We study four different approaches to model time-dependent extremal behavior: dynamics introduced by (a) a state-space model (SSM), (b) a shot-noise-type process with GPD marginals, (c) a copula-based autoregressive model with GPD marginals, and (d) a GLM with GPD marginals (and previous extremal events as regressors). Each of the models is fit against data, and from the fitted data, we simulate corresponding paths according to the respective fitted models. At this simulated data, the respective dependence structure is analyzed in copula plots and judged against its capacity to fit the corresponding inter-arrival distribution.

It has been established in Schwarzschild spacetime (and more generally in Kerr spacetime) that pairs of geometrically different timelike geodesics with the same radial and azimuthal frequencies exist in the strong field regime. The occurrence of this socalled isofrequency pairing is of relevance in view of gravitational-wave observations. In this paper we generalize the results on isofrequency pairing in two directions. Firstly, we allow for a (positive) cosmological constant, i.e., we replace the Schwarzschild spacetime with the Schwarzschild-de Sitter spacetime. Secondly, we consider not only spinless test-particles (i.e., timelike geodesics) but also test-particles with spin. In the latter case we restrict to the case that the motion is in the equatorial plane with the spin perpendicular to this plane. We find that the cosmological constant as well as the spin have distinct impacts on the description of bound motion in the frequency domain.

We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus, in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions.