The mathematical model consists of an explicit, arithmetic, sequential order of equations with logical steps, which converts numerical inputs into numerical outputs (Dingman 2002).
One random generation step then needs O (n 2 ) arithmetic operations when using the sequential method and O n ⋅ log (n ) operations when using the boustrophedon method (for details we refer to [ 25]).
The dendrogram was generated based on Jaccard's coefficient with Unweighted Pair-Group Method using Arithmetic average (UPGMA) method in Sequential, Agglomerative, Hierarchical and Nested Clustering module of Numerical Taxonomy and Multivariate Analysis System for personal computers software (NTSYS-pc), version 2.21.
Similarity coefficients were used to construct the UPGMA (unweighted pair group method with arithmetic average) dendrograms [41] using the SHAN (sequential, hierarchical, agglomerative, and nested cluster methods) clustering and a tree was displayed through the tree plot routine in the software.
The binary data were evaluated according to the Jaccard coefficient of similarity and a phylogenetic tree (dendrogram) was constructed using the unweighted pair group method with arithmetic mean (UPGMA) [ 23] following sequential agglomerative hierarchical nested (SAHN) cluster analysis using NTYsysPC version 2.003e (Applied Biostatics Inc).
Pettijohn et al. [17, 18] proposed two sequential decoding algorithms, depth first and breadth first, for decoding arithmetic codes in the presence of channel errors.
The decision tool allows the user to input quantitative estimates of probability and time for each step in the surveillance process; the tool then calculates the net probability (product of the sequential probabilities in each step along a given path) and total time (arithmetic sum of time required for each step in the path) to reach the final step of laboratory confirmation.
To eliminate possible selfings that occurred during the BC1 crossing process (see Hooftman et al. 2005), we conducted a SAHN (Sequential Agglomerative Hierarchical Nested) cluster analysis using UPGMA parameters (Unweighted Pair-Group Method, arithmetic Average).
The similarity matrix was subjected to Sequential Agglomerative Hieratical Nested Clustering (SAHN) and dendograms were constructed employing the Unweighted Pair Group Method of Arithmetic Averages (UPGMA) of Sneath and Sokal [ 25] to group the progenies into clusters.
Sayir [12] used an arithmetic encoder adding redundancy in the compressed bit-stream by introducing gaps in the coding space, and performs sequential decoding.
