Math 410(510) Student Project

The purpose of group project is to learn some bio/math modeling material outside of class, become familiar with the literature and journals of mathematical biology, apply some mathematical techniques learned from the class to some real world problems, and learn to write short science paper. The final product is a short paper to be submitted in December 7th (the last day of the class.) Your report should be typed (see Writing Tools below.) Your report should record all your works, including possible graphic illustrations.  You should submit a title and a (less than) 200 word abstract by email to the instructor by November 3rd. The abstract should be in plain text or MS Word format, and it includes the author's names (all group members), email address and a short introduction not more than 200 words. You should include main references and source of your paper in the abtract. A rough draft of the paper could be turned in one week before the final deadline (so, around Dec. 1st), I will make suggestions for improvement. In the week of Dec. 3-Dec. 7, one or more members from each group will give a 30-40 minute presentation of your research work. In the presentation, you can use overhead projector, computer projector, chalk board or combination of these.

Each research group consists of 3-5 people, the group can elect a coordinator who is responsible to organize the whole research activity, one (or more) speaker(s) who will give a 30-40 minute presentation in the last week of the class, and maybe a designated writer who will put information together into a paper. But everyone needs to be involved in understanding and working on the problem. Each group needs to choose a topic from the list below, and one topic can only be chosen by one group. Each group submit one paper which is at least 8 pages and at most 20 pages in normal font size and page size (including all graphs).

You shall research and give a report on work that has been previously (but recently, after 1995) published in refereed research journals (a list of journals, and some possible articles are listed below.) The work on which you elaborate and report must contain mathematical modeling of a life science problem. In the first part of the paper, you should explain the background of the model, show that you completely understand the modeling they did. (A bad sentence in your paper would: "please see reference [JP] for the derivation of this differential equation".) In the second part of the paper, you should try to reproduce their mathematical analysis (sometimes may fill in some omitted details), reproduce their graphs (using dfield, pplane, Matlab or Maple), and explain the results in the context of the model. You report could include a short survey of the research in that direction, but must include the modeling, mathematical analysis of a more specific model. The model needs to be a single differential equation or a system of differential equations. You can also discuss the open problems which you find in your research but do not know how to solve, which may become future research topics.

When using other people's work, you must quote the original paper with title, names of all authors, name, volume number and issue number of journal, date of publication. If quoted work is on a webpage, you must provide the full name of the link to the referred webpage. You should list and index your references at the end of the paper, and quote them in a name like [1], [2], or [S], [K]. In any case, people who plagiarizes other's work will receive an automatic zero point for the project. Graphs related to differential equations discussed in the paper can be properly used in the paper, and they should be clearly labeled, indexed and quoted in the paper.

The grading criteria will be almost completely subjective since the projects are open-ended. The grades I assign on the project will be based on the depth, clarity and precision of (mathematical) thought, correctness of mathematical calculation involved, writing style, organization of the paper, involvement in the group research and effort put into giving the oral presentation. Each member of the group will receive same grade for the work subject to the involvement in the group, which will be determined by answering a question in final exam, instructor's perception, and designated roles in the project (you could list in your report: coordinator: p1, writer: p2, speaker: p3, etc.)

Topics and Suggested Material: (you can not use the articles listed here as your primary source of your paper, you need to search one by yourself)

Population Biology, Ecology  Textbook, many books, journals. You should consider a concrete example instead of generic models like predator-prey or logistic.
Examples of article:
(1) Andrew Dobson, Mary Meagher. The population dynamics of brucellosis in the Yellowstone National Park. Ecology 77: 1026-1036, (1999).
(2)  M. Gyllenberg, J. Hemminki, T. Tammaru. Allee Effects Can Both Conserve and Create Spatial Heterogeneity in Population Densities. Theoretical Population Biology 56: 231-242, (1999).
 
Epedemiology   Textbook, book by Brauer and Castillo-Chavez, book by Mazumdar
Examples of article:
(1) Ivana Beardmore, K.A. Jane White. Spreading Disease through Social Groupings in Competition. Journal of Theoretical Biology 212: 253-269, (2001).
(2) L. H. A. Monteiro, C. H. O. Goncalves,  J. R. C. Piqueira. A condition for Successful Escape of a Mutant after Primary HIV Infection. Journal of Theoretical Biology 203: 399-406, (2000).

Neurobiology   Textbook (Fitzhugh-Nagumo model)
Examples of article:
(1)  Charles B. Nemeroff. The Neurobiology of Depression.  Scientific American 1998-6.
http://www.sciam.com/1998/0698issue/0698nemeroff.html

Biochemistry and Mathematical Physiology  Textbook (chemotaxis model), book by Mazumdar, book by Keener and Sneyd
Examples of article:
(1) S. R. -J. Jang,  J. Baglama. Qualitative behavior of a variable-yield simple food chain with an inhibiting nutrient. Mathematical Biosciences 164: 65-80, (2000).
 
Fishery management    book by Brauer and Castillo-Chavez
Examples of article:
(1)

Mathematical Pharamacology
Examples of article:
(1) Doris A. Behrens, Jonathan P. Caulkins, Gernot Tragler, Josef L. Haunschmied and Gustav Feichtinger. A dynamic model of drug initiation: implications for treatment and drug control,  Mathematical Biosciences 159: 1-20, (1999).
 
