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In contrast, many genes involved in host colonization, toxin production, gene regulation, iron metabolism and antibiotic resistance had an almost 10-fold greater average dn∶ds ratio in the ET3-1 genome relative to human associated sequenced SA isolates (Table 2).
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In conjunction with these properties, we examine their interrelations and define their associated sequences.
In this section, we study the powers under umbral composition applied to associated sequences.
For example, Xing et al. [4] consider a strictly stationary negatively associated sequence of random variables.
A small number of highly designable structures emerge with a number of associated sequences much larger than the average.
Obviously, PNQD sequence includes many negatively associated sequences, and NA and pairwise independent random sequence are the most common special cases.
We refer to Kuczmaszewska [16] for -mixing and -mixing sequences, Kuczmaszewska [17] for negatively associated sequence, and Baek and Park [18] for negatively dependent sequence.
Structures differ drastically in terms of their designability; highly designable structures emerge with a number of associated sequences much larger than the average.
Liang and Su [8] extended the results of Thrum [6], and Li et al. [7] showed the complete convergence of weighted sums of negatively associated sequence.
It is natural to extend them to the dependent case, for example, martingale difference, negatively associated sequence, mixing random variables and so on.
We obtain the Binet form and generating functions of Vieta-Pell and Vieta-Pell-Lucas polynomials and define their associated sequences.
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