Hence the null vector field ξ is normal to M, thus M is a null hypersurface.
Finally, lowercase boldface letters denote column vectors, × the component-wise product between two vectors and, finally, 0 denotes the null vector.
Furthermore, for any vector x, the inner product T⋅x is either the null vector or a vector in the direction of s. (Note that the complement of T is also an attractor of the network, but we will focus here only on T itself, as there is no guarantee that its complement in a real biological system would be physically or physiologically reachable).
If the θref is the null-vector, the corresponding regularization scheme is often referred as ridge regularization.
The unique null vector of this new matrix gives the estimate of the unknown vector.
Co-transfections were performed as described above using 1.8 µg of RP DNA and 0.2 µg of either the Pactag null vector (based on pACTAG-2) or DNA encoding for a hypophosphorylated version of 4E-BP1 [33].
A vector field N as defined in (8) is called a null rigging of M. It is noteworthy that the choice of a null transversal vector field N along M determines the null transversal vector bundle, the screen distribution and a unique radical vector field ξ, say the rigged vector field, satisfying (8).
An outstanding property of a rigging is that it allows a definition of geometric objects globally on M. We say that we have a null rigging when the restriction of L to the null hypersurface is a null vector field.
Using Euclidean distances between estimated sparse factor analysis weights and a null vector as reference, we separated informative images from the non-informative ones (for a full description see Pruteanu-Malinici et al., 2011).
RAW264.7 cells, a mouse monocytic cell line, were infected with retroviruses expressing Mitf-A, Mitf-dA, Mitf-dAB or a null vector as control.
