Today you can make your name and fortune by finding a good representation system.
This nonlinear property means that finding a sparse representation is inherently more difficult than in the two-dimensional (2D) case.
A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors.
But before this step, (hat{mathbf {S}}) must be estimated using the sparsity assumption which implies finding a sparse representation of (hat{mathbf {Z}}) that captures its intrinsic degrees of freedom.
The problem of finding a sparse representation which uses the minimum number of blocks of D is given as the following optimization problem begin{array}{*{20}l} & text{minimize} quad sum_{i=0}^{d-1} Ileft |tilde{mathbf{h}}[!i]|_{q}right) & text{subject to} quad {tilde{mathbf{y}}}=mathbf{D}{tilde{mathbf{h}}}, end{array} (12).
The local comparison problem comprises two different tasks: finding a suitable representation for the protein structure searching for the correspondence between the descriptors used that is optimal according to some criteria (e.g. length, RMSD, or a combination of both).
Here, we focus on finding a global representation that captures the bulk of the genetic interactions, without requiring additional information, and employ a module hierarchy to capture functional specialization of different sub-modules.
The following lemma is crucial in finding an integral representation of the fractional boundary value problem (1.10 - 1.11).
In this paper, the Bromwich integral for the inverse Mellin transform is used for finding an integral representation for a fractional exponential operator.
Challenged in finding an appropriate representation of Balzac given the author's rotund physique, Rodin produced many studies: portraits, full-length figures in the nude, wearing a frock coat, or in a robe – a replica of which Rodin had requested.
