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A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Q k for all k (from 0 to ∞).
A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.
Eukaryotes initiate DNA replication at multiple points in the chromosome, so replication forks meet and terminate at many points in the chromosome. Because eukaryotes have linear chromosomes, DNA replication is unable to reach the very end of the chromosomes. Due to this problem, DNA is lost in each replication cycle from the end of the chromosome.
A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. [6] For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless ...
During DNA replication, the replisome will unwind the parental duplex DNA into a two single-stranded DNA template replication fork in a 5' to 3' direction. The leading strand is the template strand that is being replicated in the same direction as the movement of the replication fork.
Semiconservative replication describes the mechanism of DNA replication in all known cells. DNA replication occurs on multiple origins of replication along the DNA template strands. As the DNA double helix is unwound by helicase, replication occurs separately on each template strand in antiparallel directions. This process is known as semi ...
More than five decades ago, Jacob, Brenner, and Cuzin proposed the replicon hypothesis to explain the regulation of chromosomal DNA synthesis in E. coli. [18] The model postulates that a diffusible, trans-acting factor, a so-called initiator, interacts with a cis-acting DNA element, the replicator, to promote replication onset at a nearby origin.
As a result, it has a unique stationary distribution = {,}, where corresponds to the proportion of time spent in state after the Markov chain has run for an infinite amount of time. In DNA evolution, under the assumption of a common process for each site, the stationary frequencies π A , π G , π C , π T {\displaystyle \pi _{A},\,\pi _{G ...