Backyard STEM

This is the first in what will hopefully be an intermittent series of appreciation posts of other people's papers. Here it goes: One of the big statistical problems during the COVID pandemic was that the official case counts were never the whole story. The number reported each day depended not only on how many people were actually infected, but also on how many were tested, how quickly laboratories processed samples, and how public health systems recorded cases. In other words, the observed data were only a partial and noisy picture of the real epidemic. This is exactly the kind of problem state-space models, or SSMs, are designed to handle. In the 2020 work of Fernández-Fontelo, Moriña, Cabaña, Arratia, and Puig, the main idea was to separate the epidemic into two layers: a hidden layer representing the true number of infections, and an observed layer representing the reported ...

  Applied math has various definitions depending on the person. We will list and study the prominent definitions, as understanding what applied math is—or should be—directly informs the vision and mission of an applied math community. Applied Math as a Lubricant for Science and Engineering Some view applied math as a lubricant that facilitates the progress of other sciences. In this perspective, a biologist might provide experimental data to an applied mathematician in order to add resolution and certainty to their observations. For example, in a  2022 Open Biology paper , we studied the motion reversal behavior of algae called diatoms. Using stochastic differential equations and asymptotic methods, we explained how this behavior enhances the diatom’s diffusion and spreading. While biologists could have empirically reached this conclusion by comparing diatoms that reverse direction more often to those that reverse less frequently, we helped them reach the conclusion more ...

The news these days is filled with the tit-for-tat conflict between Israel and Iran. Both countries are volleying missiles at each other while the defending nation is using some means to intercept and destroy said missiles. Israel in particular is known for its Iron Dome, a mobile air defense system. During a 2014 war the Iron Dome was said to be nearly 90% effective. The idea of such an air defense system is currently being contemplated by the US and Canada. Obviously, any nation would love to simply zap all missiles coming their way. But how does one build an Iron Dome? Well, there is a lot that goes into building it (primary among which might be money) but let’s focus on one aspect: how does the interceptor catch up with the missile? To answer this question, we delve into the math of pursuit curves. Pursuit curves describe the path taken by a pursuer/chaser that is always moving directly toward a moving target. Let the pursuer’s position be given by \( \vec{P}\) and the targe...