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Homework 3 1. Define zero and first order Markov models for the sequence (seqeuence1_A2) provided in the course content. Sequence1_A2 is...

Homework 31.Â Â Â Â Â Â Define zero and first order Markov models for the sequence (seqeuence1_A2) provided in the course content. Sequence1_A2 is Mycobacterium tuberculosis gene mtb48 (15 pts)Hints:-Â Â Â Â Â Â Â Â Â For this and higher order Markov models read 3.2.1 of Borodovsky and Ekisheva-Â Â Â Â Â Â Â Â Â Zero order Markov model is defined by P(i), where i= {A,T,G,C}For this you simply need the nucleotide counts and total number of nucleotides.Zero order Markov model for DNA sequence should have four parameters-Â Â Â Â Â Â Â Â Â First order Markov Model is defined by P(i|j), where i,j ={A,T,G,C}.Â For example P(A|T) is probability of observing A after T in DNA sequenceFor this you'll need the number of occurrences of di-nucleotides and the total number of di-nucleotidesFirst order Markov model for DNA sequence should have sixteen parameters.-Â Â Â Â Â Â Â Â Â To implement this, it would be easiest to write a small script in R using a alphabetFrequency() Â and dinucleotideFrequency() function of the Biostrings package. Or you can use perl or any other programming language of your choice. Otherwise, if you really have to (you exhausted all the options, see no other way and hopelessly behind on your schedule) you can use Microsoft Word or Excel substitute function or MS word's find/replace.2.Â Â Â Â Â Â Using models you derived in (1) determine the probability of DNA fragment AGTAGCTTCCAG (this fragment was also used in A1) (25 pts)3.Â Â Â Â Â Â Given hidden Markov Model framework (10pts)a.Â Â Â Â Â Â What is hidden?b.Â Â Â Â Â What is emitted?Feel free to use examples4.Â Â Â Â Â Â a) Define zero order Markov model for sequence2_A2, which represents portion of non-coding sequence of Â Mycobacterium tuberculosis (refer to course content) (5 pts)b) Use zero order Markov models defined for sequence1_A2 and sequence2_A2 and apply Viterbi algorithm to find the most likely path for sequence CGCGTTCATTCAATG in frame 1 only (45 pts)Assume: Initial transition probabilities a0c= a0n =0.5ann= anc =0.5acc =0.55 acn= 0.45where, aij is transition probability, c- coding, n-non-codingUSE COMPLEMENTARY EXCELL FILE TO FILL IN YOU VITERBI RECURSION. Check out the comments in cells D2, D6, F2, and F6.

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