In this paper we introduce the robust random number generation problem where the goal is to design an abstract tile assembly system (aTAM system) whose terminal assemblies can be split into n partitions such that a resulting assembly of the system lies within each partition with probability 1/n, regardless of the relative concentration assignment of the tile types in the system.
As an application, we combine our coin-flip system with a result of Chandran, Gopalkrishnan, and Reif to show that for any positive integer n, there exists a O logn) tile system that assembles a constant-width linear assembly of expected length n for any concentration assignment.
For a summary of exposure concentration assignments, see Supplemental Material, Table 1 (http://dx.doi.org/10.1289/ehp.1103729).org/10.1289/ehp.1103729
Because U1, U2, and U3 are generated independently of the original water concentration assignments C0,i,j, this model simulates additional classical (as opposed to Berkson) measurement error in the drinking water concentrations.
The slight deviation from unity observed between the two methods in this correlation analysis probably arose from differences in NGAL concentration assignments for the samples used to calibrate these two assays.
For inhalation exposure intensity, air concentration data permitted assignment of exposure units (parts per million), but for dermal exposure intensity, the lack of historical dermal exposure measurements resulted in a unitless measure of exposure.
Concordance smaller than 75% could be caused by (i) hybridization failure (due to low probe concentration), (ii) improper assignment of clones to genes, (iii) sequencing errors, (iv) alternative splicing, (v) chance (false negatives).
In summary, we observed the expected changes in urine Tx-M and PGI-M concentrations by treatment assignment and by ASA use among compliant ADAPT participants, and by ASA use among non-compliant donors.
For NMR measurements, the protein samples were prepared at 0.8 mM concentration (for resonance assignments and relaxation measurements) or 0.3 mM (for ligand titrations) in buffer A, supplemented with 10% v/v D2O.
Don't be tempted to do something easy right away, as you will need to devote better concentration to harder assignments.
For the nearest monitor assignment, we assigned for each day a concentration from the operational monitor closest to the postal code of interest and within 10 km.
