Pseudo-nonstationarity in the scaling exponents of finite-interval time series

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents computed from an interval of N observations is known for finite variance processes to vary as ~1/N as N for certain statistical estimators; however, the convergence to this behavior will depend on the details of the process, and may be slow. We study the variation in the scaling of second-order moments of the time-series increments with N for a variety of synthetic and “real world” time series, and we find that in particular for heavy tailed processes, for realizable N, one is far from this ~1/N limiting behavior. We propose a semiempirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents for model stochastic processes and compare these with some “real world” time series

Delayed Germination of Seeds: A Look at the Effects of Adult Longevity, the Timing of Reproduction, and Population Age/Stage Structure

The effects of adult longevity, the timing of reproduction, and population age/stage structure on the evolution of seed dormancy are explored in both constant and variable environment models. In the constant environment models complete germination is the evolutionarily stable strategy (ESS) regardless of adult longevity. Incorporating a cost of reproduction on subsequent survival does not alter this result. In contrast, in a variable environment changes in adult longevity can exert a strong selection pressure against seed dormancy. Incorporating a cost of reproduction for iteroparous species reduces adult longevity, which selects for more seed dormancy. The magnitude of the change in ESS germination probability depends on several factors, including which life-history stage is variable (e.g., fecundity, seedling survival), whether seeds can detect favorable sites for establishment, and the age/stage structure of the population. In general, increases in adult longevity select against seed dormancy, but exceptions to this pattern are discussed. The idea that established plant traits are uncoupled from those of the regenerative phase, as assumed by J. P. Grime's competition-stress-ruderal model, is considered critically

Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems

We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for Lipschitz continuity known in the uniformly elliptic one and provide a unified approach between non-uniformly and uniformly elliptic problems