The BIG SIGMAA News

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The BIG SIGMAA NewsVolume 9, Number 1April 2013Business, Industry, and Government Special Interest Group of the MathematicalAssociation of AmericaUsing Mathematical Models to Predict a Biological ResponseEditor’s note:This is my first issue aseditor of the BIG SIGMAA newsletter. In January I took over the dutiesof Vice Chair for Servicesof the BIG SIGMAA fromGreg Cosxon, who is nowVice Chair for Membership.Thanks to Greg for contributed an interestingarticle for this issue.Thanks also to CollinCarbno for continuing toprovide interesting artwork. If you would like tocontribute an article, apoem, an puzzle, a limerick, or anything else tofuture issues of the newsletter, please let me know.Jim FifeVice Chair for ServicesBIG SIGMAAjfife@ets.org.Inside this issue:Poetry: Arithmetic2Art: Energizer Field2adapted, with permission, fromthe University of MassachusettsLowell Mathematics DepartmentnewsletterBoehringer Ingelheim, a pharmaceutical company based in Ingelheim, Germany, had a problem:In medical research it is veryimportant to know the biologicalresponses to the compounds indrugs, but it is very expensive todetermine this in trials because ofthe enormous number of possiblecombinations which must betested. They needed a reliablemethod to determine the response to these compounds basedsolely on knowledge of theirmolecular properties (like size,shape, or elemental constitution).They had an extensive databaseof existing compounds and responses and wanted to use it totry to predict the response to newcompounds.Filling the Blank – My Time Helping SAT Preppersby Greg CoxsonSestinas3Poetry: Sestina of theTramp-Royal3San Diego Meetings4Limerick4Puzzle Corner:Chocolate Pudding5So they approached Kaggle, a San Franciscobasedcompany thatspecializes inpredictive modeling competitions. Companies, governmen ts,an dresearcherspresentdata Jeremy Achin and Tom Degodoysets and problems and scientists then compete data scientists. Competitors wereto produce the best solutions. At given 1,776 different variables,the end of a competition, the host each representing a molecularpays prize money in exchange descriptor pertaining to a characfor the intellectual property be- teristic of the molecule, and experimental data relating to actualhind the winning models.biological responses. The aimThus was born the “Predicting a was to predict which compoundsBiological Response” competi- hold the greatest promise sotion which, by the end of its three experimental efforts could be-month run (March 16 to June focused on them, while avoiding15, 2012), had attracted close to having to test others, only to9,000 entries from more than 800(Continued on page 4)Several months ago, like toomany engineers of my age, Ifound myself with a layoff noticeand two weeks to start running .Having a family and a mortgage,I knew I needed a source of income while I looked for full-timework. One of my first stops wasthe local SAT prep office.The timing was not the best, toput it mildly. The defense electronics industry, where I hadworked for a number of years,was bracing for unprecedentedrounds of cuts. When a colleaguesuggested I try tutoring, I was notexcited about the idea. It did nottake me long, however, to see thewisdom of his advice. If nothingelse, I thought it might keep mebusy and help keep my mind offof my situation.There are a number of optionsfor working as a tutor, and workat an SAT prep company is likelynot the easiest. Another option isto sign up with a tutoring company and hang out an onlineshingle for professional one-onone tutoring. It is possible tomake quite a lot of money goingthis route; a colleague told me hewas making nearly 1000 on agood Sunday tutoring timepressed cadets at a military academy. While the money tends notto be as good at an SAT prepcenter, the hours are more reliable and all the materials youneed (textbooks, folders of SAT(Continued on page 4)

Page 2The BIG SIGMAA NewsArithmeticby Carl SandburgArithmetic is where numbers fly like pigeons in and out of your head.Arithmetic tells you how many you lose or win if you know how many you had before you lost or won.Arithmetic is seven eleven all good children go to heaven – or five six bundle of sticks.Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.Arithmetic is where the answer is right and everything is nice and you can look out of the window and see the blue sky – or the answeris wrong and you have to start all over and try again and see how it comes out this time.If you take a number and double it and double it again and then double it a few more times, the number gets bigger and bigger and goeshigher and higher and only arithmetic can tell you what the number is when you decide to quit doubling.Arithmetic is where you have to multiply – and you carry the multiplication table in your head and hope you won't lose it.If you have two animal crackers, one good and one bad, and you eat one and a striped zebra with streaks all over him eats the other,how many animal crackers will you have if somebody offers you five six seven and you say No no no and you say Nay naynay and you say Nix nix nix?If you ask your mother for one fried egg for breakfast and she gives you two fried eggs and you eat both of them, who is better in arithmetic, you or your mother?Energizer Field by Collin Carbno

