Browsing by Subject "Random sampling"

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    Generating tree method and applications to pattern-avoiding inversion sequences
    (2024-05) Gezer, Melis
    An inversion sequence of length n is an integer sequence e = e1 · · · en such that 0 ≤ ei < i for each 0 ≤ i ≤ n. We use In to denote the set of inversion sequences of length n. Let [k] := {0, 1, · · · , k − 1} denote the alphabet and τ be a word of length k over this alphabet. A pattern of length k is simply a word over the alphabet [k]. We say an inversion sequence e ∈ In contains the pattern τ of length k if it contains a sub-sequence of length k that is order isomorphic to τ; otherwise, e avoids the pattern τ . For a given pattern τ , we use In(τ ) to denote the set of all τ -avoiding inversion sequences of length n. Firstly, we review the enumeration of inversion sequences that avoid patterns of length three. We then study an enumeration method based on generating trees and the kernel method to enumerate pattern-avoiding inversion sequences for general patterns. Then, we provide sampling algorithms for pattern-avoiding inversion sequences and apply them to some specific patterns. Based on extensive simulations, we study some statistics such as the number of zeros, the number of distinct elements, the number of repeated elements, and the maximum elements. Finally, we present a bijection between In(0312) and In(0321) that preserves these statistics.
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    Synthetic TEC mapping with kriging and random field priors
    (IEEE, 2007) Sayın, I.; Arıkan, F.; Arıkan, Orhan
    Total Electron Content (TEC) can be used for analyzing the variability of the ionosphere in space and time. In this study, spatial interpolation is implemented by Kriging and Random Field Priors (RFP), which are widely used in geostatistics. Performance of Kriging and RFP methods are analyzed on synthetic TEC data for different trend functions, sampling patterns, sampling numbers, variance and range values of covariance function which is used to simulate the synthetic data, by comparing the normalized errors of interpolations. In regular sampling patterns, as opposed to random sampling, the normalized average error is very close to each other for all methods and trend assumptions. The error increases with variance and decreases with range. As the number of samples increase, the normalized error also decreases.