See also: Blog on Math Blogs: Two mathematicians tour the mathematical blogosphere. Editors Brie Finegold and Evelyn Lamb, both PhD mathematicians, blog on blogs --on topics related to mathematics research, applied mathematics, mathematicians, math in the news, mathematics education, math and the arts and more.
"Jerome Karle (1918–2013)," Nature, 25 July 2013, page 410.
In this obituary of his postdoctoral mentor and collaborator of 15 years, Wayne Hendrickson describes Jerome "Jerry" Karle's Nobel-prize winning contributions to the field of X-ray crystallography, and gives an overview of Karle's long, collaborative, and interdisciplinary career. X-ray crystallography is a method of determining (probabilistically) the locations of the atoms in a crystal lattice, by shooting the crystal with X-rays and observing the resulting diffraction patterns. It turns out that the intensity of the X-rays scattered by the crystal is proportional to the magnitude of the Fourier transform of the crystal's electron density, and the mean position of the atoms within the crystal can be deduced from the electron density. The trick is figuring out a way to estimate the phase of the Fourier transform. This is possible because there are many more X-rays than there are atoms in the crystal. Working with mathematician Herbert Hauptman, Karle used the fact that the electron density must be positive to determine statistical relationships between diffracted X-rays that can be used to reconstruct the missing phase information. But Karle and Hauptman's 1952 theoretical opus "Solution of the Phase Problem" went largely ignored by skeptical chemists until Jerry and his wife, Isabella Karle, published a landmark paper laying out step-by-step methods for applying this theoretical work. Isabella used her husband's "direct method" to solve the structures of (crystals of) complex molecules, including proteins, and the method is used widely to this day. A graduate of New York's City University, Karle went on to get a master's at Harvard (in biology) and a doctorate at the University of Michigan (in chemistry), where he met Isabella. The two worked on the Manhattan Project together at the University of Chicago, Isabella being one of the youngest and one of the few female scientists on the project, before settling down at Washington D.C.'s Naval Research Labs. Jerry continued to make influential discoveries late into his career, doing seminal work on methods to solve the crystal structures of large macromolecules by identifying resonant atoms. According to Hendrickson, despite the collaborative nature of his early and most influential work, Karle was "a lone theoretician" whose "main working interaction was with a computer programmer who tested his theories"--a theoretician who, nevertheless, must have been gratified to see his theories have such a broad impact on the applied sciences.
--- Ben Polletta
"Summer School for Math," Letter to the Editor by Alfred S. Posamentier. The New York Times, 2 July 2013.
Posamentier, dean and professor of the School of Education at Mercy College, NY, wrote a letter to the editor on the potential of summer math programs "to show off the beauty and power of mathematics." The letter was written in response to a front page article in The New York Times, "At Retooled Summer Schools, Creativity, Not Just Catch-Up" (by Motoko Rich, June 30). That article promoted the advantages and new approaches of summer programs but barely mentioned math programs, so Posamentier took the opportunity to advocate that "summer school would be an excellent time to expose students to some of the wonders of mathematics that lie outside prescribed curriculums," and suggest that "it might be interesting to demonstrate how great artists and musicians (like Leonardo and Wagner) used mathematical principles in their work," to complement the math--and other subjects--taught in school. He concludes, "Doing this might also keep future generations from bemoaning how mathematics has no place in the real world and encourage a lifetime appreciation of mathematics."
--- Annette Emerson
"How algorithms rule the world," by Leo Hickman. The Guardian, 1 July 2013.
Hickman writes an extensive piece about how sophisticated algorithms are becoming more prevalent in our everyday lives. He chronicles some well-known algorithm success stories such as how Google rose to the top with its ingenious search algorithm (an algorithm that is now a closely guarded commercial secret) and algorithm failures such as how the algorithms used to perform high-frequency trading caused the "flash crash" of May 6, 2010, when the Dow Jones industrial average fell 1,000 points in just a few minutes, only to see the market right itself 20 minutes later.
