fuzzyen

Fuzzy Entropy Of The Inter-Beat-Intervals (Ibis).

Definition

Calculate the fuzzy entropy of the Inter-Beat-Intervals (IBIs).

What does normal look like?

Fitted normative prior: Normal(μ = 2.143, σ = 0.4106), KS p = 1.7e-18, n = 61715.

Empirical distribution over the pooled nsrdb+nsr2db normative windows (360-beat windows, 120-beat stride), overlaid with the fitted Normal prior density. Vertical lines mark the median and the 5–95% range.

Normal-range summary (pooled nsrdb+nsr2db)

n varies by feature only through per-window validity over the full pooled nsrdb+nsr2db table (n up to 61 715; e.g. sampen/mse drop windows where the statistic is undefined). ulf is the one exception: a 360-beat (~5 min) window contains no ULF-band power, so it uses a long-window NSRDB-only extraction (see its own page).

Use cases

• Smoother, more consistent complexity estimate than SampEn on short/noisy records.
• Robustness to parameter and threshold choice.
• Nonlinear autonomic-control research.

Applications by area

Evidence is reported at the measure-family level; a specific variant may not be the exact index measured in every cited study.

Clinical

Coverage: statistics. A pooled literature; reviews or meta-analyses exist.

Genuinely common here: a 2026 PRISMA review found 55 studies (2011–2025) applying fuzzy/Shannon/spectral/SVD/permutation/multiscale entropy, concentrated in diabetes, cardiovascular disease and neurological conditions, with classification accuracies up to 92.5%. The dominant direction is lower entropy/complexity in disease: with one notable reversal (higher multiscale entropy predicted incident stroke in atrial fibrillation).

Dominant reported direction: down: lower entropy/complexity in disease (one AF-stroke reversal).

Key references: (Yang et al., 2026).

Sports & peak performance

Coverage: individual papers. A small, scattered literature with no pooled meta-analysis.

Uncommon: no dedicated meta-analyses exist, and a 2025 systematic review of 19 soccer-overtraining studies found none used any nonlinear/entropy index at all. The handful of small papers that do exist (n = 9–27, sometimes animal models) give mixed directions.

Dominant reported direction: mixed / essentially unstudied.

Key references: (Yang et al., 2026).

Contemplative practice

Coverage: individual papers. A small, scattered literature with no pooled meta-analysis.

One dedicated review (26 studies) covers Shannon/ApEn/SampEn/permutation/Renyi/multiscale entropy in meditation/yoga: most studies report reduced complexity during meditation, but this is not unanimous (some report increases, especially multiscale entropy at long scales), and effect sizes are frequently small/non-significant.

Dominant reported direction: mostly down, with scale- and measure-dependent exceptions.

Key references: (Deka and Deka, 2023).

See the effect-distribution meta-analysis page for the harvested per-study effect sizes/p-values behind these domain summaries (docs/zoo_gen/effect_stats.csv).

Resources

Resource-intensity rank ◍◍◍◍◍ very high is measured: median wall-clock time and allocations over a 360-beat window on synthetic realistic RR (docs/zoo_gen/bench_resources.jl; full grid in resource_bench.csv).

Cold = fresh memoization caches (builds every shared representation from scratch); warm = shared representations (diff, periodogram, Poincaré coords, DFA fluctuation) already cached, so only this feature is recomputed. The tier is derived from the cold cost; see Nonlinear subgraph (template matching / embedding — O(N²) worst case).

Citation

Fuzzy entropy, Chen et al. (2007), replacing SampEn's hard threshold with a fuzzy membership.

Seminal reference(s): (Chen et al., 2007).

See the References page for the full bibliography.