Gaussian Random Measures Generated by Berry’s Nodal Sets

We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry’s random wave model to a finite collection of (possibly overlapping) smooth compact subsets of R2. Our main result shows that, as the energy diverges to infinity and after an adequate normalisation, these random elements converge in distribution to a Gaussian vector, whose covariance structure reproduces that of a homogeneous independently scattered random measure. A by-product of our analysis is that, when restricted to rectangles, the dominant chaotic projection of the nodal length field weakly converges to a standard Wiener sheet, in the Banach space of real-valued continuous mappings over a fixed compact set. An analogous study is performed for complex-valued random waves, in which case the nodal set is a locally finite collection of random points

Fourth moment theorems on the Poisson space in any dimension

We extend to any dimension the quantitative fourth moment theorem on the Poisson setting, recently proved by C. Döbler and G. Peccati (2017). In particular, by adapting the exchangeable pairs couplings construction introduced by I. Nourdin and G. Zheng (2017) to the Poisson framework, we prove our results under the weakest possible assumption of finite fourth moments. This yields a Peccati-Tudor type theorem, as well as an optimal improvement in the univariate case. Finally, a transfer principle “from-Poisson-to-Gaussian” is derived, which is closely related to the universality phenomenon for homogeneous multilinear sums

Measurement of change in health status with Rasch models

Background: The traditional approach to the measurement of change presents important drawbacks (no information at individual level, ordinal scores, variance of the measurement instrument across time points), which Rasch models overcome. The article aims to illustrate the features of the measurement of change with Rasch models. Methods: To illustrate the measurement of change using Rasch models, the quantitative data of a longitudinal study of heart-surgery patients (N=98) were used. The scale "Perception of Positive Change" was used as an example of measurement instrument. All patients underwent cardiac rehabilitation, individual psychological intervention, and educational intervention. Nineteen patients also attended progressive muscle relaxation group trainings. The scale was administered before and after the interventions. Three Rasch approaches were used. Two separate analyses were run on the data from the two time points to test the invariance of the instrument. An analysis was run on the stacked data from both time points to measure change in a common frame of reference. Results of the latter analysis were compared with those of an analysis that removed the influence of local dependency on patient measures. Statistics t, \u3a72 and F were used for comparing the patient and item measures estimated in the Rasch analyses (a-priori \u3b1=.05). Infit, Outfit, R and item Strata were used for investigating Rasch model fit, reliability, and validity of the instrument. Results: Data of all 98 patients were included in the analyses. The instrument was reliable, valid, and substantively unidimensional (Infit, Outfit<2 for all items, R=.84, item Strata range=3.93-6.07). Changes in the functioning of the instrument occurred across the two time, which prevented the use of the two separate analyses to unambiguously measure change. Local dependency had a negligible effect on patient measures (p 65.8674). Thirteen patients improved, whereas 3 worsened. The patients who attended the relaxation group trainings did not report greater improvement than those who did not (p=.1007). Conclusions: Rasch models represent a valid framework for the measurement of change and a useful complement to traditional approaches. \ua9 Anselmi et al

Signatures of Star-planet interactions

Planets interact with their host stars through gravity, radiation and magnetic fields, and for those giant planets that orbit their stars within $\sim$10 stellar radii ($\sim$0.1 AU for a sun-like star), star-planet interactions (SPI) are observable with a wide variety of photometric, spectroscopic and spectropolarimetric studies. At such close distances, the planet orbits within the sub-alfv\'enic radius of the star in which the transfer of energy and angular momentum between the two bodies is particularly efficient. The magnetic interactions appear as enhanced stellar activity modulated by the planet as it orbits the star rather than only by stellar rotation. These SPI effects are informative for the study of the internal dynamics and atmospheric evolution of exoplanets. The nature of magnetic SPI is modeled to be strongly affected by both the stellar and planetary magnetic fields, possibly influencing the magnetic activity of both, as well as affecting the irradiation and even the migration of the planet and rotational evolution of the star. As phase-resolved observational techniques are applied to a large statistical sample of hot Jupiter systems, extensions to other tightly orbiting stellar systems, such as smaller planets close to M dwarfs become possible. In these systems, star-planet separations of tens of stellar radii begin to coincide with the radiative habitable zone where planetary magnetic fields are likely a necessary condition for surface habitability.Comment: Accepted for publication in the handbook of exoplanet

Stellar Coronal and Wind Models: Impact on Exoplanets

Surface magnetism is believed to be the main driver of coronal heating and stellar wind acceleration. Coronae are believed to be formed by plasma confined in closed magnetic coronal loops of the stars, with winds mainly originating in open magnetic field line regions. In this Chapter, we review some basic properties of stellar coronae and winds and present some existing models. In the last part of this Chapter, we discuss the effects of coronal winds on exoplanets.Comment: Chapter published in the "Handbook of Exoplanets", Editors in Chief: Juan Antonio Belmonte and Hans Deeg, Section Editor: Nuccio Lanza. Springer Reference Work