Modeling Spatial Dependence with Cauchy Convolution Processes

We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on different types of kernel functions. We show that the resulting spatial processes have appealing tail dependence properties, such as tail dependence at short distances and independence at long distances with suitable kernel functions. We derive the extreme-value limits of these processes, study their smoothness properties, and detail some interesting special cases. To get higher flexibility at sub-asymptotic levels and separately control the bulk and the tail dependence properties, we further propose spatial models constructed by mixing a Cauchy convolution process with a Gaussian process. We demonstrate that this framework indeed provides a rich class of models for the joint modeling of the bulk and the tail behaviors. Our proposed inference approach relies on matching model-based and empirical summary statistics, and an extensive simulation study shows that it yields accurate estimates. We demonstrate our new methodology by application to a temperature dataset measured at 97 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a very good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.Comment: 36 pages, 7 figure

Magnetic structures of δ\delta-O2_2 resulting from competition of interplane exchange interactions

Solid oxygen is a unique molecular crystal whose phase diagram is mostly imposed by magnetic ordering, i.e., each crystal phase has a specific magnetic structure. However, recent experiments showed that high-pressure $\delta$-phase is implemented in different magnetic structures. In the present paper we study the role of interplane exchange interactions in formation of the magnetic structures with different stacking sequences of the close-packed planes. We show that temperature-induced variation of intermolecular distances can give rise to compensation of the exchange coupling between the nearest close-packed planes and result in the phase transition between different magnetic structures within $\delta$-O$_2$. Variation of the magnetic ordering is, in turn, accompanied by the step-wise variation of interplane distance governed by space and angular dependence of interplane exchange constants.Comment: 16 pages, 6 figure

On factor copula-based mixed regression models

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and the effect of a common latent variable pertaining to a cluster is modelled with a factor copula. We show how to estimate the parameters of the copula and the parameters of the margins, and we find the asymptotic behaviour of the estimation errors. Numerical experiments are performed to assess the precision of the estimators for finite samples. An example of an application is given using COVID-19 vaccination hesitancy from several countries. Computations are based on R package CopulaGAMM

Saturn's Icy Moon Rhea: a Prediction for Bulk Chemical Composition and Physical Structure at the Time of the Cassini Spacecraft First Flyby

I report a model for the formation of Saturn's family of mid-sized icy moons to coincide with the first flypast of Rhea by the Cassini Orbiter spacecraft on 26 November 2005. It is proposed that these moons had condensed from a concentric family of orbiting gas rings that were cast off some 4600 Myr ago by the contracting proto-Saturnian cloud. Numerical and structural models for Rhea are constructed on the basis of a computed bulk chemical mix of hydrated rock (mass fraction 0.385), H2O ice (0.395), and NH3 ice (0.220). The large proportion of NH3 in the ice mass inhibits the formation of the dense crystalline phase II of H2O ice at the satellite's centre. This may explain the absence of compressional features on the surface. The favoured model of Rhea has a chemically uniform interior and is very cold. The satellite is nearly isodense and the predicted value of the axial moment-of-inertia factor is C/MR^2 = 0.399 +/- 0.004. NH3 is unstable at Saturn's distance from the Sun, except near the polar regions of the satellite. Perhaps the Cassini Orbiter will discover indirect evidence for NH3 through the sublimative escape of this ice from the outer layers, especially near the equatorial zones. Wasting of NH3 would weaken the residual soil, so making the edges of craters soft and prone to landslides. It will be exciting to learn what Cassini discovers.Comment: This paper was submitted to the Publications of the Astronomical Society of Australia (PASA) on 30 November 200

Magnetoelastic nature of solid oxygen epsilon-phase structure

For a long time a crystal structure of high-pressure epsilon-phase of solid oxygen was a mistery. Basing on the results of recent experiments that have solved this riddle we show that the magnetic and crystal structure of epsilon-phase can be explained by strong exchange interactions of antiferromagnetic nature. The singlet state implemented on quaters of O2 molecules has the minimal exchange energy if compared to other possible singlet states (dimers, trimers). Magnetoelastic forces that arise from the spatial dependence of the exchange integral give rise to transformation of 4(O2) rhombuses into the almost regular quadrates. Antiferromagnetic character of the exchange interactions stabilizes distortion of crystal lattice in epsilon-phase and impedes such a distortion in long-range alpha- and delta-phases.Comment: 11 pages, 4 figures, Changes: corrected typos, reference to the recent paper is adde

Effects of spin-elastic interactions in frustrated Heisenberg antiferromagnets

The Heisenberg antiferromagnet on a compressible triangular lattice in the spin- wave approximation is considered. It is shown that the interaction between quantum fluctuations and elastic degrees of freedom stabilizes the low symmetric L-phase with a collinear Neel magnetic ordering. Multi-stability in the dependence of the on-site magnetization on an unaxial pressure is found.Comment: Revtex, 4 pages, 2 eps figure