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

2. 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.

3. 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]

4. 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]

5. 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]

6. Boolean Invariants

7. 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

8. 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

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

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

11. A 4-bit counter circuit

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