A Comparative Study of Several EOF Based Imputation Methods for Long Gap Missing Values in a Single-Site Temporal Time Dependent (SSTTD) Air Quality (PM10) Dataset

Missing values are often a major problem in many scientific fields of environmental research, leading to prediction inaccuracy and biased analysis results. This study compares the performance of existing Empirical Orthogonal Functions (EOF) based imputation methods. The EOF mean centred approach (EOF-mean) with several proposed EOF based methods, which include the EOF-median, EOF-trimmean and the newly applied Regularised Expectation-Maximisation Principal Component Analysis based method, namely R-EMPCA in estimating missing values for long gap sequence of missing values problem that exists in a Single Site Temporal Time-Dependent (SSTTD) multivariate structure air quality (PM10) data set. The study was conducted using real PM10 data set from the Klang air quality monitoring station. Performance assessment and evaluation of the methods were conducted via a simulation plan which was carried out according to four percentages (5, 10, 20 and 30) of missing values with respect to several long gap sequences (12, 24, 168 and 720) of missing points (hours). Based on several performance indicators such as RMSE, MAE, R-Square and AI, the results have shown that R-EMPCA outperformed the other methods. The results also conclude that the proposed EOF-median and EOF-trimmean have better performance than the existing EOF-mean based method in which EOF-trimmean is the best among the three. The methodology and findings of this study contribute as a solution to the problem of missing values with long gap sequences for the SSTTD data set.

A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms

Let a d -prime be a positive integer number with d divisors. From this definition, the usual prime numbers correspond to the particular case d = 2 . Here, the seemingly random sequence of gaps between consecutive d -primes is numerically investigated. First, the variability of the gap sequences for d ∈ 2,3 , … , 11 is evaluated by calculating the informational entropy. Then, these sequences are mapped into graphs by employing two visibility algorithms. Computer simulations reveal that the degree distribution of most of these graphs follows a power law. Conjectures on how some topological features of these graphs depend on d are proposed.

GAP SEQUENCES OF GRAPH-DIRECTED SETS

This paper studies the gap sequences of graph-directed sets satisfying the strong separation condition. An interesting application is to investigate the gap sequences of self-similar sets with overlaps.

An empirical study of the gap sequences for Shell sort

We present an improved version of the Shell sort algorithm. Using the algorithm, we study various geometrical sequences and the performance of Shell sort. We demonstrate that neither number of assignments nor the number of comparisons is sufficient to properly evaluate Shell sort and pick the optimal gap sequence. We argue that one should count both operations, as well as measure actual running times.