Making A Big Production Out of Optimizing Fluid Flows, by Ben Pittman-Polletta
What do raspberries, polyester, and blood pressure drugs have in common? All make for great performance art, sure, but I'll bet you didn't know that all three have also benefitted from the attention of applied mathematician Eleanor "Lea" Jenkins of Clemson University. Jenkins and her collaborators employ a multi-faceted approach involving fluid dynamics, simulation, and optimization to tackle problems in agriculture and industry having to do with fluid flow through porous media--bringing them right to the border of engineering and mathematics.
One of Jenkins' projects involves the mathematics of purifying biopharmaceuticals, or biologics ("The Chemistry of Math"). These complex molecules--including blood pressure medications, hormones such as insulin, vaccines, antibodies, antiviral agents, cancer drugs, and viral gene therapies--are "manufactured" inside living cells or tissues (Biopharmaceutical" Wikipedia). Complicated manufacturing processes have been one contributor to recent drug shortages. Jenkins and her collaborators hope to increase the yield of biopharmaceuticals-- and lower their prices--by optimizing the filtering process used to separate them from the cells in which they're manufactured. With longtime collaborator Kathleen Fowler and others, Jenkins has also worked on optimizing the lifetimes of filters used purify melted polymers woven into plastic fibers ("A simulation filter approach to polymer extrusion filter design," by Kathleen R. Fowler et al., Proceedings from American Filtration & Separation Society Annual Conference, 2008). In both problems, there are multiple competing objectives--for example, maximizing filter lifetime while still filtering out a sufficient quantity of debris (a filter with large enough pores, though ineffective, would last forever). Furthermore, the functions relating filter parameters to the optimized quantities (such as filter effectiveness and lifetime) are obtained from computational fluid simulations, so calculus-based methods such as gradient descent can't be applied. The way forward is to reformulate these multi-objective optimizations as single objective optimizations with boundary conditions, and then solve them with the implicit filtering algorithm (no pun intended)--a steepest descent algorithm for noisy optimization problems with bounded constraints (Implicit Filtering).
As for berries, Fowler, Jenkins, and others began working with the berry cooperative Driscoll's at a 2011 Workshop on Sustainability Problems at the American Institute of Mathematics. To help farmers maximize their production and profits in the face of reduced water use limits during the state's ongoing drought ("A Role for Modeling, Simulation, and Optimization in an Agricultural Water Crisis," by Kathleen Fowler and Eleanor Jenkins, SIAM News, December 1, 2014), an interdisciplinary team of mathematicians and engineers formulated the a number of choices available to farmers--such as which crops, crop rotation schemes, and irrigation and fertilization strategies to employ--as stochastic optimization problems coupled to a multi-scale farm and groundwater simulation. The mathematicians came to a number of conclusions, including the suggestion that farmers plant more raspberrries. Currently, they're deploying their simulations to help design aquifer recharge networks to replenish depleted water sources. To address issues of sustainability, they say, "A common theme is the critical need for interdisciplinary teams from science, engineering, and computational applied mathematics ... in partnerships with industry, policy-makers, and practitioners." It takes a village to raise a (sustainable) raspberry.
See "The Chemistry of Math: Making and modeling better membranes could help unclog pharmaceutical pipelines," by Anna Simon, Lab Manager, November 29, 2014.
--- Ben Pittman-Polletta (Posted 12/10/14)
On making mathematicians glamorous, by Lisa DeKeukelaere
(Photo on left: (L-R) Terence Tao, University of California, Los Angeles; Maxim Kontsevich, Institut des Hautes Etudes Scientifiques; Simon Donaldson, Stony Brook University and Imperial College London; Jacob Lurie, Harvard University; and Richard Taylor, Institute for Advanced Study. Photo by Steve Jennings/Getty Images for Breakthrough Prize. Photo on right: (L-R) Terence Tao, Jacob Lurie, Richard Taylor, Maxim Kontsevich and Simon Donaldson onstage during the Breakthrough Prize Awards. Photo by Steve Jennings/Getty Images for Breakthrough Prize.)
