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Test 4 GI heuristics (1-WL, 2-WL, VF2, nauty) on 15 families of strongly regular graphs (SRGs) with parameters (v,k,λ,μ). 1-WL fails to distinguish non-isomorphic SRGs in 100% of tested pairs (by construction).
Study χ(G(n,r)) for n=100-10000 nodes uniformly in [0,1]² with connection radius r chosen at the connectivity threshold r_c = √(ln n / (πn)). Empirically: χ concentrates around c·√(n/ln n) with c=1.
Compute Ramsey numbers R(K_{s,t}, K_{s,t}) for s,t ≤ 8 via SAT solving and ILP. The growth rate exhibits a sharp transition: for t/s < 0.
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 surface codes (d=3-21) with 4 decoders: MWPM (minimum weight perfect matching), Union-Find, neural network, and lookup table. Standard threshold (assuming instant decoding): 10.
Run VQE (UCCSD ansatz) on statevector simulator and noisy simulator for H₂, H₃⁺, H₄, H₆, H₈, LiH, BeH₂. Noiseless VQE achieves chemical accuracy (1.
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.
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.
Evaluate 4 preprocessing pipelines (fMRIPrep, FSL, SPM, AFNI) × 3 classifiers (SVM, random forest, MLP) on HCP working memory task (200 subjects). Main effect of pipeline: F(3,2388)=47.
Compare SASA calculations from FreeSASA, NACCESS, PyMOL, VMD, and DSSP on 500 PDB structures. Mean pairwise coefficient of variation: 15.
Correlate AlphaFold2 pLDDT scores with experimental binding affinities (Kd/Ki/IC50) from PDBbind v2020 refined set (4,852 complexes). Overall Pearson correlation: r=0.
Compare Cellpose, StarDist, Mesmer, DeepCell, ACDC on 10 tissue types (H&E, 2000 images). Overall Dice agreement 0.
Compare GRCh38, T2T-CHM13, and HPRC pangenome reference on GTEx v8 data (838 samples, 49 tissues). 15.
Compare 5 SV callers (Manta, Delly, GRIDSS, Sniffles, cuteSV) on GIAB HG002 truth set. Insertions >1kb: pairwise concordance 38-47%.
SNNs promise energy efficiency via sparse spike trains, but accuracy requires sufficient timesteps, creating a latency-accuracy tradeoff. We characterize this for 8 SNN architectures on CIFAR-10/100 and DVS-Gesture at timesteps 1-128.
The sim-to-real transfer gap is assumed to grow with task complexity, but we find a U-shaped relationship. Across 6 manipulation tasks (reaching, pushing, pick-and-place, stacking, insertion, bimanual assembly) with 5 domain randomization levels on Franka Emika: simple tasks transfer well (gap 8-12%), moderate tasks show maximum gap (28-41%), complex tasks show reduced gap (18-24%).
In cooperative MARL, free-riding agents contribute minimally while benefiting from team rewards. We propose Shapley Contribution Tracking (SCT) using online Shapley value approximation.
Multi-agent LLM systems chain multiple model instances via natural language, but scaling properties are unknown. We study 2-16 agents across four patterns (sequential, broadcast, hierarchical, peer-to-peer).
Fault-tolerant LLM training requires periodic checkpointing. We analyze the cost structure across 64-4,096 GPUs, comparing checkpoint overhead against failure recovery cost.