dfa2

Dfa Long-Term Scaling Exponent Alpha2

Definition

DFA long-term scaling exponent alpha2. Formally: alpha2 from DFA (scales 4-64).

What does normal look like?

Fitted normative prior: Normal(μ = 0.9749, σ = 0.2498), KS p = 5e-30, 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

• Long-term fractal scaling exponent α2 of the RR series (Peng et al. 1995).
• Ageing and cardiac-disease fractal-breakdown studies.
• Report with α1 and adequate record length.

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

The DFA mortality literature is overwhelmingly about the short-term exponent α1 (dfa1); where studies additionally measured the long-term exponent α2, evidence is thin and inconsistent. One ESRD cohort measured α2 alongside α1 and found it carried no significant mortality effect once α1 was accounted for; one elderly community cohort (LILAC) reported both α1 and α2 associated with mortality without isolating which exponent drove the effect. No dedicated α2 meta-analysis or systematic review exists.

Dominant reported direction: weak/mostly null: α2 rarely reaches significance on its own; no independent α2 effect size is established in the harvested literature.

Key references: (Sen and McGill, 2018).

Sports & peak performance

Coverage: sparse or none. Essentially no dedicated application literature found.

The DFA-based aerobic/anaerobic exercise-threshold research program is specifically built on the short-term exponent α1 (declining from ~1.5 at rest toward ~0.5 near exhaustion); none of the harvested threshold-detection studies isolate α2 as a distinct sports metric, so no application evidence was harvested for α2 in this domain.

Dominant reported direction: no data harvested for this domain.

Contemplative practice

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

One small study (deep-meditation practitioners) explicitly measured both α1 and α2 and reported a contrary, significant increase in both during deep meditation; the broader meditation-DFA literature synthesized in the review below is otherwise dominated by α1-only findings, so this single α2 data point cannot establish a reliable direction.

Dominant reported direction: unresolved: one small study reports an increase; otherwise essentially unstudied.

Key references: (Deka and Deka, 2023).

The strong prognostic DFA evidence in the literature is specific to the short-term exponent α1 (dfa1): α2 (long-term) associations are weak, inconsistent, or explicitly non-significant in the harvested literature; treat any "lower DFA exponent → higher mortality" claim you encounter elsewhere as an α1 claim, not an α2 one, unless the source specifically isolates α2.

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 ◍◍◍◍◌ 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). Warm (shared representation cached) is 1018× cheaper.

Citation

Long-term scaling exponent α2, Peng et al. (1995); DFA algorithm, Peng et al. (1994); window convention Francis et al. (2002); age-related range Iyengar et al. (1996).

Seminal reference(s): (Peng et al., 1995); (Peng et al., 1994); (Francis et al., 2002); (Iyengar et al., 1996).

See the References page for the full bibliography.