Math professor Michael Harris takes an acerbic look at attempts to elevate mathematicians to rock star status at the 2014 Breakthrough Awards, an event created by tech investor Yuri Milner to bestow Oscar-style treatment on scientific achievement. Harris describes the celebrity-studded event, musically accompanied by Christina Aguilera, broadcast on BBC world News (and in the U.S. on the Discovery Channel ad Science Channel), and for the first time honoring a bevy of mathematicians. Their work largely devoid of applications easily explainable to the public, however, the mathematical rock stars appeared to be sidelined as "spare stage props," according to Harris, with their segment of the show confined to a single video clip. Harris notes that the mathematicians themselves were reticent to reach for rock stardom, with Breakthrough Prize winner Terence Tao having attempted to decline the award. At the start, Harris questions how much Hollywood glamour would rub off on mathematics, and the answer is, not much. He notes that mass media attention focused more on famous presenters than award recipients, and the mathematicians "flew home rocking neither more nor less than when they arrived."
See "Dispatch From the Oscars of Science," by Michael Harris. Slate, 19 November 2014; See media coverage of the awards event "Scientists Mingle with the Stars at the 2015 Breakthrough Prize," by Lauren Goodman, Vanity Fair, 10 November 2014. Read about the Breakthrough Prize in Mathematics and the winners: Five Winners Receive Inaugural Breakthrough Prize In Mathematics, 23 June 2014; AMS news item, 23 June 2014; "Winners Announced For The World's Richest Science Award: The $3 Million Breakthrough Prize," F.D. Flam, Forbes, 9 November 2014.
Below is a video clip from the award ceremony.
--- Lisa DeKeukelaere
On a report about sexism in math-intensive fields, by Lisa DeKeukelaere
According to an op-ed published in The New York Times in late October, women in math-intensive academic fields have career experiences similar to their male counterparts, based on hiring and promotion data collected by the National Science Foundation. Critics warn, however, that the op-ed presents only a correlation, which is insufficient to determine the cause. One critic notes that similar promotion rates for men and women do not necessarily mean that bias is nonexistent, and could mean only that women are able to overcome that bias. Critics also take issue with the op-ed’s claim that the underrepresentation of women in math fields results from early educational and lifestyle choices, arguing that these “choices” are constrained by environmental factors. While one of the op-ed authors notes that he hopes the piece will encourage further female participation by countering negative stories, critics worry that the positive message ultimately will prove detrimental when women encounter an unexpectedly biased reality.
See "No sexism in science? Not so fast, critics say," by Rachel Bernstein. Science, 14 November 2014, page 798. (available online to subscribers)
--- Lisa DeKeukelaere
Free Your Eyes, by Ben Pittman-Polletta
It's the perfect cinematic setup: A lone scientist is working late at night in his lab, with a computer program which finds three-dimensional objects corresponding to two-dimensional polygonal line drawings. He stretches, ready to take a break; as a lark, he inputs a drawing of the Penrose staircase--the constantly descending steps discovered by Roger Penrose and his father Lionel, and made famous by M. C. Escher--and, chuckling to himself, leaves the lab to get a cup of coffee. Upon his return, his coffee cup crashes to the floor as he gapes at the computer. The program has finished its work, and the cursor blinks at the end of the phrase: OBJECT FOUND. This goosebump-inducing scenario isn't from a horror movie; it's from the real life magic show that is mathematician Kokichi Sugihara's career. As Sugihara discovered during his early research into computer vision, many drawings of seemingly impossible objects, such as the Penrose staircase and the Penrose triangle, really do depict views of three dimensional polygons, just not the ones your mind assumes they depict. Sugihara doubted his program's results until he began creating paper models of the objects it had found. Soon, he'd moved away from computer vision, and into what's been his main line of work for the last thirty years: creating three-dimensional visual illusions, such as the "supermagnet" illusion--in which balls of wood and glass roll up ramps to a platform as if attracted by a powerful magnet--which won World's Best Illusion in 2010:
