UNDERGRADUATE MATH SEMINAR

Before Ebola There Was AIDS: Evaluating the Connection between Gender Based Violence and HIV/AIDS

Professor Roger Hoerl

ABSTRACT: While the media has been focusing primarily on the recent outbreak of the Ebola virus, HIV/AIDS continues to infect and kill millions of people around the globe. Fortunately, organizations such as the World Health Organization, the Gates Foundation, and several others, are providing billions of dollars in funding to combat the spread of HIV, and save the lives of those infected. In order to effectively deploy these funds for greatest impact, many agencies utilize mathematical models that predict progression of the pandemic. One of these models is the Modes of Transmission Model (MoT), developed for UNAIDS, the global HIV/AIDS consortium led by the United Nations. Recent Math graduate Keilah Creedon focused her senior thesis on studying this model, and in particular, addressing one of its limitations; inability to account for the impact of gender based violence. Significant research has been published that demonstrates the negative impact of violence against women in spreading HIV. Keilah modified the MoT model to account for such violence, and to determine the relative impact of violence against women versus other factors contributing to the spread of the disease. Further, she conducted a sensitivity analysis to quantify the uncertainty of the model outputs to uncertainty in model inputs. When Keilah presented her thesis at the 2014 Steinmetz Symposium, she did not yet have results. I will therefore review her original research design, and then share the results we obtained from her modified model.

DATE: MONDAY, November 3 Time & 4:45pm – Refreshments in Bailey 204 Location: 5:00pm – Seminar in Bailey 207 In this week’s seminar, Professor Roger Hoerl from the Department of Mathematics at Union College will present the following talk:

Draw a square. Divide it into a 3x3 tic-tac-toe grid of 9 smaller squares. After taking a minute to play a game of tic-tac-toe on it (which will probably end in a draw; can you show why?), cut out the middle square. Divide each of the 8 remaining outer squares into a smaller 3x3 grid and cut the middle square out of each grid. If you keep on doing this indefinitely, you'll end up with a self-similar lacework of smaller and smaller square-holed grids, a fractal figure known as "Sierpinski's carpet". Now think about doing the same thing in 3D: that is, imagine a cube divided into 3x3x3=27 smaller cubes, and extract the central cube from each face and also the one buried in the interior. You'll get a "peekaboo cube" with a hole going through its middle on every side. If you do the same thing to each of the 20 remaining smaller cubes and continue the process indefinitely, you'll have a 3D

Union and the MegaMenger Distributed Fractal Build 2014 By Professor Kim Plofker and Susan Beckhardt ‘08

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Department of Mathematics October 31, 2014

