An algebraic integer is a complex number that is a root of some polynomial with integer coefficients and leading coefficient 1. A root of unity is a complex number z such that z n = 1 for some positive integer n. 7. For an integer n > 0, let μ(n) = 0 if n has...
First, we define some new concepts including the hesitant fuzzy variance, covariance, and correlation coefficient. Based on these concepts and the idea of the traditional Mahalanobis distance, the hesitant Mahalanobis distance between two HFSs is developed. Then we discuss the properties of the new ...
Coefficient estimates for the regression analysis. The dependent variable, Successful, is a dummy taking the value 1 if the Kickstarter campaign was successful. The coefficient estimates are for dummies indicating a campaign goal in the range specified by the variable name. The dummy for goals smal...
S5). In general, the reconstructed trees were more similar to the ground truth with more mutations and the distances of reconstructed trees to simulated true trees increased almost linearly with the number of samples, with the coefficient being around 0.01 for normalized RF distance and around ...
MATLAB simulations were performed to generate various data sets that corresponded to site variability, with the coefficient of variation (CoV) ranging from 10 to 80%. Studies were performed based on coefficient of variation (CoV) and regression analysis. This study provides two important charts for...
The following simple observation will be used at different places throughout this article: If a is the leading coefficient of a minimal polynomial of in and are the conjugates of that lie outside the open unit disk, then (see Propositions 1.6.5 and 1.6.6 in [3]). We can write instead...
Randomly choose a correlation coefficient from a normal distribution with mean 0.5 and standard deviation 0.1. 6. For each of the five kinds of correlation structures, simulate a dataset using the selected parameters. 7. Add two noise objects (from standard normal distributions) to each data set...
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The average path length is almost constant for all the simulation and, as we will explain later, we have ruled out the influence of the clustering coefficient. It seems that the heterogeneity in the degree of the vertex has an important role in the possible outcome of the reduction process,...
In practice, one builds a standard scale of functions whose coefficient expansion is known, expands a generic generating function over the standard scale (assuming that the scale is rich enough to admit the generating function of interest in its linear span), and uses the transfer theorem to gua...