Volume 9, Number 1Page 3SestinasAt the 2009 Joint Meetings, the lasttime the meetings were in Washington, Michael Saclolo of St. EdwardsUniversity gave a talk in the ArtsSIGMAA session about the mathematics behind a form of poetrycalled a sestina. A sestina is a poemconsisting of six 6-line stanzas,followed by one 3-line stanza. Thereis no rhyme scheme; instead theending words of the lines in eachstanza are a particular permutationof the ending words of the lines in the previous stanza; this permutation can be obtained from the spiral figure shown on theright. If the numbers 123456 represent the ending words of thefirst stanza, then the order in which these words appear in thesecond stanza can be read from the spiral by starting at the bottom, with 6, and following the spiral; the order is 615243. Theword at the end of line 6 in the first stanza becomes the word atthe end of the first line of the second stanza, the word at the endof line 1 in the first stanza becomes the word at the end of thesecond line in the second stanza, and so on. This permutation canbe represented schematically as6 11 25 32 44 53 6This is the cycle (1 2 4 5 3 6). The permutation must be a six-cycle so that each endingword is in a different line in each stanza. Theform was developed by the French troubadourArnout Daniel de Riberac in the twelfth century.If the number of lines in each stanza equalssome number n 6, the permutation need not be an n-cycle. Forexample, if n 4 we see from the spiral figure on the right thatthe order is 4132, which is the permutation (1 2 4) (3). The wordending the third line in never permuted; it ends the third line ofeach stanza.There is a necessary condition that the permutation be an n-cycle:If the permutation is an n-cycle, then 2n 1 is prime. The condition is not sufficient, however. For example, if n 8, the permutation is the product of two 4-cycles: (1 2 4 8)(3 6 5 7), and hencethe pattern of ending words would repeat after four lines.More details can be found in Dr. Saclolo’s paper “How a Medieval Troubadour Became a Mathematical Figure”, Notices of theAMS 58 (5): 682-7.Here is a famous sestina by Rudyard Kipling, in which he delivers the twelfth-century French form in a Cockney accent.Sestina of the Tramp-RoyalSPEAKIN’ in general, I ’ave tried ’em all—The ’appy roads that take you o’er the world.Speakin’ in general, I ’ave found them goodFor such as cannot use one bed too long,But must get ’ence, the same as I ’ave done,An’ go observin’ matters till they die.What do it matter where or ’ow we die,So long as we’ve our ’ealth to watch it all —The different ways that different things are done,An’ men an’ women lovin’ in this world —Takin’ our chances as they come along,An’ when they ain’t, pretendin’ they are good?In cash or credit—no, it aren’t no good;You ’ave to ’ave the ’abit or you’d die,Unless you lived your life but one day long,Nor didn’t prophesy nor fret at all,But drew your tucker some’ow from the world,An’ never bothered what you might ha’ done.But, Gawd, what things are they I ’aven’t done?I’ve turned my ’and to most, an’ turned it good,In various situations round the world—For ‘im that doth not work must surely die;But that’s no reason man should labour all‘Is life on one same shift—life’s none so long.Therefore, from job to job I’ve moved along.Pay couldn’t ’old me when my time was done,For something in my ’ead upset me all,Till I ’ad dropped whatever ’twas for good,An’, out at sea, be’eld the dock-lights die,An’ met my mate—the wind that tramps the world!It’s like a book, I think, this bloomin’ world,Which you can read and care for just so long,But presently you feel that you will dieUnless you get the page you’re readin’ done,An’ turn another—likely not so good;But what you’re after is to turn ’em all.Gawd bless this world! Whatever she ’ath done—Excep’ when awful long—I’ve found it good.So write, before I die, “’E liked it all!”

