Research News

How does innovation take hold in a community? Math modeling can provide clues

nugget_icon2Philadelphia, PA—Mathematical models can be used to study the spread of technological innovations among individuals connected to each other by a network of peer-to-peer influences, such as in a physical community or neighborhood. One such model was introduced in a paper published yesterday in the SIAM Journal on Applied Dynamical Systems.

Authors N. J. McCullen, A. M. Rucklidge, C. S. E. Bale, T. J. Foxon, and W. F. Gale focus on one main application: The adoption of energy-efficient technologies in a population, and consequently, a means to control energy consumption. By using a network model for adoption of energy technologies and behaviors, the model helps evaluate the potential for using networks in a physical community to shape energy policy. Read the rest of this entry »

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Finding answers in big data sets

 Philadelphia, PA—Whether you’ve watched an elaborate weather forecast, made an online purchase, or received personalized news stories in your inbox in recent years, you’ve likely seen “big data” in action.

Big data is everywhere these days, be it personalized ad targeting, weather and climate modeling, or flu trend analysis to mention just a few.

Ever-increasing amounts of data are now available thanks to many modern realities: e-commerce and transaction-based information that has been stored over the years,  data streaming in from growing social media activity and rising Web traffic, and sensor data from the increased use of digital sensors in industrial equipment, electrical meters, automobiles, and satellites, for example. With decreasing storage costs, archiving this data has also become easier than ever. Read the rest of this entry »

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Mathematicians tackle global issues

 Philadelphia, PA– More than 100 academic institutions and scholarly societies have joined in a major world-wide initiative: Mathematics of Planet Earth (MPE) 2013. This year-long effort will highlight the contributions made by mathematics in tackling global problems, including natural disasters such as hurricanes, earthquakes, and tsunamis; climate change; sustainability; and pandemics. MPE2013 partners will sponsor workshops, research conferences, public lectures, outreach events, and educational opportunities for all ages.  Each country from a partner institution will host a special launch to the year.

MPE2013 enjoys the patronage of UNESCO, the United Nations Educational, Scientific, and Cultural Organization.  The Director-General of UNESCO, Irena Bokova, said, “UNESCO strongly supports this extraordinary collaboration of mathematicians around the world to advance research on fundamental questions about planet Earth, to nurture a better understanding of global issues, to help inform the public, and to enrich the school curriculum about the essential role of mathematics in the challenges facing our planet.” Read the rest of this entry »

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Mathematics and fine art: Digitizing paintings through image processing

Philadelphia, PA – September 25, 2012—The current trend to digitize everything is not lost on fine art. Documenting, distributing, conserving, storing and restoring paintings require that digital copies be made. The Google Art Project, which brings art from galleries around the world to online audiences, was launched in early 2011 for precisely these reasons.  Google’s project has been a complex undertaking, however, carried out under carefully controlled settings using state-of-the-art equipment and requiring rigorous post-production work.

In a paper published this month in the SIAM Journal on Imaging Sciences, authors Gloria Haro, Antoni Buades and Jean-Michel Morel propose a far simpler technique that can achieve reliable reproductions of paintings using fusion of photographs taken from different angles through statistical methods. One of the main advantages of the method described is that image fusion obviates the need for a high-performance camera.

“This article demonstrates the possibility of acquiring a good quality image of a painting from amateur snapshots taken in bursts from different angles, in normal museum illumination,” senior author Jean-Michel Morel said via e-mail. “The photographing procedure is simple and can be done with a commercial hand-held camera by an amateur photographer.” Thus, paintings can be digitized even under poor light conditions, and this includes museum pieces that may be protected by glass screens that reflect light from other objects in the room.

The simple photographic procedure eliminates the need for sophisticated illumination and acquisition requirements. The postproduction process, while intensive, is fully automated. The fusion of multiple images of a painting from well-chosen angles can eliminate glare, highlights and motion blur. Robust statistical methods reduce noise and compensate for optical distortion, thus addressing the problem of uncontrolled illumination and destructive reflection that tends to be seen in many digitized paintings.

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Using dynamical systems concepts to understand the climate change tipping point

With rising global temperatures accompanied by changes in weather and climate there is no question that the Earth is warming: the average temperature has risen by 1.4°F over the past century. But how do we know when we reach a tipping point, if we haven’t already?

With ongoing abrupt shifts of the climate system that have happened for decades, it’s hard to say when a threshold is reached. Hence, some scientists are now using mathematical observations and tools to answer the tipping-point question.

Marten Scheffer, a biologist at Wageningen University in the Netherlands, is trying to identify early-warning signals for climate change by using dynamical systems techniques to determine abrupt transitions that would precede such a tipping point.

