Question
Rose Yu led the development of a 2023 generative adversarial network, or GAN, for the discovery of these properties. For 10 points each:
[10m] Name these properties that correspond to elements of certain groups, like the Lorentz group. Noether's ("NURR-tuh's") theorem relates conservation laws to these properties.
ANSWER: symmetries [or symmetry; accept continuous symmetries of the action]
[10h] The GAN is named for this mathematician's "theory." The exponential map connects this mathematician's namesake algebra to groups that behave as differentiable manifolds.
ANSWER: Sophus Lie ("LEE") [or Marius Sophus Lie; accept Lie algebra]
[10e] By studying N-body simulations, LieGAN rediscovered the restricted Lorentz group and the group of these transformations. In this transformation, an object moves around its own axis.
ANSWER: rotations [accept rotate or rotating]
<Science - Physics>
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| Adlai E. Stevenson A | Innovation Academy A | 0 | 0 | 10 | 10 |
| Audrain County AT | Montgomery Blair A | 10 | 0 | 10 | 20 |
| Detroit Catholic Central A | Strake Jesuit A | 0 | 0 | 10 | 10 |
| Fremd | Thomas Jefferson A | 10 | 10 | 10 | 30 |
| Hinsdale Central A | Lindbergh | 10 | 0 | 10 | 20 |
| Hunter A | Lexington | 0 | 0 | 10 | 10 |
| Johns Creek | Eastchester | 0 | 0 | 10 | 10 |
| Lambert A | Northview | 0 | 0 | 10 | 10 |
| Richard Montgomery | Northmont | 10 | 0 | 10 | 20 |
| Strake Jesuit B | Alabama Cyber Tech | 10 | 0 | 10 | 20 |
| Uni of Illinois Laboratory | Belmont | 0 | 0 | 10 | 10 |
| Walter Payton A | Westwood | 0 | 0 | 10 | 10 |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2025 PACE NSC | 06/07/2025 | Y | 12 | 15.00 | 100% | 42% | 8% |