Modelos formales en bioinformática » Material

One-dimensional nearest-neighbour random walks

Javier Campos — Mon, 22 Oct 2012 07:00:59 +0000

A random walk is a random process consisting of a sequence of discrete steps of fixed length. In the case of one-dimensional nearest-neighbour random walks, the reachable states are integer (or natural) numbers and at each step, the process jumps to the nearest-neighbour to the right with probability p or to the nearest-neighbour to the left with probability 1 - p.

A random walk with state space equal to Z (integer numbers) can be transient or null recurrent depending on p. If p=1/2 then it is null recurrent and in other cases it is transient. Look at the book by S. Ross (Example 4.3d).

A random walk with reflectant barrier at 0 (i.e., state space equal to non negative integers) can be transient, null recurrent or positive recurrent. Look here (local copy).

Some more slides on SSA

Jorge Júlvez — Thu, 02 Dec 2010 08:27:31 +0000

The SECOND part of the slides about “Stochastic Simulation of Biochemical Reactions” is available here.

Stochastic Simulation Algorithms

Jorge Júlvez — Thu, 25 Nov 2010 09:47:46 +0000

The first part of the slides about “Stochastic Simulation of Biochemical Reactions” is available here.

Birth-Death processes

Jorge Júlvez — Wed, 10 Nov 2010 13:37:32 +0000

The slides for birth-death processes are available here.

On the octopus Paul (and 3)

Javier Campos — Tue, 09 Nov 2010 11:41:00 +0000

On the octopus Paul (2)

Javier Campos — Fri, 05 Nov 2010 15:41:27 +0000

¹ Technique not explained in the classroom, see for instance these notes.

On the octopus Paul (1)

Javier Campos — Fri, 05 Nov 2010 08:47:14 +0000

When I commented in the classroom the two first questions of the exercise of the octopus Paul (modelling its mind states with a DTMC), I misinterpreted the words “it is in state 1 just before…” as “it has been always in the state 1 before…”. Obviously, if we interpret the sentence correctly (“it is in state 1 at step n…”), we need to compute the transient probability distribution (after n steps), using the expression

I will publish here a solution for the exercise in the next days.