On the excursion area of perturbed Gaussian fields

We investigate Lipschitz-Killing curvatures for excursion sets of random fields on ℝ2 under a very specific perturbation, namely a small spatial-invariant random perturbation with zero mean. An expansion formula for mean curvatures is derived when the magnitude of the perturbation vanishes, which recovers the Gaussian Kinematic Formula at the limit by contiguity of the model. We develop an asymptotic study of the perturbed excursion area behaviour that leads to a quantitative non-Gaussian limit theorem, in Wasserstein distance, for fixed small perturbations and growing domain. When letting both the perturbation vanish and the domain grow, a standard Central Limit Theorem follows. Taking advantage of these results, we propose an estimator for the perturbation variance which turns out to be asymptotically normal and unbiased, allowing to make inference through sparse information on the field.

Nature of cross-talk transitions and ΔI = 1 energy staggering in signature partners of odd mass superdeformed nuclei

Two-way cross-talk transitions between pairs of signature partners superdeformed (SD) bands in [Formula: see text]Hg (SD2,SD3), [Formula: see text]Hg (SD3,SD4) and [Formula: see text]T1(SD1,SD2) built on the configurations [Formula: see text], respectively, are proposed. The [Formula: see text] energy staggering presented in these odd SD nuclei are investigated and parametrized by proposing two staggering functions depending on the dipole transitions linking the signature partners. These staggering functions differ from the conventional staggering functions employed in previous works which depend on the quadruple transitions within each band. For parametrization, we used the two-term formula of Bohr–Mottelson collective rotational model. The model parameters and the bandhead spins of the considered signature partners are determined by using a simulated fitting search program and the values of the adopted parameters are used to calculate transition energies [Formula: see text], rotational frequencies [Formula: see text], kinematic [Formula: see text] and dynamic [Formula: see text] moments of inertia. The calculated results agree very well with the experimental ones. The bands exhibit the usual increasing trend. Large amplitude staggering has been found in the considered three signature partner pairs in [Formula: see text]Hg and [Formula: see text]T1 nuclei.

Cosmological Applications of the Gaussian Kinematic Formula

The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for cosmological data collections. In this paper, we implement Minkowski functionals on multipoles and needlet components of CMB fields, thus allowing a better control of cosmic variance and extraction of information on both harmonic and real domains; we then exploit the GKF to provide their expected values on spherical maps, in the presence of arbitrary sky masks, and under nonGaussian circumstances.