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Equilibrium Modeling Increases Contact Lens Comfort

According to the Vision Council of America, roughly 75% of adults in the United States require some form of vision correction. Yet only 10% of Americans wear contact lenses. Studies estimate that one in four initial contact-users finds the lenses uncomfortable and stops wearing them. Thus, increasing the comfort level of contact lenses and expanding the market is a continual objective in the vision industry.

In order to understand the factors that contribute to lens comfort, it is important to study the solid and fluid mechanics of a lens’ interaction with an eye. In an article publishing this week in the SIAM Journal on Applied Mathematics, authors David Ross, Kara Maki, and Emily Holz design an equilibrium model to demonstrate the elastic stresses and suction pressure distribution between a soft hydrogel contact lens and an eye. Read the rest of this entry »

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Segmenting Ultrasound Video with a Wavelet Variational Model

Image segmentation, the process of separating a digital image into multiple sections for individual examination, is frequently used in medical image analysis. For example, segmentation in ultrasound footage helps identify boundaries and regions of interest (ROI) that facilitate image interpretation. Efficient segmentation of ultrasound videos, however, is often complicated by low contrast, shadow effects, and complex “noise” statistics (unexplained variations). In addition, real-time applications such as navigation during operational surgery require efficient algorithms.

In an article published this month in the SIAM Journal on Imaging Sciences, authors Jiulong Liu, Xiaoqun Zhang, Bin Dong, Zuowei Shen, and Lixu Gu propose a video segmentation model to recognize ROI in ultrasounds. 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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Math detects contamination in water distribution networks

Philadelphia, PA—None of us want to experience events like the Camelford water pollution incident in Cornwall, England, in the late eighties, or more recently, the Crestwood, Illinois, water contamination episode in 2009 where accidental pollution of drinking water led to heart-wrenching consequences to consumers, including brain damage, high cancer risk, and even death. In the case of such catastrophes, it is important to have a method to identify and curtail contaminations immediately to minimize impact on the public.
A paper published earlier this month in the SIAM Journal on Applied Mathematics considers the identification of contaminants in a water distribution network as an optimal control problem within a networked system. Read the rest of this entry »

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Persistence or extinction: Through a mathematical lens

Philadelphia, PA—Scientists have estimated that there are 1.7 million species of animals, plants and algae on earth, and new species continue to be discovered. Unfortunately, as new species are found, many are also disappearing, contributing to a net decrease in biodiversity. The more diversity there is in a population, the longer the ecosystem can sustain itself. Hence, biodiversity is key to ecosystem resilience.

Disease, destruction of habitats, pollution, chemical and pesticide use, increased UV-B radiation, and even the presence of new species are some of the causes for disappearing species. “Allee effect,” the phenomenon by which a population’s growth declines at low densities, is another key reason for perishing populations, and is an overriding feature of a paper published last month in the SIAM Journal on Applied Mathematics. Read the rest of this entry »

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Mathematics and the Ocean: Movement, Mixing and Climate Modeling

Emily Shuckburgh of the British Atlantic survey uses mathematical ideas from dynamical systems to study mixing in the Southern Ocean

Philadelphia, PA—Studying the dynamics of the ocean system can greatly improve our understanding of key processes of ocean circulations, which have implications for future climate. Can applying mathematics to the research help? Dr. Emily Shuckburgh of the British Antarctic Survey, speaking at the 2012 SIAM Annual Meeting, thinks the answer is an emphatic “yes.”

Dr. Shuckburgh described mathematical ideas from dynamical systems used by her group, along with numerical modeling and experimental observations, to analyze circulation in the Southern Ocean. The Southern Ocean is unique in that it connects three major ocean basins—the Pacific, the Atlantic and the Indian oceans—with a powerful current that circulates all the way around Antarctica. This circumpolar current travels from the North Atlantic, sinking down to the bottom of the ocean and coming up to the surface around Antarctica, thus connecting the deep ocean with the atmosphere above. When water from the deep ocean comes up to the surface, it can exchange heat and carbon dioxide from the atmosphere, thus making it highly significant for climate change. Read the rest of this entry »

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Toward an artificial pancreas: math modeling and diabetes control

Philadelphia, PA – October 4, 2012—Diabetes mellitus is a chronic disease in which individuals exhibit high levels of sugar in the blood, either due to insufficient production of insulin—the hormone that allows glucose to be absorbed by body cells—or the body’s lack of response to insulin. Type 1 diabetes occurs due to loss or dysfunction of β-cells of the pancreas, the organ that produces insulin. Type 2 diabetes is caused by a defective glucose-insulin regulatory system. The most common control for diabetes is by subcutaneous injection of insulin analogues through insulin pumps.

In a paper published today in the SIAM Journal on Applied Mathematics, authors Mingzhan Huang, Jiaxu Li, Xinyu Song, and Hongjian Guo propose novel mathematical models for injection of insulin in type 1 and type 2 diabetes. The models simulate injections of insulin in the manner of insulin pumps, which deliver periodic impulses in diabetes patients. 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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The math of malaria

Philadelphia, PA – June 20, 2012—Malaria affects over 200 million individuals every year and kills hundreds of thousands of people worldwide. The disease varies greatly from region to region in the species that cause it and in the carriers that spread it. It is easily transmitted across regions through travel and migration. This results in outbreaks of the disease even in regions that are essentially malaria-free, such as the United States. Malaria has been nearly eliminated in the U.S. since the 1950s, but the country continues to see roughly 1,500 cases a year, most of them from travelers. Hence, the movement or dispersal of populations becomes important in the study of the disease.

In a paper published this month in the SIAM Journal on Applied Mathematics, authors Daozhou Gao and Shigui Ruan propose a mathematical model to study malaria transmission. Read the rest of this entry »

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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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