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SIAM Nuggets

Bayesian Model Improves Use of X-ray Radiography in National Security

Quantitative radiography is an imaging technique that uses electromagnetic radiation, such as X-rays, to gather quantitative data about the interior of nontransparent objects that vary in density and composition. For example, radiography is particularly helpful when reconstructing objects composed of multiple materials, such as different types of metal. In order to generate these images, most high-energy technologies pulse X-rays through the “scene” in question; objects in the scene absorb some of the rays, while a scintillator – which measures the strength of the passing X-rays – collects the rest and fluoresces (emits visible light) in response to the collected rays. Possible scenes include parts of the human body, thermal explosions, nuclear testing sites, and other applications of national security. The resulting images directly measure the intensity of visible light, yielding information about the objects’ internal structure.

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NPZ Model: Maturity in the Juvenile Zooplankton

Planktonic ecosystems make up the bottom nutritive levels of aquatic food webs, providing a vital source of food to many large marine organisms. Researchers build nutrient-phytoplankton-zooplankton (NPZ) mathematical models in order to describe the bottom trophic levels of aquatic ecosystems, aiding future research of phytoplankton.

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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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Applying Parameter Selection and Verification Techniques to an HIV Model

Physical and biological models often have hundreds of inputs, many of which may have a negligible effect on a model’s response. Establishing parameters that can be fixed at nominal values without significantly affecting model outputs is often difficult; sometimes these parameters cannot be simply discerned by the outputs. Thus, verifying that a parameter is noninfluential is both computationally challenging and quite expensive. Read the rest of this entry »

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Optimizing flutter shutter to minimize camera blur

Whether taking photos recreationally or professionally, photographers understandably want their snapshots to appear sharp and clear. Image clarity is dependent on exposure time, or the amount of time that a camera’s sensor is exposed to light while a photograph is being taken. During this period, the shutter opens and the camera counts the number of photons emitted by the subject. Read the rest of this entry »

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Dynamical systems theory enhances knowledge of Jupiter’s atmosphere

Jupiter, which has a mass more than twice that of all the planets combined, continues to fascinate researchers. The planet is characterized most often by its powerful jet streams and Great Red Spot (GRS), the biggest and longest-lasting known atmospheric vortex. Although still images provide some insight into the features of Jupiter’s atmosphere, the atmosphere itself is unsteady and turbulent, and its features are time-dependent.

In a paper published this month in SIAM Review, authors Alireza Hadjighasem and George Haller use video footage to analyze Jupiter’s transport barriers and examine prior conclusions about Jupiter’s atmosphere. Read the rest of this entry »

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Modeling robust use of pesticides

Adaptive control techniques can help manage pests more effectively

nugget_iconAs population growth, greater food consumption, competition for land use, and climate change pose challenges to world food production, managing loss of crop due to pests and weeds becomes increasingly important. While chemical pesticides offer effective means for control, potential loss of crop yield  is still significant, as is cost. Global potential loss from pests has been estimated to be between 50% and 80% of yield based on crop type.

In a paper published last week in the SIAM Journal on Applied Mathematics, authors Chris Guiver et al propose adaptive control techniques to model pest dynamics and management as a control system. Read the rest of this entry »

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Nugget: Improving Musical Synchronization with Mathematical Modeling

Music functions as a universal connector that pervades most cultures. More specifically, rhythm and synchronization – both within and beyond the realm of music – are forms of communication that stimulate brain activity. Read the rest of this entry »

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Nugget: New SIR-Network Model Helps Predict Dengue Fever Epidemic in Urban Areas

Mathematics is often implemented in healthcare and medical research. From health management to the bio-pharmaceutical fields, math modeling can be used to predict the spread of diseases, how to prevent epidemics and so much more. An article “SIR-Network Model And its Application to Dengue Fever,” authored by Lucas M. Stolerman, Daniel Coombs and Stefanella Boatto, published recently in the SIAM Journal on Applied Mathematics introduces a new mathematical model which offers a simplified approach to studying the spread of the infectious virus, Dengue fever, in urban areas, specifically breaking down the epidemic dynamics across a city and its varying neighborhoods and populations. Read the rest of this entry »

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