Signal Detection Theory is a popular and well-established idea that has influenced behavioral science for around 50 years. Essentially, the theory holds that in a predator-prey relationship, prey animals will show more wariness and be more prone to flee as predators become more common. Danger signals are ambiguous, so in what appears to be a threatening situation, animals are better off running than hanging around to see if a predator really does strike.
Now Pete Trimmer, a postdoctoral research at UC Davis, has taken a fresh look at signal detection theory and come up with what at first look like counterintuitive results. In many cases, he says, animals should actually become less cautious as the risk of predation rises.
Applying mathematics to detect chemical weapons, hidden explosives or other threats is the goal of an ongoing project at the UC Davis Department of Mathematics, supported by grants from the National Science Foundation.
Blind deconvolution is a mathematical method to clarify a blurred image without knowledge of the original image, or how it was blurred. Top, original image; bottom, blurred image after blind deconvolution (Original image by Steve Byland).
Threat detection involves math at a range of levels, said Professor Thomas Strohmer, who leads the project. It can include quickly processing large amounts of data, coordinating multiple sensors, or extracting clarity from background noise.
Full post: NSF Grant Funds Math For National Security
(455 words, 1 image, estimated 1:49 mins reading time)
Hobby 3-D Printing Leads to New Insights into Moving Sofa Problem
By Becky Oskin
Most of us have struggled with the mathematical puzzle known as the “moving sofa problem.” It poses a deceptively simple question: What is the largest sofa that can pivot around an L-shaped hallway corner?
A mover will tell you to just stand the sofa on end. But imagine the sofa is impossible to lift, squish or tilt. Although it still seems easy to solve, the moving sofa problem has stymied math sleuths for more than 50 years. That’s because the challenge for mathematicians is both finding the largest sofa and proving it to be the largest. Without a proof, it’s always possible someone will come along with a better solution.
With gold medals in three sprinting events at three Olympic Games, Usain Bolt has written himself into the record books as arguably the fastest human of all time. But just how fast is the Jamaican sprinter?
Three mathematicians, Sebastian Schreiber of UC Davis, Wayne Getz of UC Berkeley and Karl Smith of Santa Rosa Junior College, show how to calculate Bolt’s maximum velocity in the 100 meters at the 2008 Beijing Olympics in their 2014 textbook, “Calculus for the Life Sciences.”
This plot shows Usain Bolt’s velocity measured at 10 meter intervals.
Full post: Calculating just how fast Usain Bolt runs
(331 words, 3 images, estimated 1:19 mins reading time)