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For smaller data sets which produce weaker constraints, more accurate results can be obtained from a brute-force likelihood analysis of the sky map, as was done for COBE (Tegmark & Bunn 1995, Hinshaw et al 1996).
Extensive numerical examples in both one and two space dimensions and analytical considerations based on the Wigner transform e ven show that weaker constraints (e.g., k independent of ϵ, and h=O are admissible for obtaining "correct" observables.
for a new real sequence under the weaker constraints (3.16).
We will show below that (GRT) is also in conflict with weaker constraints on *, which are uncontroversially required by Ramsey in his own formulation of 'the Ramsey test'.
This observation suggests that weaker constraints should work on the 22- and 24-nt-MmiRNAs, leading to the generation of new miRNAs or alteration their functions.
For weaker constraints (i.e., larger values for the tolerance, right-hand-side panels), the absolute value of the recovered anomaly becomes more consistent with the assumed anomaly, but fake anomalies (smears) increase.
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Symmetry is a demonstrably weaker constraint on probability than independence.
The possibility of punishing less than deserved is also normatively significant, but it provides a much weaker constraint.
The algorithm searches for an optimal solution to the binary integer programming problem by solving a series of LP relaxation problems, in which the binary integer requirement on the variables is replaced by the weaker constraint 0≤b k,l ≤1.
The weaker constraint is evident in the higher density and higher population frequencies of nSNPs in younger genes.
Thomas and Hill (2002) and Wang (2004) imposed the weaker constraint that parents of only one sex are permitted to have multiple mates.
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