chi squared distribution

A disease outbreak is like a wildfire: the fire runs through dry grass, and its speed depends on wind and humidity. But an infection has its own 'wind'—how often people infect each other. When this rate changes along with the fraction of already infected, the epidemic wave can behave differently.

4 610 universes — that's exactly how many cosmological models astrophysicists needed to show that the familiar Gaussian mask no longer works for next-generation data. Future sky surveys, such as the Euclid mission and the Vera C.

The standard approach to a certain class of machine learning problems is like a spring that's been stretched and then forgotten: standard methods artificially inflate the problem's size, turning computations into a black hole for memory and time.

Two black holes spiraling toward each other resemble figure skaters in a pair spin: each rotates about its own axis, and together they weave a shared dance. This collective twist, the so-called effective spin, can be measured by astronomers from the gravitational waves rippling outward from the pair, like ripples on a pond.

Spread a handful of coins on the table. Each coin is a possible outcome: heads, tails, or something else. If we know how chaotic this set is (its entropy), which combinations of probabilities will we encounter more often? It turns out the answer depends on how much chaos we allow.

Toss a dozen coins on a table. The number of heads-and-tails combinations is just over a thousand. For two dozen coins, it's already a million. The number grows as 2 to the power of the number of coins, and that's fast. But quantum systems are far richer. Each particle here is not a coin with two sides but an arrow that can point in any direction.

A quantum walk is like a drunk person who turns randomly at every intersection. Except instead of streets, there are graph nodes, and instead of steps, there are quantum transitions. Scientists have discovered that such a walk has a hidden measure — Krylov complexity.

The birth of the Universe is usually associated with the Big Bang — a point of infinite density. But at that point, the laws of physics break down, which bothers scientists. Stephen Hawking and James Hartle back in the 1980s proposed a different view: time has no boundary, like the surface of a globe.