We compute Gini coefficients for 87 countries from Luxembourg Income Study microdata under 5 alternative top-income imputation methods: raw survey, Pareto tail replacement at the 95th percentile, Pareto tail replacement at the 99th percentile, log-normal tail fitting, and tax-data calibration. The mean Gini swing across methods is 3.
We construct the smallest known graded Artinian Gorenstein algebras whose Hilbert functions fail to be unimodal. In codimension 5 we exhibit an algebra with Hilbert function (1, 5, 15, 34, 55, 53, 55, 34, 15, 5, 1), featuring a dip at degree 5 that violates unimodality.
We train 480 models spanning 8 architectures, 6 RandAugment magnitude levels, and 10 random seeds on ImageNet-1K to measure the architecture-specific augmentation saturation point (ASP). CNNs reach saturation at magnitude 9, while Vision Transformers saturate later at magnitude 14.
Analog-to-digital converter datasheets report effective number of bits (ENOB), but this single figure conceals a nonlinear transition in how quantization noise accumulates as resolution increases. We define the Quantization Degradation Index (QDI) as the gap between ideal and measured signal-to-noise ratio and characterize it across a full factorial design of 7 converter architectures, 5 signal types, 9 resolutions (4 to 20 bits), and 9 oversampling ratios (1x to 256x), totalling 2,835 configurations tested in calibrated simulation.
Backtesting Value-at-Risk (VaR) models conventionally counts how many exceedances occur in a window and checks whether the count matches the nominal rate. This approach discards all information about when exceedances happen relative to each other.
Minor surface-level changes to a prompt — synonym substitution, whitespace adjustment, instruction reordering — can shift large language model accuracy by double-digit percentage points, yet no quantitative law describes how this fragility evolves with the number of in-context examples. We define the Prompt Sensitivity Index (PSI) as the standard deviation of accuracy across 50 semantically equivalent rephrasings of the same prompt template and measure it for 6 LLMs on 4 benchmarks at 7 context lengths from zero-shot to 32-shot.
Optimal growth temperature (OGT) shapes every level of molecular composition in prokaryotes, yet the strongest genomic predictors reported so far — whole-genome GC content, dinucleotide frequencies, amino acid composition — plateau around R-squared 0.3 to 0.
Purchasing-power parity (PPP) models commonly predict real effective exchange rates (REER) using variables derived from price-level comparisons, creating a methodological circularity that inflates goodness-of-fit. We introduce the PPP Residual Decomposition (PPP-RD), a two-stage framework that (1) predicts REER using four strictly non-circular macroeconomic fundamentals (trade openness, commodity export share, institutional quality, and inflation differential) via gradient boosted trees, and (2) decomposes prediction residuals into structural and cyclical components using wavelet time-frequency separation.
The modified Omori law, the standard model for earthquake aftershock decay, implicitly assumes proportional hazards: that the ratio of aftershock rates between different magnitude classes remains constant over time. We introduce the Hazard Crossover Audit (HCA), a four-gate diagnostic framework that systematically tests this assumption using nonparametric survival analysis.
The number of tRNA gene copies per amino acid varies widely across bacterial genomes, and the dominant explanation attributes this variation to translational selection. We test this hypothesis by introducing the Drift-Selection Ratio (DSR), a statistic comparing observed tRNA copy number variance to the variance expected under a neutral birth-death process calibrated to each genome.
The minimum dominating set problem in Kneser graphs K(n,k) is a classical question in combinatorial optimization, yet the monotonicity of the domination number gamma(K(n,k)) in n for fixed k has remained unresolved for k >= 3. We introduce the Spectral Degeneracy Index (SDI), defined as the ratio of the second-largest eigenvalue to the algebraic connectivity, and prove that non-monotonicity of gamma occurs precisely when SDI exceeds an explicitly computable threshold tau_k.
Subword tokenizers underpin every modern language model, yet their coverage characteristics across the world's languages remain poorly quantified. We introduce the Fertility-Gap Predictor (FGP), a diagnostic framework that exactly enumerates the character-to-subword mapping for every Unicode codepoint attested in 47 languages across 8 widely deployed tokenizers (GPT-4 cl100k, LLaMA-3 tiktoken, Gemma SentencePiece, Mistral SentencePiece, BLOOM BPE, mBERT WordPiece, XLM-R SentencePiece, and Qwen BPE).
Implement Jegadeesh-Titman (1993) 12-1 momentum strategy on CRSP data (1990-2023), stratified into 3 market cap tiers: large (>$10B), mid ($500M-$10B), small (<$500M). Gross returns: large 0.
Backtest Almgren-Chriss (AC) optimal execution vs TWAP on 200 US equities over 24 months, stratified by liquidity (ADV percentile). Above 50th percentile ADV: AC outperforms TWAP by 3.
Evaluate 5 systemic risk indicators (CoVaR, SRISK, MES, DCC-GARCH volatility, credit-to-GDP gap) as early warning signals for 5 crises: 1997 Asian, 2000 dot-com, 2008 GFC, 2011 European debt, 2020 COVID. Success criterion: indicator exceeds 90th historical percentile ≥3 months before crisis onset.
Evaluate 3 credit risk models (logistic regression, XGBoost, neural network) on a loan portfolio (N=120,000) under 3 default definitions: 90 days past due (DPD90, Basel standard), 180 DPD, and 60 DPD. Model rankings change: at DPD90, XGBoost leads (AUC=0.
Train ECAPA-TDNN speaker verification on VoxCeleb2 with 4 augmentation strategies: none, noise-only (MUSAN), reverb-only (simulated RIR), full (noise+reverb+speed). Test on VOiCES corpus at 5 RT60 conditions (0.
Evaluate 3 segmentation models (nnU-Net, Swin-UNETR, TransUNet) on 4 organs (liver, kidney, pancreas, spleen) from Medical Segmentation Decathlon. Compute Dice, 95th-percentile Hausdorff Distance (HD95), Average Surface Distance (ASD), and Normalized Surface Dice (NSD).
Benchmark 5 QP solvers (OSQP, qpOASES, Gurobi, ECOS, CVXPY+SCS) on MPC problems with horizon N=5-200 for 3 system dimensions (2-state, 10-state, 50-state). Computation time t(N): theoretical O(N³) for dense QP.
Compare 5 PID tuning methods (Ziegler-Nichols ZN, Cohen-Coon CC, IMC, SIMC, autotuning relay) on 8 nonlinear plant models (pH neutralization, exothermic CSTR, inverted pendulum, ball-and-beam, hydraulic servo, thermal process, bioreactor, DC motor with backlash). Performance metric: IAE (integral absolute error) normalized to optimal PID (found via Bayesian optimization).