Localization of the optimal solution and a posteriori bounds for aggregation

After an aggregated problem has been solved, it is often desirable to estimate the accuracy loss due to the fact that a simpler problem than the original one has been solved. One way of measuring this loss in accuracy is the difference in objective function values. To get the bounds for this difference, Zipkin (Operations Research 1980;28:406) has assumed, that a simple (knapsack-type) localization of an original optimal solution is known. Since then various extensions of Zipkin's bound have been proposed, but under the same assumption. A method to compute the bounds for variable aggregation for convex problems, based on general localization of the original solution is proposed. For some classes of the original problem it is shown how to construct the localization. Examples are given to illustrate the main constructions and a small numerical study is presented.

A CLUSTER MODEL FOR HYBRIDS

A model for describing hybrid spectroscopy similar to the diquark model for baryons is presented. Mass and r.m.s. radii are calculated and compared with experimental results.

Aggregation in the generalized transportation problem

Aggregation disaggregation is used to reduce the analysis of a large generalized transportation problem to a smaller one. Bounds for the actual difference between the aggregated objective and the original optimal value are used to quantify the error due to aggregation and estimate the quality of the aggregation. The bounds can be calculated either before optimization of the aggregated problem (a priori) or after (a posteriori). Both types of the bounds are derived and numerically compared. A computational experiment was designed to (a) study the correlation between the bounds and the actual error and (b) quantify the difference of the error bounds from the actual error. The experiment shows a significant correlation between some a priori bounds, the a posteriori bounds and the actual error. These preliminary results indicate that calculating the a priori error bound is a useful strategy to select the appropriate aggregation level, since the a priori bound varies in the same way that the actual error does. After the aggregated problem has been selected and optimized, the a posteriori bound provides a good quantitative measure for the error due to aggregation.

Small-angle X-ray scattering study of gelation and aging of Eu3+-doped sol-gel-derived siloxane-poly(oxyethylene) nanocomposites

The aggregation, gelation, and aging of urea-cross-linked siloxane-poly(oxyethylene) nanohybrids [(U600)-n] containing two different amounts of europium triflate initially dissolved in an ethanol-water mixture were investigated by in situ small-angle X-ray scattering (SAXS). For both low (n = [O]/[Eu] = 80) and high (n = 25) europium contents, the SAXS intensity was attributed to the formation of siloxane clusters of about 8-11 Angstrom in size. Siloxane cluster formation and growth is a rapid process in hybrids with low Eu contents and slow in Eu-rich hybrids. An additional contribution to the scattering intensity at very low angles was attributed to the formation of a coarse structure level. At this secondary level, the structure can be described as a set of dense domains containing siloxane clusters embedded in a depleted matrix composed of unfolded polymer chains and solvent. By fitting a theoretical function for this model to the experimental SAXS curves, relevant structural parameters were determined as functions of time during the sol-gel transition and gel aging. For hybrids with low europium contents (n = 80), the size of the siloxane clusters remains essentially invariant, whereas the dense segregation domains progressively grow. In hybrids with high doping contents (n = 25), the preponderant structure variation during the first stages of the sol-gel transformation is the slow growth of siloxane clusters. For these hybrids, the segregation of siloxane clusters forming dense domains occurs only during advanced stages of the process.

Esterase patterns and phylogenetic relationships of species and strains included in the Drosophila buzzatii cluster

Ten strains of two species in the Drosophila buzzatii cluster (D. serido and D. seriema) were examined as to esterase patterns using polyacrylamide gel electrophoresis. The migration rate of esterases, and their substrate specificity to alpha and beta naphthyl acetates, were analysed. Other esterase features such as inhibition behaviour, presence in males and females and location in the head, thorax or abdomen of flies, were also examined. The present data,together with results obtained by others for eight strains of D. koepferae, D. serido, D. seriema and D. buzzatii, show that 69 bands have been detected in the eighteen strains studied. This total number of bands was used for comparison of strains and species by similarity index, analysis of dependence and cluster analysis. The comparisons confirmed the existence of a high degree of similarity among D. seriema strains and among D. koepferae strains, but indicated differentiation among the D. serido strains. Two strains (D69R2 and D69R5) which differed from the others of the latter species, showed closer affinities with D. buzzatii, which indicates the need for further work on those strains classified as D. serido.

Aggregation behaviour of hydrophobically modified poly(allylammonium) chloride

The behaviour of hydrophobically modified poly(allylammonium) chloride having octyl, decyl, dodecyl and hexadecyl side chains has been studied in aqueous solution using fluorescence emission techniques. Micropolarity studies using the I-1/I-3 ratio of the vibronic bands of pyrene show that the formation of hydrophobic microdomains depends on both the length of the side chain and the polymer concentration. The I-1/I-3 ratio of the polymers with low hydrophobe content (less than 5% mel) changes substantially when reaching a certain concentration. These changes are assigned to aggregation originating from interchain interactions. This behaviour is also confirmed by the behaviour of the monomer/excimer emission intensities of pyrene- dodecanoic acid used as a probe. For polymers having dodecyl side chains and hydrophobe contents higher than 10%, aggregates are formed independently of the polymer concentration. Anisotropy measurements show that microdomains resulting from the inter- and/or intramolecular interactions are similar to those observed for cationic surfactants. Viscosity measurements show that the coil dimensions are substantially decreased for the polymers having high hydrophobe contents, indicating intramolecular associations.

Use of spin label EPR spectra to monitor peptide chain aggregation inside resin beads.

An EPR approach to monitor peptide chain aggregation inside resin beads is introduced. Model low and highly peptide-loaded resins containing an aggregating sequence were labeled with a paramagnetic amino acid derivative and studied with regard to their solvation behavior in different solvent systems. For the first time in the peptide synthesis, EPR spectroscopic has allowed the detection of differentiated levels of peptide chain aggregation as a function of solvent and resin loading. (C) 1997, Elsevier B.V. Ltd. All rights reserved.

Adsorption processes in layer-by-layer films of poly(o-methoxyaniline): the role of aggregation

In this work we investigate the effect from the solution concentration on aggregation in layer-by-layer (LBL) films of poly(omethoxyaniline) (POMA) alternated with poly(vinyl sulfonic acid). Films are adsorbed on hydrophilized glass substrates and characterized with UV-Vis spectroscopy and atomic force microscopy. The formation of aggregates is favored in more concentrated solutions, leading to an increase in the diameter of the domains. This is caused by stronger polymer-polymer interactions under high concentrations. The size of POMA aggregates in solution is estimated to be larger than in LBL films, which is surprising because one should expect aggregates from solution to coalesce into larger aggregates in the deposited films. This unexpected result may be explained by a swelling effect of aggregates in the aqueous POMA solutions, consistent with other reports in the literature which consider the aggregates in solution to be made up of smaller aggregates. Upon adsorption on a solid substrate to form the LBL film, a molecular reorganization probably takes place, resulting in smaller aggregates. It is also found that the size distribution of the POMA domains in the LBL films is determined by the concentration of the solution. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Aggregation-based decomposition for multi-divisional models

The aggregation theory of mathematical programming is used to study decentralization in convex programming models. A two-level organization is considered and a aggregation-disaggregation scheme is applied to such a divisionally organized enterprise. In contrast to the known aggregation techniques, where the decision variables/production planes are aggregated, it is proposed to aggregate resources allocated by the central planning department among the divisions. This approach results in a decomposition procedure, in which the central unit has no optimization problem to solve and should only average local information provided by the divisions.