Douglas and Gupta [15] proposed to impose a scaling constraint to the separation matrix W t (f) to maintain a constant gradient magnitude along the algorithm iterations.
Applying this scaling constraint, our update function becomes: W t + 1 ( f ) = c t ( f ) W t ( f ) - μ c t 2 ( f ) G t ( f ) W t ( f ) (21). with c t ( f ) = 1 1 N ∑ i = 1 N ∑ j = 1 N g t i j ( f ) and g t i j ( f ) = G t ( f ) i j.
Images from the two time-points of each subject were linearly coregistered to a halfway position, using the skull-based scaling constraint as implemented in the SIENA software (structural brain change analysis, for estimating brain atrophy), part of the FSL suite (http://www.fmrib.ox.ac.uk/fsl/ ) [ 20 ].
Category theory provides a way of stating wide scale constraints.
These constraints lead to a set of design guidelines, which maintain the wide scale constraints under increasing detail.
Relative sea level (RSL) data provide important long-term (century to millennial-scale) constraints on ice load history in Greenland.
Comparing with other optimization algorithms, simulations suggest that RNN has strong ability to search for exact solutions under the condition of large scale constraints.
Along with additional storage, removal of constraints on weak transportation capacity, limited production scale, poor information access, weak risk-bearing capacity, limited management skills, scarce labor supply, low food processing capacity, and absolute scale constraints, all can raise the economic value of additional irrigation capacity development.
Due to time scale constraints in experiments, it is rather difficult to measure the deformation process with the strain rate below 10−9 s−1, in Figs. 2 and 3 we put two creep equations not only for comparison but also as an extrapolation of the data which were observed in experiments.
Note that the second set of scaling exponents is valid when γ≤1 based on the time scale constraints given in Table 4.