fractal called a "Menger sponge" (with zero volume but infinite surface area!). Named after the geometer/graph theorist Karl Menger who described it in 1926 ("General spaces and Cartesian spaces", in Edgar, Gerald A., ed., Classics on Fractals, 2004, 103-117), the Menger sponge didn't get much attention from fractal enthusiasts until somebody cut it open. In 2007, the economist-statistician and recreational geometer Sebastien Perez-Duarte published a remarkable illustration of the cross-section of a Menger sponge sliced by a plane perpendicular to a diagonal through its center. (Can you imagine what such a cross-section would look like? Give it some thought and then check your mental image against the description at http://www.simonsfoundation.org/multimedia/mathematical-impressions-the-surprising-menger-sponge-slice/.) Engineer and mathematical sculptor George W. Hart of SUNY Stony Brook later made a physical model of a Menger sponge on a 3D printer. Hart is also one of the founders of the Museum of Mathematics (MoMath.org) in New York City, so it's not surprising that when it was proposed (by "Stand-Up Mathematician" Matt Parker and Professor Laura Taalman of James Madison University) to build an immense Menger sponge as the world's largest fractal, MoMath joined in. The MegaMenger.com project has coordinated with MoMath and 19 other organizations worldwide to build 20 Menger sponges of the so-called "Level 3" order, i.e., with three layers of self-similarity. (Alas, given that the 20 Level 3 builds are scattered from New York to Auckland to Edinburgh, it will not be possible to bring the resulting fractals together to form a physical Level 4 Menger sponge with a side length of over 13 feet!) MoMath needed volunteers to help supply the 20 Level 2 fractals that would be used to construct its Level 3, and Professor Mary O'Keeffe of Union's Department of Economics thought this would be a great activity for her middle- and high-school students in the Science Technology Entry Program (STEP). The cubes that make up a Level 1 fractal are formed out of ordinary business cards or similarly-sized cardboard rectangles, according to a construction procedure devised by the mathematical origami artist and engineer Dr. Jeannine Mosely (http://theiff.org/oexhibits/menger02.html). Each card is folded into a central square with a rectangular flap at each side. Six cards are hooked together, flap over face, to make a plain cube (or Level 0 fractal), and 20 cubes are connected to make a Level 1 fractal. (No cheating with glue or tape! You can connect cubes by just fitting the flaps together, although it takes some patience and dexterity: see MegaMenger.com for instructions.) Then 20 of the Level 1 components combine in the same way to make the Level 2 fractal. A little arithmetic reveals that Union's Level 2 fractal required folding and assembling 2400 cards, not counting the decorative black-and-white "panel" cards that were affixed to the exposed faces of the cubes! In the week of the build, culminating with its completion in Schaffer Library on the evening of Friday October 24, volunteer fractal-builders included not just the STEP students but various Union undergraduates, faculty, staff, and alumni, as well as members of the Albany Area Math Circle and students and faculty from UAlbany, SCCC, and RPI. Several of the builders accompanied Union's finished Level 2 down to MoMath on Saturday October 25, where it was quickly approved as one of the best-constructed contributions and the volunteers were designated expert assistants on the Level 3 build. A weekend's hard work didn't quite suffice to finish the Level 3 fractal, so if you can make it to NYC this weekend (Oct 31-Nov 1), you still have a chance to participate in the build! Professor O'Keeffe (okeeffem@union.edu) writes: "Anyone who is interested in helping out in Manhattan this weekend should contact me. Great family fun. You can get free museum admission if you commit to a three-hour stint of helping out with construction either Friday afternoon 2 to 5 or any three-hour window Saturday from 10 to 5. Preteens on up can usefully contribute to this project if they enjoy things like origami."

Once the Level 3 Menger sponge is completed and displayed at MoMath, it will eventually need a "forever home". If you know of any museum or educational institution that would like to add the MoMath Menger

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sponge to their permanent collection, please contact MoMath and/or Professor O'Keeffe to let them know. In the meantime, if you're heading to NYC in the near future, don't miss a visit to MoMath and their Union-assisted MegaMenger!

Tired but happy fractal-builders with the completed Union Level 2 in Schaffer Library on Friday 10/24/14

Union STEP students and others with Union's contribution (top left) and additional Level 2 fractals at the MoMath build on Saturday 10/25/14

The 4.5-foot-high Level 3 build in progress, on display at MoMath

Last week’s problem: Congratulations to Joshua Chin ’18, Miaoqing (Andie) Jia ’17 and alumnus Brandon Bartell for solving last week’s problem. Brandon’s solution has been posted on the bulletin boards around Bailey Hall This week’s problem: Suppose a Level 3 Menger sponge is constructed by assembling groups of 20 1-inch cubes (Level 0) into Level 1 Menger sponges, then assembling groups of 20 Level 1 sponges into Level 2 sponges, and finally assembling 20 Level 2 sponges into a single Level 3 sponge. What is the surface area of the resulting object? Submit solutions to Professor Paul Friedman (friedmap@union.edu, Bailey 107D) by noon on Thursday, November 6.

Problem of the Newsletter: October 31, 2014

Said a mathematician named Menger 'What doesn't destroy makes you strenger Anyone who concocts This big fractal box Will become a real master at Jenga!'

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