SIAM Undergraduate Research Online, SIAM’s web-based publication often referred to as SIURO, publishes outstanding undergraduate research in applied and computational mathematics. Two types of articles can be found in SIURO: papers to which undergraduates have made a significant contribution, and expository (survey) papers of high quality written by a faculty member or researcher for an undergrad audience.
The latest five papers published last month in SIURO provide insights into a breadth of topics from finding a needle in a haystack and iterative games to the spread of a rumor.Modeling Learning and Cooperation in Iterative Games by Aleksey Chernobelskiy, Vineet Dixit, Agostino Cala, Siddharth Pandya, and Hector Javier Rosas (University of Arizona) describes the general framework of neural networks and how such frameworks can be adapted to model human game play and the learning that takes place during iterative games.
Finding a Needle in a Haystack: An Image Processing Approach by Emily Beylerian (University of California, Los Angeles) delves into the process of dividing an image into its constituent parts using information about the boundaries between objects, edges within objects, variations in intensity, etc. The method used in the paper applies to the classic example of finding a needle in a haystack, as well as real images where the texture component and noise cause problems for standard techniques.
Sensitivity to Noise in Particle Filters for 2-D Tracking Algorithms by Dong-Hyeon Park, Stephanie Porter, and Sarah Warkentin (Harvey Mudd College) explains how a particle filter algorithm was used to simulate a Remotely Operated underwater Vehicle (ROV) tracking a moving target in 2-D space. The simulation modeled the behavior of a Sea Perch ROV modified with mounted cameras to perform blob-tracking on the target.
The Effects of Spatial and Temporal Grids on Simulations of Thin Films with Surfactant by Greg Kronmiller, Eric Autry, and Celeste Conti (Harvey Mudd College) investigates a numerical solver that combines Alternating Direction Implicit (ADI) methods with CLAWPACK to address mixed-type equations, such as the parabolic-hyperbolic systems of PDEs describing surfactant spreading on a thin liquid film.
Spread of a Rumor by Nickolas Fedewa, Emily Krause, and Alexandra Sisson (Central Michigan University) points out that the random spread of a rumor has a long history. The article therefore considers a random process that is based on sampling without replacement leading to the use of the discrete hypergeometric distribution. A model with only spreaders and ignorants is explored followed by more general models with spreaders, ignorant, and stiers.
Additional papers will be posted online as they are accepted.