For decades, the motions of stars near the center of our Milky Way Galaxy have been treated as some of the clearest evidence for a supermassive black hole.
All life on Earth shares a common ancestor that lived roughly four billion years ago. This so-called “last universal common ancestor” (LUCA) represents the most ancient organism that researchers can study. Previous research on the last universal common ancestor has found that all the characteristics we see in organisms today, like having a cell membrane and a DNA genome, were already present by the time of this ancestor. So, if we want to understand how these foundational characteristics of life first emerged, then we need to be able to study evolutionary history prior to the last universal common ancestor.
In an article published in the journal Cell Genomics, scientists Aaron Goldman (Oberlin College), Greg Fournier (MIT), and Betül Kaçar (University of Wisconsin‑Madison) describe a method to do just that.
“While the last universal common ancestor is the most ancient organism we can study with evolutionary methods,” said Goldman, “some of the genes in its genome were much older.” The authors describe a type of gene family known as a “universal paralog,” which provides evidence of evolutionary events that occurred before the last universal common ancestor.
Despite decades of research, the mechanisms behind fast flashes of insight that change how a person perceives their world, termed “one-shot learning,” have remained unknown. A mysterious type of one-shot learning is perceptual learning, in which seeing something once dramatically alters our ability to recognize it again.
The trajectory of a storm, the evolution of stock prices, the spread of disease — mathematicians can describe any phenomenon that changes in time or space using what are known as partial differential equations. But there’s a problem: These “PDEs” are often so complicated that it’s impossible to solve them directly.
Mathematicians instead rely on a clever workaround. They might not know how to compute the exact solution to a given equation, but they can try to show that this solution must be “regular,” or well-behaved in a certain sense — that its values won’t suddenly jump in a physically impossible way, for instance. If a solution is regular, mathematicians can use a variety of tools to approximate it, gaining a better understanding of the phenomenon they want to study.
But many of the PDEs that describe realistic situations have remained out of reach. Mathematicians haven’t been able to show that their solutions are regular. In particular, some of these out-of-reach equations belong to a special class of PDEs that researchers spent a century developing a theory of — a theory that no one could get to work for this one subclass. They’d hit a wall.