The paper develops inferential methodology for detecting a change in the annual pattern of an environmental variable measured at fixed locations in a spatial region. Using a framework built on functional data analysis, we model observations as a collection of functionvalued time sequences available at many sites. Each sequence is modelled as an annual mean function, which may change, plus a sequence of error functions, which are spatially correlated.The tests statistics extend the cumulative sum paradigm to this more complex setting. Their asymptotic distributions are not parameter free because of the spatial dependence but can be effectively approximated by Monte Carlo simulations. The new methodology is applied to precipitation data. Its finite sample performance is assessed by a simulation study.
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves X(s k ; t), t ∈ [0, T ], observed at spatial locations s1, s2, . . . , sN . We propose several methods, and evaluate them by means of a simulation study. Next, we develop a significance test for the correlation of two such functional spatial fields. After validating the finite sample performance of this test by means of a simulation study, we apply it to determine if there is correlation between long-term trends in the so-called critical ionospheric frequency and decadal changes in the direction of the internal magnetic field of the Earth. The test provides conclusive evidence for correlation, thus solving a long-standing space physics conjecture. This conclusion is not apparent if the spatial dependence of the curves is neglected.
In this work we extend recent study of the properties of the dense packing of "superdisks," by Y. Jiao [Phys. Rev. Lett. 100, 245504 (2008)] to the jammed state formed by these objects in random sequential adsorption. The superdisks are two-dimensional shapes bound by the curves of the form |x|2p+|y|2p=1, with p>0. We use Monte Carlo simulations and theoretical arguments to establish that p=1/2 is a special point at which the jamming density, rhoJ(p), has a discontinuous derivative as a function of p . The existence of this point can be also argued for by a phenomenological excluded-area argument.
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