Question
The Barabasí-Albert model generates networks with an approximate form of this property. For 10 points each:
[10h] Give this property of systems that look the same under arbitrary magnification, which is stronger than self-similarity. Many real-world networks, like the Internet, are assumed to have an approximate form of this property, characterized by a few highly-connected hubs.
ANSWER: scale-invariant [accept scale-free network; accept, but DO NOT REVEAL, power law network]
[10m] These functions are the only scale-invariant functions, so they characterize the degree distribution of scale-free networks and fluctuations in systems at phase transitions. These functions take the form “C times x to the negative alpha.”
ANSWER: power laws
[10e] Power law distributions for observables are characteristic of physical states with this property. A “point” named for this property lies at the endpoint of a phase boundary, at which liquid and vapor are indistinguishable.
ANSWER: critical [accept critical point]
<VD, Physics>
Summary
| 2023 ARCADIA at UC Berkeley | Premiere | Y | 2 | 25.00 | 100% | 50% | 100% |
| 2023 ARCADIA at Carleton University | Premiere | Y | 3 | 6.67 | 67% | 0% | 0% |
| 2023 ARCADIA at Claremont Colleges | Premiere | Y | 1 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at Indiana | Premiere | Y | 5 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at RIT | Premiere | Y | 2 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at WUSTL | Premiere | Y | 3 | 6.67 | 67% | 0% | 0% |
Data
| Syracuse+Rochester | Cornell MATLAB | 0 | 0 | 10 | 10 |
| Cornell R | RIT | 0 | 0 | 10 | 10 |