Volume 1, Issue 1Page 4Filling the Blank – My Time Helping SAT Preppers(Continued from page 1)and other tests, with answer keys) areclose at hand.At the place I chose, it is necessary to takeSAT tests to show some mastery of thematerial. That was actually kind of fun,and I came home joking “I’ve still gotit” (my kids told their friends I did theSAT “without a calculator!”). In addition,there are mandatory online trainingcourses on how to tutor. Having workedas a teaching assistant in Mathematics forseveral years, I found this a bit of an annoyance at first. I quickly cast off thatfeeling; the training was serious andtaught me new skills.I worked two or three days a week, in twoor three consecutive two-hour sessions. Ineach session, I would have from one tothree students. Because I was more specialized than other tutors, I tended to getmostly Mathematics assignments, everything from Trigonometry to Calculus.; Ieven helped one cute earnest secondgrader through exercises like “measureyour textbook”. Each session tended toinvolve both weak and strong students. Iwas trained to spend more time with theweaker students, allowing the strongerstudents more independence to work onexercises that I would return to check atintervals. Ultimately, I also got assignments to work with a competition-Mathstudent; those sessions tended to be oneon-one work since the problems requiredmore focus.I came to respect my peers on the tutoringstaff. Most of the tutors are young, eitherabout to start graduate school or in somestage of PhD programs. Some are parentswho needed the extra income. Some areretired teachers. One had left a PhD program in Chemistry to do day trading,before losing millions in the stock marketcrash. What impressed me the most werethe tutors who could work in several topics, and provide timely help using an arrayof tutoring skills. It takes a special personto be able to take on AP Calculus, HonorsSpanish, American Government, andChemistry, all in one evening. At times itseemed I had found a hidden world ofRenaissance scholars.I learned a lot from my students as well.The environment is more competitive thanwhen I was in high school. Many of thesestudents have a keen idea of what collegethey can hope to gain entry to, as early assophomore year. I got to know theirdreams and plans. One student wants todesign high-performance cars for the general market, another wants to be an international lawyer focused on children’sissues, another is working on adding 2mph to his fastball. The experienceopened my eyes to the level of competition my kids face. It also gave me an inside look at the relative strengths of almost every private or public high schoolwithin about 20 miles of the center.Eventually my tutoring tailed off. I startedteaching a Calculus I course at a localcommunity college. After six months, Ibegan full-time employment in my field.Still, I value the time I spent in the worldof SAT prep.Joint Mathematics Meetings—San Diego MeetingThe 2013 version of the Joint Mathematics Meetings met in San Diego in January.Over 6,600 people attended the conference, enjoying mathematics lectures, exhibits, and artwork. It was also an opportunity to see old friends and make newones. Usually, when the Joint Meetingsare in San Diego, it’s also an opportunityfor those of us who live in the colder partsof the country to experience some warmthand sunshine in January. But this year theweatherperson seems not to have receivedthe memo, as the weather was cool andquite windy.LimerickPredicting a Biological ResponseA mathematician I knowCan count to a million or so.But should he regress,He'll then coalesceAnd back to the mean he will go.(Continued from page 1)But the conference was amazing, nonetheless, with many fine sessions. In particular, the BIG SIGMAA sponsored a wellattended talk by Mario Livio, the authorof the book Is God a Mathematician? Dr.Livio’s talk, along with the shorter talks inthe BIG SIGMAA paper session, are de-have them ultimately prove ineffective.In one of the first times “gamification” hasprovided such a practical contribution todrug development, and despite the factthat the competitors had no particularknowledge of the pharmaceutical industry,scribed in Carla Martin’s article in theFebruary/March issue of FOCUS; you candownload the issue from the MAA’s website .Next year’s Joint Meetings in Baltimore isshaping up to be just as interesting. Watchthe MAA website and the BIG SIGMAAwebsite (sigmaa.maa.org/big) for detailsas they become available. We hope to seeall of you in Baltimore.results of the competition revealed thebest models to be more than 25% moreeffective than those currently in use. Thewinning model was submitted by a teamof three data scientists, Jeremy Achin andTom Dogedoy (both alumni of the University of Massachusetts Lowell) andSergey Yurgenson, a Research Associatein Neurobiology at Harvard MedicalSchool. The winning team won a 10,000prize.

Business, Industry, and Government Special Interest Groupof the Mathematical Association of AmericaPhil Gustafson, ChairGregory Coxson, Vice Chair for MembershipCarla D. Martin, Vice Chair for ProgramsJames H. Fife, Vice Chair for ServicesThomas Hoft, Secretary/Treasurersigmaa.maa.org/bigfrom the MAA Website:BIG SIGMAA serves as a unifying link between business, industry and governmentmathematicians, academic mathematicians, and mathematics students. TheSIGMAA provides resources and a forumfor MAA members who share an interestin mathematics used in business, industryand government, aids in professional development, helps build partnerships between industry and academics, and increases awareness of opportunities formathematicians in business, industry andgovernment.Puzzle Corner: Chocolate PuddingThis is an old puzzle, but it’s still interesting. I was reminded of it when a colleaguesent it to me a couple of years ago.A mathematician was attending a party atthe host’s house and had a conversationwith the host:Mathematician: How many children doyou have?Host: I have three daughters.Mathematician: What are their ages?Host: The product of their ages equals 72.Mathematician: That’s not enough information for me to determine their ages.Host: The sum of their ages equals myhouse number.Mathematician: I still don’t have enoughinformation to determine their ages.Host: My oldest daughter likes chocolatepudding.Mathematician: Ah, in that case, the agesof your daughters are .What are the ages of the host’s daughters?(Assume the ages of the daughters arewhole numbers.)Of course, knowing only that the productof the ages is 72 and the sum is the unknown house number is not sufficient todetermine the ages. But, although wedon’t know the host’s house number, themathematician presumably does (after all,he’s at the host’s house) and the mathematician cannot determine the ages, either.Therefore there must be at least two setsof three integers whose product is 72 andwhose sum is the host’s house number.By looking at all possible sets of threeintegers whose product is 72, it is easy tosee that 14 is the only integer that can beexpressed in two ways as the sum of threeintegers whose product is 72 (14 6 6 2 and 14 8 3 3). Thus the ages of thehost’s daughters are either 6, 6, and 2 or 8,3, and 3.This is where the clue about chocolatepudding comes in. The significance of thatclue is that the host has an oldest daughter; in other words, the oldest two daughters are not twins. Therefore the ages ofthe daughters are 8, 3, and 3.

Sestina of the Tramp-Royal At the 2009 Joint Meetings, the last time the meetings were in Washing-ton, Michael Saclolo of St. Edwards University gave a talk in the Arts SIGMAA session about the mathe-matics behind a form of poetry called a sestina. A sestina is a poem consisting of six 6-line stanzas, followed by one 3-line stanza.

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