where K is a random variable from 0 to N , and k is a particular value of K. Variance is defined as a measure of statistical dispersion [2], essentially measuring how far out from the mean observed results go. It is given by σ = E[(k − μ)] = E[k]− μ (2) For any known distribution, the generating function is G(s) = E[S ] (3) whereG is the function and s is a variable. Therefore, S {S, S, S, ...,...

Background and Aims: The caspases are unique proteases that mediate the host cell apoptosis during viral infection. In this study, we identified the caspase cleavage motifs of H5N1 and H9N2 influenza viruses isolated during 1998-2012. Materials and Methods: Amino acid sequences of the eleven proteins encoded by the viruses as the caspase substrates downloaded from NCBI. The caspase cleavage mot...

Finding similar patterns (motifs) in a set of sequences is an important problem in Computational Molecular Biology. Pevzner and Sze [18] defined the planted (l,d)-motif problem as trying to find a lengthl pattern that occurs in each input sequence with at most d substitutions. When d is large, this problem is difficult to solve because the input sequences do not contain enough information on th...

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use approximate counting, and all them obtain square-root like speedups over fastest classical in various settings. In order to counting context clustering, we show that general weighted performance spect...