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Mathematicians Cross the Line to Get to the Point
A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.
The Physical Process That Powers a New Type of Generative AI
Some modern image generators rely on the principles of diffusion to create images. Alternatives based on the process behind the distribution of charged particles may yield even better results.
‘Species Repulsion’ Enables High Biodiversity in Tropical Trees
Because tree seedlings don’t grow as well when close to their parents, more tree species can be packed into tropical forests.
A Tower of Conjectures That Rests Upon a Needle
On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.
How Scientists Are Tackling the Tricky Task of Solar Cycle Prediction
Scientists have struggled to accurately forecast the strength of the sun’s 11-year cycle — even after centuries of solar observations.
Alan Turing and the Power of Negative Thinking
Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.
The Usefulness of a Memory Guides Where the Brain Saves It
New research finds that the memories useful for future generalizations are held in the brain separately from those recording unusual events.
New Codes Could Make Quantum Computing 10 Times More Efficient
Quantum computing is still really, really hard. But the rise of a powerful class of error-correcting codes suggests that the task might be slightly more feasible than many feared.
The AI Tools Making Images Look Better
Researchers have discovered ways around a fundamental trade-off between accuracy and beauty in digital images.