FACTOID #53: If you thought Antarctica was inhospitable, think again - its land area is only ninety-eight percent ice. Reassuringly, the other 2% is categorised as "barren rock".
In computability theory a computation problem is determining whether or not there exists a computation procedure or algorithm for a class S of questions requiring a non-Boolean value (i.e., a value from {1, 2, 3...}). These are also known as what-questions and differ from the class of questions requiring a Boolean value (see decision problem). For example, the computation problem for the class of questions "What is the sum of two positive integers x and y?" is computable because there exists a mechanical procedure, namely addition, which allows us to determine for any x and any y the value of x + y (or the value of "What is the sum of two positive integers x and y?"). In other words, the function f(x,y) = x + y is computable.
The class of functions that are computable is countably infinite whereas the class of all functions is uncountable. This suggests that there are uncomputable functions. Refer to the list of undecidable problems for examples.
In this sense, a decision problem is equivalent to a formal language.
Nearly every problem can be cast as a decision problem by using reductions, often with little effect on the amount of time or space needed to solve the problem.
In computational complexity, decision problems which are complete are used to characterize complexity classes of decision problems.
The computation is simplified dramatically by (1) approximating the multi-dimensional joint probabilities of all the data by the product of marginal probabilities (hence the name pseudo-likelihood), (2) exploiting the special properties of transition matrix and (3) using a hidden Markov chain algorithm.
This is because the computational requirement for simulating samples increases exponentially with the selection rate and also due to needing to simulate a sample of size one from the population at equilibrium.
Computations indicate that the genome organization of wild-type T7 is nearly optimal for growth: only 2.8% of random genome permutations were computed to grow faster, the highest 31% faster, than wild type.
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