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The measurement of large scale anisotropies in cosmic ray arrival directions at energies above 10^13 eV is performed through the detection of Extensive Air Showers produced by cosmic ray interactions in the atmosphere. The observed anisotropies are small, so accurate measurements require small statistical uncertainties, i.e. large datasets. These can be obtained by employing ground detector arrays with large extensions (from 10^4 to 10^9 m^2) and long operation time (up to 20 years). The control of such arrays is challenging and spurious variations in the counting rate due to instrumental effects (e.g. data taking interruptions or changes in the acceptance) and atmospheric effects (e.g. air temperature and pressure effects on EAS development) are usually present. These modulations must be corrected very precisely before performing standard anisotropy analyses, i.e. harmonic analysis of the counting rate versus local sidereal time. In this paper we discuss an alternative method to measure large scale anisotropies, the East-West method, originally proposed by Nagashima in 1989. It is a differential method, as it is based on the analysis of the difference of the counting rates in the East and West directions. Besides explaining the principle, we present here its mathematical derivation, showing that the method is largely independent of experimental effects, that is, it does not require corrections for acceptance and/or for atmospheric effects. We explain the use of the method to derive the amplitude and phase of the anisotropy and we demonstrate its power under different conditions of detector operation.
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The Galactic magnetic field, locally observed to be on the order of a few $mu$G, is sufficiently strong to induce deflections in the arrival directions of ultra-high energy cosmic rays. We present a method that establishes measures of self-consistenc
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To simulate the interaction of cosmic rays with the Earth atmosphere requires highly complex computational resources and several statistical techniques have been developed to simplify those calculations. It is common to implement the thinning algorit
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian for each e