Measure gradient variance ⟨(∂C/∂θᵢ)²⟩ as a function of qubit count n (4-24) for 3 ansatz types: hardware-efficient (HEA, random 2-qubit gates), chemistry-inspired (UCCSD), and QAOA. HEA: variance decays as 2^{-2n} (barren plateau at n≈12).
Simulate random Clifford circuits (up to 256 qubits) with variable measurement rate p (fraction of qubits measured per layer). Entanglement entropy S_A of half-chain: at p=0 (no measurement), S_A scales as volume law S_A ∝ L.
Analyze MODIS land surface temperature (LST) for 2,000 cities globally (2003-2023). UHI intensity (ΔT between urban core and rural surroundings) vs log(population).
Compare LSTM, Transformer, GRU, random forest against simple persistence (forecast = current value) for 1-min to 60-min ahead wind speed at 5 NREL stations (3 years data). Persistence outperforms all ML methods for horizons ≤15 min (RMSE ratio ML/persistence > 1.
Record AE events during uniaxial compression of glass (brittle), concrete (quasi-brittle), and alumina ceramics. Waiting time distributions: glass follows exponential (Poisson process, KS p=0.
Apply 5 TI methods (Monocle3, Slingshot, PAGA, Palantir, scVelo) to 3 gold-standard datasets with known ground truth (synthetic + lineage tracing). Pairwise Kendall τ between pseudotime orderings: mean 0.
Evaluate pose ranking for 285 CASF-2016 complexes using AutoDock Vina rescored with AMBER ff14SB, CHARMM36, and OPLS-AA/M force fields. The top-ranked pose agrees between force fields in only 41% of cases.
Quantify phylogenetic signal (Fritz-Purvis D statistic and Pagel's λ) across evolutionary rate classes in SARS-CoV-2, Influenza A/H3N2, and HIV-1. Signal decays exponentially with substitution rate: λ(r) = exp(-4.