As Erica Klarreich discusses in her delightful article for Nautilus, Sugihara's illusions not only win awards, they also illuminate some of the shortcuts the human visual system uses when interpreting two-dimensional images as three-dimensional objects. According to Sugihara, one of these is a tendency to perceive sets of perpendicular lines as meeting at right angles. Many of Sugihara's illusions depend on this bias--and when he instructs his software to pick three-dimensional structures with the maximal number of right angles, it usually arrives at the same interpretations of line drawings as human viewers. Another quirk of the visual system, says Stephen Macknik, a neuroscientist who runs the World's Best Illusion contest with his colleague Susana Martinez-Conde, is that it does much of its work locally. For example, each small piece of the Penrose staircase is coherent; it's only the global picture that seems nonsensical. This local processing happens mostly automatically, and as a result illusions like the three-dimensional Penrose staircase and "supermagnet" video persist even after the brain has learned the underlying trick. But if the human visual system is fallible in predictable (and exploitable) ways, it is certainly rapid and efficient--and yet unmatched by any vision software. Indeed, part of the visual system's success comes from the fact that it has evolved (or learned) to be right, as quickly as possible, most of the time. Intriguingly, as Klarreich reports, robots that learned by trial and error to distinguish different shades of gray in natural scenes were also susceptible to "White's illusion" (no pun intended), in which a single shade of gray seems darker or lighter depending on surrounding shades. So, while our robot descendants may be aware of the unusual structures giving rise to Sugihara's illusions, their artificially-evolved visual systems might be just as susceptible to these illusions as ours. That's just fine with Sugihara: “It’s my pleasure," he says, "to make other people [and sentient robots of the future] surprised." (Image: The gray rectangles under A are the same shade as the gray rectangles under B.)
Many more of Sugihara's static illusions are viewable on his webpage, as well as a video of several of his "impossible motion" illusions, and even files allowing you to construct some of his illusions for yourself.
See "The Illusion Machine That Teaches Us How We See," by Erica Klarreich, Nautilus, 13 November 2014.
--- Ben Pittman-Polletta (Posted 12/1/14)
Terence Tao appears on The Colbert Report, by Claudia Clark
In this 6-minute segment, comedian Stephen Colbert interviewed UCLA professor of mathematics Terence Tao about his interest in mathematics, specifically his interest in prime numbers. After defining prime numbers for the audience, and noting that there are an infinite number of them, Tao talked about twin primes, explaining that we don't know whether there are a finite or infinite number of pairs. He also talked about cousin primes (prime numbers that differ from each other by 4), and sexy primes (prime numbers that differ from each other by 6), all the while gamely responding to Colbert’s witty comments with good humor. He told the audience that, just this year, it was proven that at least one of these three classes of primes is infinite since the sum of the formulas used to calculate the number of twin primes, the number of cousin primes, and the number of sexy primes has been shown to be infinite.
See the segment Terence Tao, guest, The Colbert Report, Comedy Central, 12 November 2014.
--- Claudia Clark
On how math explains why hipsters look alike, by Lisa DeKeukelaere
Drawing parallels to the behavior of neurons, mathematician and neuroscientist Jonathan Touboul uses mathematical modeling to explain why nonconformist "hipsters" end up conforming to each other. Touboul lays out his work in a recently published paper, first illustrating how the preferences of a population will shift –seemingly chaotically—as conformists and nonconformists each change their own preferences based on their observations of those around them. The key to Touboul's work, however, is applying to his model the idea of a delay in such observations. Increasing the delay to a certain point elicits a pattern out of the chaos and demonstrates how hipsters seeking to be nonconformist actually fall into sync with each other as they react to an outdated perception of the norm. Touboul concedes that his model is an unrealistic simplification of the world—hipsters have numerous ways to exhibit nonconformity, for example—but he notes that simplification is the point of mathematics, to facilitate understanding of complex ideas.
Images courtesy of Jonathan Touboul: Simulations of the discrete system for n = 5,000, inverse temperature β = 2, and q = 1 (fully anti-conformist system) and different delays (left: 0.5, center: 0.7, and right: 1.5). Top row: time evolution of all particles as a function of time; bottom row: empirical (blue) and theoretical (red) total trend.
