  One of the most active areas of physics in the last decades has been that of
critical phenomena, and Monte Carlo simulations have played an important role
as a guide for the validation and prediction of system properties close to the
critical points. The kind of phase transitions occurring for the Betts lattice
(lattice constructed removing 1/7 of the sites from the triangular lattice)
have been studied before with the Potts model for the values q=3, ferromagnetic
and antiferromagnetic regime. Here, we add up to this research line the
ferromagnetic case for q=4 and 5. In the first case, the critical exponents are
estimated for the second order transition, whereas for the latter case the
histogram method is applied for the occurring first order transition.
Additionally, Domany's Monte Carlo based clustering technique mainly used to
group genes similar in their expression levels is reviewed. Finally, a control
theory tool --an adaptive observer-- is applied to estimate the exponent
parameter involved in the well-known Gompertz curve. By treating all these
subjects our aim is to stress the importance of cooperation between distinct
disciplines in addressing the complex problems arising in biology.
  Contents: Chapter 1 - Monte Carlo simulations in stat. physics; Chapter 2: MC
simulations in biology; Chapter 3: Gompertz equation