By studying yearly recurring patterns of climate— rather than global average temperatures —Tim Lenton, a climate scientist at the University of Exeter in England has detected climate systems that could reach tipping points not too far in the future.

Research such as this, using principles from dynamical systems, could give valuable insights into the future of the climate system.

Read the full article on the New York Times site.

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Nonlinear math may help dolphins locate prey underwater

Dolphins are not called man’s best friends for nothing. The aquatic mammals’ ability to think nonlinearly may help improve man-made sonar.

Recent research, published in the latest Proceedings of the Royal Society A, shows that the aquatic mammals may be able to pinpoint prey hidden in bubbles by using some complex mental math.

The research was inspired when lead author Tim Leighton watched dolphins blow multiple tiny bubbles around their prey as they hunted during an episode of the Discovery Channel’s “Blue Planet.” Leighton speculated that these mammals—well-known for their superior intelligence—were probably using a sonar techniqute to track their prey, because the alternative explanation would be that they were just ‘blinding’ their sensory apparatus when hunting, which would likely deter the objective.

Based on this assumption, his research team modeled the types of echolocation pulses emitted by dolphins. Processing them using nonlinear mathematics was able to explain how dolphins are able to successfully hunt their prey with bubbles. While it is not conclusive that dolphins use nonlinear processing, using dolphin-like sonar pulses may help humans detect and identify objects in bubbly water. This may especially be helpful for the military to find objects, such as mines, in breaking waves and shallow waters.

Read a detailed article on Discovery News.

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Predicting burglary patterns through math modeling of crime

Philadelphia – May 31, 2012 -  Pattern formation in physical, biological, and sociological systems has been studied for many years. Despite the fact that these subject areas are completely diverse, the mathematics that describes underlying patterns in these systems can be surprisingly similar. Mathematical tools can be used to study such systems and predict their patterns. Read the rest of this entry »

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Mathematical modeling and the dynamics of obesity

Math can often provide quicker and more reliable answers to medical questions where experimental research could take years.  So it is with obesity, as Dr. Carson Chow of the NIH’s National Institute of Diabetes and Digestive and Kidney Diseases explained in a recent interview with the New York Times.

At the 2010 SIAM Annual Meeting, Dr. Chow gave an overview of mathematical models on obesity, giving a very engaging account of “The Dynamics of Obesity” in an invited presentation.

Weight change in the human body can be viewed simply as the difference between the rate of food intake and energy expenditure, Dr. Chow explained, going on to detail the various factors that can influence obesity. The energy density of various body components including water, bones, minerals, fat, protein and carbohydrates influence weight gain, in addition to fuel sources or macronutrients. By applying mathematical models, Dr. Chow illustrated that the “food push” in America is the primary reason for increasing obesity in the U.S. population. The high amount of food available per capita in the U.S. should be mitigated in order to control the obesity epidemic, he concluded.

Dr. Chow’s complete presentation from SIAM AN10 can be viewed on the SIAM Presents archives here.

You can also read detailed insights and a summary of his AN10 talk on his blog here.

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Aiding cancer therapy by mathematically modeling tumor-immune interactions

Cancer is one of the five leading causes of death. And yet, despite decades of research, there is no standardized first-line treatment for most cancers. In addition, disappointing results from predominant second-line treatments like chemotherapy have established the need for alternative methods.

Mathematical modeling of cancer usually involves describing the evolution of tumors in terms of differential equations and stochastic or agent-based models, and testing the effectiveness of various treatments within the chosen mathematical framework. Tumor progression (or regression) is evaluated by studying the dynamics of tumor cells under different treatments, such as immune therapy, chemotherapy and drug therapeutics while optimizing dosage, duration and frequencies. Read the rest of this entry »

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The faster-than-fast Fourier transform at SODA12

The following article, reprinted from MIT News, describes a new algorithm to improve on the fast Fourier transform, which was presented by MIT researchers at the 2012 Symposium on Discrete Algorithms organized by SIAM and co-sponsored by the Association for Computing Machinery and the SIAG on Discrete Mathematics.

The faster-than-fast Fourier transform

For a large range of practically useful cases, MIT researchers find a way to increase the speed of one of the most important algorithms in the information sciences.

Larry Hardesty, MIT News Office

The Fourier transform is one of the most fundamental concepts in the information sciences. It’s a method for representing an irregular signal — such as the voltage fluctuations in the wire that connects an MP3 player to a loudspeaker — as a combination of pure frequencies. It’s universal in signal processing, but it can also be used to compress image and audio files, solve differential equations and price stock options, among other things.

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