 

Journals and Books of mathematical Biology:

All journals and books listed here are available from W&M library, instructor or campus computer network. If you need additional material, please use inter-library loan (you should do that early since it takes a few weeks to get the material you request.)

Journals

Books


A Suggested Agenda:

Oct. 18-21:        Initial meeting of the group----choose topic, assign reading jobs.
Oct. 22-28:        Search and browse literature, journals and web for related articles, books.
Oct. 29-Nov. 4:  Second group meeting----discuss the topic, write abstract, submit abstract.
Nov. 5-11:         Reading literature, modeling, computer experiment, discussion
Nov. 12-18:       Reading literature, modeling, computer experiment, discussion
Nov. 19-25:       Thanksgiving...
Nov. 26-Dec. 2: Writing the paper, submit the first draft by email
Dec. 3-Dec. 7:   Presentation in class, submit the final draft by email

Writing Tools: The best typesetting software for writing scientific paper is LaTeX originally designed by renown computer theorist Don Knuth. Today most scientific journals use LaTeX (or TeX or their variants) as typesetting software. (All my test, quizzes, and lecture slides are prepared in LaTeX.) So using LaTeX will have the best display and printing results. But LaTeX is a kind of program language with its own syntax, and it takes time to learn the syntax. So I only suggest the students with more free time, more desire to learn a good typesetting, (especially mathematics, physics, chemistry or computer sciences majors) to learn LaTeX. A short guideline is given below. For those who do not have time to learn a new language, you can use Microsoft Word (or maybe Powerpoint) to write your report. Notice that mathematical notations can be entered in MS Word via MS Equation. The way to open MS Equation in MS Word 2000 is click "Insert"->"Object", then choose "MS Equation 3.0".
Using either LaTeX or MS Word, your final product should be a Adobe Acrobat pdf file (name as ******.pdf, where ****** is your last name.) Both LaTeX and MS Word files can be converted to pdf files easily.

Matlab, Maple or Dfield Graphs: There is a good chance that you would like to include some computer generated graphs in your paper. One way is to print the graph and cut and paste by hand into your paper. A better way is to include graphic files in your LaTeX or MS Word file. First you need to export your graphic files from Matlab or Maple. In Matlab, click "File"->"Export" in the window of graph, then save it as "***.eps" if you are using LaTeX or "***.jpg" if you are using MS Word. In a LaTex file, you can imbed an eps file by command

\usepackage{graphicx}  %%in the heading

\begin{center} %%in the body of paper
\includegraphics*[scale=0.4]{logistic.eps}
\end{center}

scale is the relative size of the graph, and the default is 1 (original size). In MS Word, you can insert a picture by clicking "insert"->"pic"->"from file", then choose your *.jpg file which has been put in the same directory.

Using LaTeX: (A) How to get the software? If you are math or physics major, you may have an account in Unix server in these department (domain: *.math.wm.edu or *.physics.wm.edu). All these Unix systems have LaTeX system installed. Most Linux systems also include TeX systems. If you are a PC user, then there are not so many PCs in the on-campus labs currently running a good TeX system. (As I checked in one lab, it did have a TeX system, but seems corrupted.) But if you have a PC in your dorm or home, it's not very hard to install a perfect TeX system in your PC in about 10 minutes (if you have downloaded all required elements.) All necessary softwares are free except a popular editor WinEdt which is a shareware and you can use for 30 days free, and all software are available online. Here is a list of softwares which you need to download if you want to install TeX system on a PC:
1. MikTeX (download or install MikTeX 2.1, size: about 40M, free software)
2. WinEdt (download WinEdt 5, size 3.6M, you can use the evaluation copy for 30 days)
3. GSView and Ghostscript (Download GSView 4.0 and AFPL Ghostscript 7.00 for Win32, size: about 8M, free software)
4. Adobe Acrobat Reader(Download AAR 5.0, size: about 6M, free software)
Once, you have all the softwares downloaded or get a CD-ROM containing all softwares, you should install the softwares in this order: 1)  Ghostscript 7.00 for Win32, 2) GSView 4.0, 3) Adobe Acrobat Reader, 4) MikTeX, 5) WinEdt. The key is that you have to install WinEdt last. Then start WinEdt, you will start your LaTex adventure. An alternative of downloading all these softwares is to check out a CD-ROM from Prof. Shi which contains all these softwares.
(B) How to use LaTeX? There are plenty LaTeX tutorial on the web, and you can find some good ones at . Once you have typed a LaTeX file in WinEdt window, this is the way of compiling it into a postscript file or pdf file: (suppose your LaTeX file is mypaper.tex)
1. Click "LaTeX" button, it will produce mypaper.dvi (which you can click the 2nd "dvi" button to preview.)
2. Click "dvi->ps", it will produce mypaper.ps (which you can click the button on the right side of 2nd "dvi" to start GSView 4.0 to view it, and you can print it from GSView.)
3. In GSView, click "File"->"Covert" to convert mypaper.ps to mypaper.pdf.
(In Step 2 and 3, you can also use the options "dvi->pdf", or "pdflatex" to directly generate pdf file, but it seems that these procedures will miss the postscript graphs in your paper.)