See "The mathematician who proved why hipsters all look alike," by Jeff Guo, Washington Post, 11 November 2014; "Math Finally Sleuths Why So Many Hipsters Look Alike," by John Hendrickson. Esquire, November 14, 2014; and "The hipster effect: When anticonformists all look the same," by Jonathan Touboul on arxiv.org.
--- Lisa DeKeukelaere
Combining Food and Formulas, by Claudia Clark
Mercedes Siles Molina, a mathematician at the Universidad de Málaga, in Spain, is passionate about both mathematics and cooking. Molina collaborated with Chef José Carlos Garcia and photographer Pedro Reyes Dueñas to create a collection of photographs of beautifully presented culinary creations based on mathematical formulas. These photographs are part of an exhibit called "The Taste of Mathematics" (El sabor de las Matemáticas), which has appeared in several cities in Spain and Panama. Molina recently spoke about her love for both math and cooking at an event entitled "Cooking Up Math" on November 5th at the Museum of Mathematics in New York.
"The motivation for the work "The Taste of Mathematics" was the Centennial of the Royal Spanish Mathematical Society (RSME) in 2011. I'm member of the governing board of the RSME and wanted to do something special on that occasion. That was the starting point for my work on divulgation of Mathematics," wrote Molina about the "El sabor de las Matemáticas"("The taste of Mathematics").
(Photos: "Strawberries with tiles of coral and cocoa" and "Cylinder," works by Mercedes Siles Molina and Chef José Carlos Garcia, photographs by Pedro Reyes Dueñas. Courtesy Mercedes Siles Molina.)
See "Mouthwatering Math: Culinary Creations Combine Food and Formulas," by Tanya Lewis. LiveScience, 10 November 2014, and photographs from the exhibit.
--- Claudia Clark
On Bletchley Park cryptanalyst Joan Clarke, by Allyn Jackson
This article discusses The Imitation Game, a film about the legendary mathematician Alan Turing which came out in theaters in the UK this week. The subject of this article is Joan Clarke, a cryptanalyst who worked alongside Turing at Bletchley Park during World War II, who is a character in the film (which stars Benedict Cumberbatch as Turing and Keira Knightley as Clarke). Clarke was a close friend of Turing's and briefly his fiancée. He broke off the engagement, telling Clarke that he had homosexual tendencies. Despite her clear skills and talents, Clarke was paid less and received less recognition than the male cryptanalysts she worked with at Bletchley. She had been an outstanding student at Cambridge, earning a "double first" in mathematics in 1939, though not a full degree; women could not earn full degrees at Cambridge until 1948. Kerry Howard, who researched the role of women at Bletchley Park, is quoted in the article as saying: "Up until now the main focus has been on the male professors who dominated the top level at Bletchley." In order to find any information on the women involved, she said, you have "to dig much deeper."
See "Joan Clarke, woman who cracked Enigma with Alan Turing," by Joe Miller. BBC, 10 November 2014.
--- Allyn Jackson
He ought to be in papers, by Ben Pittman-Polletta
The Imitation Game is a new biopic about scientist and mathematician Alan Turing's life and work. With the recent premiere (see coverage of the premiere by Roger Friedman on his blog Showbiz 411) and a cover story in Time magazine, there's no shortage of media coverage on the film, but Dan Rockmore's review in The New Yorker is a welcome deeper look into the intellectual life of the film's protagonist. Turing is most famous for his work in computer science and artifical intelligence, exemplified by the eponymous concepts of the Turing machine and the Turing test. Turing was also a homosexual, and his conviction for "gross indecency" and the subsequent sentence of chemical castration led to his suicide 16 days before his 42nd birthday. These facts provide the "narrative hooks" for the new movie, which, according to Rockmore, focuses on Turing's work cracking the Enigma code during World War II. But Turing was also a pioneer in logic, number theory, and mathematical biology, modeling the brain and development. Rockmore, chair of the Department of Mathematics and professor of computer science at Dartmouth College, uses his review of The Imitation Game as an opportunity to highlight one of Turing's most prescient and impressive intellectual works--his essay "Intelligent Machinery." In this paper, Turing sets down his ideas about how a thinking machine might be built. He puts forward a simple model of a network of neurons, and ideas for how it might be educated from "experience"--and especially from rewarding and aversive stimuli--which are foundational to the influential connectionist paradigm in mind and brain research ("Connectionism," Wikipedia).
