's a good example of the applicability of dynamic programming towards biological problems. Following is a Maple implementation based on this Ruby implementation. The algorithm depends on a similarity matrix which measures the "mutational distance" between two nucleobases. It takes two input strings, and returns two strings with dashes ("-") inserted to indicate insertion or deletion events between the sequences.

Free Examples in MM Free Library on mechofmat.com.

Free Examples in MM Free Library on mechofmat.com.

The Cartesian product of a sequence of m lists L1, ..., Ln, with list i having ni elements, is given by the sequence of Πi ni lists [L11,...,Lm1], ..., [L1n1,...,Lmnm], where Ljk is the k-th element of the j-th list.

The audience for this video of a blind date between exp(1) and Pi is not huge, but to the right one it is quite funny!

> f:=x->x*sqrt(1-cos(Pi/x));

> limit(f(x),x=infinity);

> L:=n->limit(f(x^n),x=infinity);

I did that for matrix inversion:

Here is some stuff for doing that by calling Maple from Excel. The reason is that one could care for extreme cases, where a really good precision is needed. I included an example how to switch to rationals, where the inversion can even be done exactly (do not use it for dimensions to high and then it would be better to do it solely in Maple + cut&paste).

To use it one must have Maple installed (I think at least version 8...

Maplesoft has just created a new promotion Tell Us Your Story. If you submit a story about how Maple and other products have helped you out, you can win an iPod. Free iPods will be given to three randomly selected people who submit their story here. http://www.maplesoft.com/community/user_experience/ Here is the text from the page: Has any Maplesoft product helped you? Tell us about it! You could win an iPod! Maplesoft is always looking for great ideas and techniques from our user base. If Maple or any of our other products has helped you work more efficiently, creatively, or just simply better with your mathematics, we want to hear from you.

 

Update: The contest has ended. Thank you for your submissions.

First time to this blog but I need help. I don't use Maple myself but I have many users that do and they are reporting to me that when using Maple 10 (with or without patch), if they go on to another application and then maximize the Maple again, it will cause the computer to re-boot. Has anyone out there run into this problem before? My users are using a 3.2 Ghz processor running WinXP SP2 with 1GB RAM and an 80 GB hard drive. They all say they have noticed this problem only with Maple! Help! Many thanks.

With this Generation of MapleStudio you can also plot complex functions in 2D and also 3D. For doing this, MapleStudio uses the conformal and the conformal3d comands of Maple 10. The following example will show you, how it works.

How to you take sin of a matrix?
MaplePrimes own Jim Herod has a wonderful set of lecture notes—accompanied by a collection of Maple worksheets—which introduce linear operators on infinite-dimensional Hilbert spaces to beginning graduate students in science and engineering. Entitled Linear Algebra, Infinite Dimensions, and Maple, these notes were developed from a one quarter course which Prof. Herod taught many times at the Georgia Institute of Technology. The notes are very concise and have been refined and improved many times over the years in response to student feedback.
FYI, there are MathML character entity errors in Maple 10. This causes problems when copying MathML output from Maple into other programs that expect valid MathML. I only checked the Greek character entities, as that's where I was running into bugs. The incorrect entities as output by the Maple MathML[ExportPresentation] command and the corresponding correct MathML entities from http://www.w3.org/TR/REC-MathML/chap6/byalpha.html are (lower and upper case Greek characters only):
dcasimir asks for an efficient way to create a list of the first n primes, without invoking nextprime, etc. An easy way to do this is to use a do loop to build up a sequence term by term. However, as Alec points out, this is not an efficient technique in Maple. It runs as O(n^2), where n is the number of items in the sequence. A way to avoid the inefficiency is to forego building a sequence and instead insert the items into a table. Then, after exiting the loop, convert the table to a list.
Dr. Sarah J. Greenwald, Appalachian State University, and Dr. Andrew Nestler, Santa Monica College have put together a site about mathematics and The Simpsons,including an exhaustive list of all math references on the show, relevant images, and the math background of the writers. They use this material to introduce concepts, motivate students and reduce math anxiety, apparently. Aside from its potential educational value, it's fun. See Simpson's Math. eithne
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