# Relationships

One important concept in bioinformatics, and in science in general, is the idea of a relationship. That is, a rule ⧋ that takes two objects, *x* and *y*, and gives back a *True* or *False* answer, represented by *x⧋y*. For example, some relationships are:

*x*is greater than*y**x*is the double of*y**x*is the father of*y**x*is classmate of*y**x*is on the same taxonomic genus as*y*

If a relationship ⧋ is *reflexive*, *symmetrical* and *transitive*, then we say that ⧋ is an *equivalence relationship*. That is

**Reflexivity:**For all*x*,*x⧋x*is True.**Symmetry:**For all*x*and all*y*,*x⧋y*is the same as*y⧋x***Transitivity:**For all*x*,*y*and*z*, if*x⧋y*and*y⧋z*, then*x⧋z*

On the other hand, if the relationship is not symmetrical, and instead it is *anti-symmetrical*, then we say that ⧋ is an *order relationship*. That is

**Symmetry:**For all*x*and all*y*, if*x⧋y*is true, and*y⧋x*is true, then*x=y*, that is*x*and*y*are the same.

Please give a list of relationships, indicting if they are *equivalence*, *order* or not. The goal of this question is to enhance your observation skills, so we aim for *quantity* and *originality*. The score of the answer will be the number of relationships that are reported by only one person.

# Distances

- What is the difference between the
*Hamming*distance and*Edit*distance - Show that the relationship “distance between
*x*and*y*is zero” is an equivalence relationship - Show that the relationship “distance between
*x*and*y*is small” is*not*an equivalence relationship

# Alignment

- What is the difference between
*global*and*local*alignment? - What is the difference between
*semi-global*and*local*alignment? - What is the ideal use case for
*global alignment*? - What is the ideal use case for
*semi-global alignment*? - What is the ideal use case for
*local alignment*? - Two bacterial strains of the same species have the same genes but they may be in different order. How would you test this hypothesis?
- How can you calculate the percentage of nucleotides conserved between the same two bacterial strains of the previous question?

# Scoring

- What is the role of λ in the scoring of alignments?
- In DNA, why the
*match*score is positive, and*mismatch*score is negative? - In proteins, why some substitution scores are positive and others are negative? What is the biological interpretation of positive scores?
- Why gap score have two parts: existence and extension?
- Why we need that the gap score be lower than the substitution score?

# Computational cost

- What is
*computational cost*? - What is the computational cost of the Smith-Waterman algorithm?
- What is an
*heuristic*? - What is the strategy that BLAST uses to speed up the local alignment?
- What is the trade-off of the
*word size*parameter in BLAST?