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graph theory

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graph theory

New Proof Shows That ‘Expander’ Graphs Synchronize

By Leila Sloman
July 24, 2023
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The proof establishes new conditions that cause connected oscillators to sway in sync.

Quantized Academy

Math That Lets You Think Locally but Act Globally

By Patrick Honner
July 21, 2023
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Knowing a little about the local connections on flight maps and other networks can reveal a lot about a system’s global structure.

Illustration of a lady walking through a hedge maze, with a man sweeping up her footprints.
quantum computing

To Move Fast, Quantum Maze Solvers Must Forget the Past

By Ben Brubaker
July 20, 2023
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Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.

geometry

Mathematicians Solve Long-Standing Coloring Problem

By Anna Kramer
July 19, 2023
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A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

Ramsey theory

The Lawlessness of Large Numbers

By Leila Sloman
July 7, 2023
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Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

An observer times birds flying between an apple tree and an orange tree that look like graphs.
computational complexity

Computer Scientists Inch Closer to Major Algorithmic Goal

By Kevin Hartnett
June 23, 2023
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A new paper finds a faster method for determining when two mathematical groups are the same.

graph theory

Mathematicians Discover Novel Way to Predict Structure in Graphs

By Jordana Cepelewicz
June 22, 2023
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Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

An illustration of a honeycomb-shaped molecular mosaic. Formed by a six-sided molecule, the hexagonal mosaic is a pattern within a pattern, with multiple levels of organization.
materials science

The Simple Geometry That Predicts Molecular Mosaics

By Elise Cutts
June 21, 2023
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By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.

A video depiction of shifting boundaries in Colorado illustrates the endless possibilities for drawing Congressional districts.
applied math

How Math Has Changed the Shape of Gerrymandering

By Mike Orcutt
June 1, 2023
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New tools make it possible to detect hidden manipulation of maps.


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