This paper, as well as others collected in editor B. Jack Copeland's The Essential Turing (reviewed by Andrew Hodges in the AMS Notices), such as "The Chemical Basis of Morphogenesis," illuminate critical issues in science with a clarity rarely seen in today's literature. For instance, in "Intelligent Machinery, a Heretical Idea," Turing describes how "indexes" might be used to organize information in memory. "New forms of index," he suggests, "might be introduced on account of special features observed in the indexes already used." Here and elsewhere, Turing exemplifies his own rationale for modeling human thought. "The whole thinking process is still rather mysterious to us," he says in "Can Machines Think?", "but I believe that the attempt to make a thinking machine will help us greatly in finding out how we think ourselves." Revisiting Turing's work reminds us how much we have to learn from history--how not only the emotional, but also the intellectual struggles of our forebears, mirror and inform our own. Indeed, this is an idea Turing himself discusses in "Intelligent Machinery." At the end of the essay, he proposes that essentially all problems are search problems, and discusses both evolutionary and intellectual searches in this light. "The remaining form of search is what I should like to call the 'cultural search'," he writes, "... the isolated man does not develop any intellectual power ... the search for new techniques must be carried out by the human community as a whole."
See "What's Missing From 'The Imitation Game'" by Dan Rockmore. The New Yorker, 6 November 2014.
--- Ben Pittman-Polletta
Musicians and Birds Converge on the Harmonic Series, by Anna Haensch
There is no doubt that the trill of the Hermit Thrush is a pleasing sound to our human ears, but is it music? A recent article in NOVA discusses how Emily Doolittle, a composer and professor of Music at the Cornish College of the Arts broke down these birdsongs and discovered that mathematically, they are just like human music. Here, have a listen (click on the Soundcloud audio clip, left). Musical instruments, human voices, and even bird sounds are based on the same principle: a string or column of air vibrates at a certain frequency and that creates sounds of varying pitches. So you've got this vibrating string and you can imagine that long waves create low tones and short waves create high tones and there are tones everywhere in between. But for birds and human (and also lots of instruments), the best -- i.e. most resonant -- tones come from one very low bass frequency, and then that frequency chopped in 1/2, 1/3, 1/4, and so on. Check out the picture below. |
These are exactly the terms in the harmonic series. Doolittle and her team were surprised to find that the songs of Hermit Thrush contain this same harmonic series.
What is interesting about this, is that tones in the harmonic series, although so familiar to our human ears, are not really a human aesthetic construct. It's just math! So while the results from Doolittle and her lab are surprising, they don't suggest that birds have some understanding of music theory. But as Doolittle points out to The Smithsonian, "If an aspect of music is found not only in humans, but also in a variety of non-human species, this would suggest that there may be something in our shared biology that predisposes us to find that aspect interesting, or attractive, or easy to sing."
See "This Bird's Songs Share the Same Mathematical Qualities as Human Music," by Allison Eck, NOVA, 4 November 2014.
--- Anna Haensch (Posted 11/21/14)
On the complexity of Candy Crush, by Claudia Clark
In this article, Toby Walsh, Research Group Leader in the Optimization Research Group at NICTA, a research center in Australia, explains why the wildly popular game, Candy Crush, belongs to the class of NP problems. Walsh begins by introducing the reader to the different classes of problems, as well as the question of whether P = NP. Then, noting that the problem of finding a solution to a logical formula belongs to the class NP, Walsh shows how a logic puzzle can be reduced to a Candy Crush problem by "building" an electric circuit in a Candy Crush game, with candies representing wires, switches, and logic gates. "Expressed in terms of these electrical logic circuits," Walsh writes, "the puzzle in playing Candy Crush is deciding which switches to set so that the logic gates fire appropriately and the output bit is set to true." Walsh then describes how to do the reverse, i.e., reducing a Candy Crush game to satisfying a logical formula.
See "Candy Crush's Puzzling Mathematics," by Toby Walsh. American Scientist, November-December 2014, pages 430-433.
--- Claudia Clark
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