We remark that our first algorithm, while unable to provide any approximation guarantee in the general case, does yield an (O(1),O(1))-approximation for a wide set of instances.
We prove the existence and approximation results for a wide class of contractive mappings in intuitionistic metric space.
Furthermore, the approximation holds for a wide range of allele frequencies, including the cases where rare alleles are used.
While previous approaches concentrated on simple target functions such as max max, the general approach presented here enables us to design a polynomial time approximation scheme (PTAS) for a wide class of target functions.
To show that these results are robust to changes in parameter values we computed the fluctuations in NANOG and compared them with the fluctuations in OCT4, using the Linear Noise Approximation (LNA) [ 46- 48] for a wide range of parameter sets (see Methods).
This allows applying the ellipsoid approximation to a wide range of tumor volumes.
Our own simulations confirmed that they provide a good approximation in a wide range of parameters (results not shown).
The analytical approximation thus produces reasonable results for a wide range of fuels.
Finally and most importantly, from a point of view of practice, we derive uniform rates, Gaussian approximations, and uniform confidence bands for a wide collection of linear functionals of the conditional expectation function, for example, the function itself, the partial derivative function, the conditional average partial derivative function, and other similar quantities.
As such, a number of statistically-based kernel functions have been developed, each providing a mapping into a generic feature space that provides a reasonable approximation to the true feature space for a wide variety of problem domains.
