Partial differential equations (PDEs) are discretized into an under-determined system of equations and a minimum Sobolev norm solution is shown to be efficient to compute and converge under very generic conditions.
We propose to use a biological network, defined between SNPs, to guide a multi-locus mapping approach that is both efficient to compute and biologically meaningful: We aim to find a set of SNPs that (i) are maximally associated with a given phenotype and (ii) tend to be connected in a given biological network.
The RRA algorithm has four key features: it is robust to noise, it can handle incomplete rankings, it assigns a significance score to each element in the resulting ranking, and it is also efficient to compute.
Indeed, it is not efficient to compute V using (7) for all frequency components.
The FFT algorithm is very efficient to compute the DFT calculations in less time.
Also, for such a complicated likelihood function, it is not efficient to compute all saddle points on the stability boundary.
However, since it is much more efficient to compute a Gröbner basis for a graded-reversed lexicographic order than for a lexicographic ordering, a Gröbner basis of f 1,f 2,…,f m is first computed for a graded-reverse lexicographic ordering and then transformed into a Gröbner basis for a lexicographic ordering using FGLM algorithm [6].
However, it is more computationally efficient to compute the distances between the subspaces using the principal angles [51].
Typically, global network properties are computationally more efficient to compute than the graphlet-based local properties.
Note that this approximation is rather strong, but efficient to compute and works well in real applications.
This paper presents a new object descriptor named Global Orthographic Object Descriptor GOODdesignedned to be robust, descriptive and efficient to compute and use.
