Small Partitioning Research Articles

Microsatellite variation in the Mexican rockfish <i>Sebastes macdonaldi</i>

The Mexican rockfish Sebastes macdonaldi is the Northeast Pacific rockfish with the southernmost distribution, featuring isolated populations in the Gulf of California. We analysed seven microsatellite loci in 111 organisms collected throughout most of its geographical range to test long-standing hypotheses regarding its disjunct distribution. One locus was fixed and the number of alleles in polymorphic loci ranged from 2 to 24 (average 13.5). We found very high levels of polymorphism (overall He = 0.75) comparable to other congeneric species but no significant differences in genetic diversity among localities or between Pacific and Gulf of California populations (p > 0.1). Significant shifts in allelic and genotypic frequencies were detected at three loci, which resulted in a small but significant partitioning of genetic variance among California, Baja California and Gulf of California populations (FST = 0.007, p = 0.03) and between Gulf and Pacific populations (FST = 0.01, p = 0.004). The latter but not the former result was corroborated by analyses of molecular variance (AMOVA) using the number of distinct alleles (FST) and the sum of square differences of allele sizes (RST) as Euclidean distances. The evidence argues against contemporary gene flow between the gulf and the Pacific ocean and against an ancient invasion of the gulf with a founder effect. The small level of divergence favours a recent dispersal but a larger data set including DNA sequences amenable to phylogenetic analyses will help to test alternative hypotheses of dispersal versus vicariance.

Optimal partitioners and end-case placers for standard-cell layout

We study alternatives to classic Fiduccia-Mattheyses (FM)-based partitioning algorithms in the context of end-case processing for top-down standard-cell placement. While the divide step in the top-down divide and conquer is usually performed heuristically, we observe that optimal solutions can be found for many sufficiently small partitioning instances. Our main motivation is that small partitioning instances frequently contain multiple cells that are larger than the prescribed partitioning tolerance, and that cannot be moved iteratively while preserving the legality of a solution. To sample the suboptimality of FM-based partitioning algorithms, we focus on optimal partitioning and placement algorithms based on either enumeration or branch-and-bound that are invoked for instances below prescribed size thresholds, e.g., <10 cells for placement and <30 cells for partitioning. Such partitioners transparently handle tight balance constraints and uneven cell sizes while typically achieving 40% smaller cuts than best of several FM starts for instances between ten and 50 movable nodes and average degree 2-3. Our branch-and-bound codes incorporate various efficiency improvements, using results for hypergraphs (1993) and a graph-specific algorithm (1996). We achieve considerable speed-ups over single FM starts on such instances on average. Enumeration-based partitioners relying on Gray codes, while easier to implement and taking less time for elementary operations, can only compete with branch-and-bound on very small instances, where optimal placers achieve reasonable performance as well. In the context of a top-down global placer, the right combination of optimal partitioners and placers can achieve up to an average of 10% wirelength reduction and 50% CPU time savings for a set of industry testcases. Our results show that run-time versus quality tradeoffs may be different for small problem instances than for common large benchmarks, resulting in different comparisons of optimization algorithms. We therefore suggest that alternative algorithms be considered and, as an example, present detailed comparisons with the flow-based balanced partitioner heuristic.

Solvent Distribution in Weakly-Ordered Block Copolymer Solutions

The distribution of solvent in block copolymer solutions near their order−disorder transitions is examined experimentally, by small-angle neutron scattering (SANS), and theoretically, by the self-consistent mean-field (SCMF) approach. Three lamellar-forming poly(styrene-b-isoprene) diblocks were employed, in toluene, a neutral good solvent, and in cyclohexane, a selective solvent. For a given copolymer concentration, two solutions were prepared, one in protonated and one in perdeuterated solvent, and the scattering profiles compared. For a neutral solvent, one expects a small partitioning of the solvent to the interface between microdomains, to screen unfavorable styrene−isoprene contacts. Such partitioning should be manifest as a difference between the h- and d-solvents in the intensities of the second (and higher order, even) harmonic peaks (i.e., I(2q*), where the lamellar spacing, L, is 2π/q*). This difference is observed experimentally, and is in quantitative agreement with SCMF predictions using literature values for the three interaction parameters. Interestingly, the predicted relative scattering intensity between solutions in h- and d-toluene varies by several orders of magnitude over a small range in copolymer composition or over a small range of relative interaction parameters of the solvent for the two blocks, suggesting that SANS could be used in this way as a very sensitive measure of copolymer composition and/or solvent selectivity. For a selective solvent, one expects partitioning of the solvent between microdomains and a concomitant change in the intensities of the primary (and higher order, odd harmonic) peaks between h- and d-solvents. This effect is seen clearly in cyclohexane, with the partitioning of the solvent into the isoprene domains increasing with decreasing temperature. However, the SCMF calculations can only match the behavior in both solvents by employing polyisoprene−cyclohexane and polystyrene−cyclohexane interaction parameters significantly different from those reported in the literature.

Electrochemical investigations in microemulsion media: 3. In situ determination of the distribution of electroactive solutes between aqueous and organic domains

The in situ analysis of the distribution of electroactive solutes between aqueous and organic domains in microemulsions using electrochemical techniques is demonstrated. The usefulness of this method is illustrated by determining apparent distribution coefficients for substituted para-phenylenediamines [4-amino-3-methyl- N-ethyl- N-(β-sulfoethyl)aniline (PPD1) and 4-amino-3-methyl- N, N-diethyl aniline (PPD2)] in oil-in-water microemulsions. Cetyltrimethylammonium bromide (CTAB) and octadecyldimethyl betaine (C 18 DMB) were used as model surfactants. These apparent distribution coefficients are lower bounds to the true distribution coefficients. The partitioning of the PPDs into the organic domains is controlled by hydrophobic interaction and also by electrostatic attraction in the case of ionic surfactants. The distribution of K 4[Fe(CN) 6] in a CTAB microemulsion is also reported. The very small partitioning of ionic K 4[Fe(CN) 6] into the organic domain in the CTAB microemulsion is ascribed to electrostatic attraction by the cationic surfactant on the microemulsion droplet.