Hickman also dives into lesser known uses of algorithms, most notably a predictive policing method called "Operation Blue Crush." In a nutshell the algorithm uses historical data to identify crime "hot spots" based on crime statistics from across the city overlaid with other datasets such as social housing maps and outside temperatures. The algorithm then directs law enforcement personnel to the areas identified. "It's putting the right people in the right places on the right day at the right time," said Dr Richard Janikowski, an associate professor in the department of criminology and criminal justice at the University of Memphis. The method was developed by a team of criminologists and data scientists at the University of Memphis and is perceived to be so successful that it has been adopted in a number of countries such as Poland and Israel. However the method has its critics, which have dubbed it Minority Report policing. [Hear Andrea Bertozzi talk about her team's work in predictive policing.] Hickman also touches on less controversial uses of algorithms such as an algorithm able to analyze and rate music by breaking up each song into its component parts and then determining common characteristics across a range of No 1 records. The algorithm has demonstrated its predictive powers by correctly identifying the debut albums by both Norah Jones and Maroon 5 as smashing hits before they were even released.
--- Baldur Hedinsson
"Ode to Prime Numbers," by Sarah Glaz. American Scientist, July-August 2013, pages 246-250.
Highlighting the elements of mystery and elegance connecting prime numbers with poetry, this article provides excerpts and explanations of poems involving primes. One poem praises primes while gracefully incorporating artistic references to their properties and distribution. Another poem is a playful rhyme about the unsolved Riemann Hypothesis, which links prime numbers and the zeros of Euler's zeta function. The author explains that not only have poets used the notion of being prime as a metaphor in poetry, they also have penned poems dedicated to specific prime numbers--especially the number seven--playing on cultural significance. In addition, the author outlines several mad-lib-like methods for generating poems using algorithms based on primes.
--- Lisa DeKeukeleare
"Walls of Water," by Dana Mackenzie. Scientific American, July 2013, pages 86-89.
A Lagrangian coherent structure is a geometric structure separating dynamically distinct regions of a time-dependent dynamical system, such as a fluid flow. As Dana Mackenzie details in his nice review of the subject, these unwieldily named structures--key to the qualitative understanding of time-dependent chaotic systems--are increasingly finding their way into real-time applications in oceanography, atmospheric science, and even biology. The fluid flows important to these sciences are governed by the Navier-Stokes equations, partial differential equations for which existence of solutions and their uniqueness remain open problems, and for which numerical solutions are plagued by the presence of chaotic, turbulent behavior. But in the past few decades, mathematicians have developed theoretical frameworks to understand the persistent structures in these flows. Analogous to the stable and unstable manifolds of time-independent systems, these structures can be attracting or repelling. Mathematician George Haller, who gave LCS's their (lengthy) name in 2001, has called them "the skeleton of turbulence." Importantly, LCSs can be computed stably in real time from real data. In 2003, Shawn C. Shadden of the Illinois Institute of Technology and his collaborators monitored surface currents in Monterey Bay using four high-frequency radar stations, and computed the Lagrangian coherent structures in the bay from three days' worth of data. They found a long transport barrier--a wall of water separating two flows moving in opposite directions--practically bisecting the bay. When they placed buoys in the bay, they found that those on one side of this barrier drifted out to sea, while those placed inside the barrier recirculated for up to 16 days.
Lagrangian coherent structures have also shed light on some of the surprises from the Deepwater Horizon oil spill. A "tiger tail" of oil that detached from the slick to travel 100 miles southeast on May 17 was predicted by the formation of an attracting Lagrangian coherent structure seven days earlier, and an abrupt westward retreat of the slick's leading edge on June 16 was predicted by the formation of a repelling structure to the east nine days earlier. Transport barriers also explain why the oil spill did not follow the Loop Current into the Atlantic, and possibly why the surface oil dissipated faster than was predicted--as oil-eating microorganisms thrived in transient ecosystems defined by stable LCSs. In the future, knowledge of these structures may enable clean-up crews to more effectively manage similar spills (God forbid). Already, the structures with the long name have been applied to study the movements of airborne pathogens--which can be ferried hundreds of miles between pairs of moving repelling LCSs--and the flow of blood in the heart, where it turns out regions of recirculating blood are greatly enhanced in patients with enlarged hearts, spelling increased risk of heart attack.
--- Ben Polletta
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