Step 1: Understanding Evolution Models
The Jukes-Cantor model is one of the simplest models for nucleotide evolution, assuming equal rates of evolution for all substitution types (i.e., transitions and transversions occur at the same rate).
Step 2: Evaluating the Options
- Jukes Cantor model: Correct, assumes constant rates of evolution with two substitution types.
- Kimura Model: Assumes different rates for transitions and transversions, not constant rates.
- BLOSUM model: Used for amino acid sequence alignments, not nucleotide evolution.
- PAM model: Based on a different evolutionary assumption, not constant rates for substitution types.
Step 3: Conclusion
The Jukes-Cantor model assumes constant rates of evolution with two substitution types.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.