Probabilistic Arithmetic Automata Applications of a Stochastic Computational Framework in Biological Sequence Analysis Inke Herms PhDthesisdefense Overview 1 Probabilistic Arithmetic Automata 2 Application I: Protein Identification by PMF 3 Modeling Protein Sequences 4 Application II: Seed Sensitivity 5 Application III: 454 Sequencing Read Statistics ProbabilisticArithmeticAutomata 2 InkeHerms ProbabilisticArithmeticAutomata Overview 1 Probabilistic Arithmetic Automata 2 Application I: Protein Identification by PMF 3 Modeling Protein Sequences 4 Application II: Seed Sensitivity 5 Application III: 454 Sequencing Read Statistics ProbabilisticArithmeticAutomata 3 InkeHerms 2 a weight according to the resp. distribution is emitted 3 arithmetic operations are performed on the emissions 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands ProbabilisticArithmeticAutomata 4 InkeHerms 3 arithmetic operations are performed on the emissions 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands 2 a weight according to the resp. distribution is emitted ProbabilisticArithmeticAutomata 4 InkeHerms 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands 2 a weight according to the resp. distribution is emitted 3 arithmetic operations are performed on the emissions ProbabilisticArithmeticAutomata 4 InkeHerms ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands 2 a weight according to the resp. distribution is emitted 3 arithmetic operations are performed on the emissions 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata 4 InkeHerms ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands 2 a weight according to the resp. distribution is emitted 3 arithmetic operations are performed on the emissions 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata 4 InkeHerms ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands 2 a weight according to the resp. distribution is emitted 3 arithmetic operations are performed on the emissions 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata 4 InkeHerms ProbabilisticArithmeticAutomata Probabilistic Arithmetic Automaton (PAA) Components 1 Markov chain: random walk describing the order of operands 2 a weight according to the resp. distribution is emitted 3 arithmetic operations are performed on the emissions 0 1 2 3 4 5 6 start 8 8 6 12 8 12 0 6 7 5 10 3 2 0 0 0 5 10 3 3 ProbabilisticArithmeticAutomata 4 InkeHerms