Department of Computer Science Boolean Analysis Debashis Sahoo Department of Computer Science CSE291 – H00 – Lecture 13

Boolean Implication Pair of genes. Four quadrants. Sparse quadrants. ACPP GABRB1 45,000 Affymetrix microarrays Pair of genes. Four quadrants. Sparse quadrants. Boolean relationships. If ACPP high, then GABRB1 low If GABRB1 high, then ACPP low Put the introductory slides How many microarrays Seems like a fundamental… If -> then Describe x and y axis. Describe a point. Statistical tests for identifying sparse quadrant.

Threshold Calculation Threshold for each gene Sort expression values StepMiner High CDH expression Intermediate Threshold Low Say about linear shape. Labels in the graph bigger. Put forbidden zone threshold. Labels. Sorted arrays [Sahoo et al. 07]

BooleanNet Statistics nAlow = (a00+ a01), nBlow = (a00+ a10) total = a00+ a01+ a10+ a11, observed = a00 expected = (nAlow/ total * nBlow/ total) * total statistic = (expected – observed) expected √ a00 (a00+ a01) (a00+ a10) + ( ) 1 2 error rate = Put the introductory slides How many microarrays Seems like a fundamental… If -> then Describe x and y axis. Describe a point. Statistical tests for identifying sparse quadrant. Boolean Implication = (statistic > 3, error rate < 0.1) [Sahoo et al. Genome Biology 08]

Six Boolean Implications Sparse quadrants are highlighted. Prepare a comparison slides. Correlation vs Boolean If then Get rid of slide numbers Divide the pictures: Two slides First show Asymmetric Symmetric [Sahoo et al. Genome Biology 08]

Boolean Invariants

Formal Models Broad View Narrow View application of discrete mathematics to software engineering Narrow View Use of a formal language a set of strings over some well-defined alphabet, with rules for distinguishing which strings belong to the language Formal reasoning about formulae in the language E.g. formal proofs: use axioms and proof rules to demonstrate that some formula is in the language What I would like to cover are these points: More formal Basic intro to boolean logic Describe with example Show how these are applied Markers vs cell types Normal vs cancer

Formal Models A finite state machine (FSM) description State Transition Table, Initial State Petri nets State charts A set of properties Invariants Temporal logic formulas What I would like to cover are these points: More formal Basic intro to boolean logic Describe with example Show how these are applied Markers vs cell types Normal vs cancer

Finite State Machine A set of states An initial state A set of transitions A set of final states

Finite State Machine A set of input variables A set of state variables State variables are logical functions of input and previous states.

A 4-bit counter circuit

Analysis of Digital Systems Boolean state space exploration Property p holds in this path