Analyzing the performance of simultaneous generalized hill climbing algorithms

Simultaneous generalized hill climbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows that the solutions generated by an SGHC algorithm are a stochastic process that satisfies the Markov property. This allows problem probability mass functions to be formulated for particular sets of problems based on the long-term behavior of the algorithm. Such results can be used to determine the proportion of iterations that an SGHC algorithm will spend optimizing over each discrete optimization problem. Sufficient conditions that guarantee that the algorithm spends an equal number of iterations in each discrete optimization problem are provided. SGHC algorithms can also be formulated such that the overall performance of the algorithm is independent of the initial discrete optimization problem chosen. Sufficient conditions are obtained guaranteeing that an SGHC algorithm will visit the globally optimal solution for each discrete optimization problem. Lastly, rates of convergence for SGHC algorithms are reported that show that given a rate of convergence for the embedded GHC algorithm, the SGHC algorithm can be designed to preserve this rate.     

A Criterion for Stability of Two-Term Recurrence Sequences Modulo 2

The authors describe a technique for characterizing stable two-term recurrence sequences and apply the technique to identify stable sequences that were not previously known to be stable.     

Fast horizontal electrophoresis. II. Development of fast automated staining procedures using PhastSystem

The development of equipment for fast automated staining is described. It is possible to handle staining procedures with up to 20 steps and nine different solutions. To increase the reaction rate in the reaction chamber, the gels are rotated and high temperatures are used. The temperature in the reaction chamber is controlled between room temperature and 50 degrees C. Increased temperature, above 20 degrees C, generally results in faster staining and destaining. However, some reactions proceed better at a low temperature, including fixation of proteins with TCA, and the development step in silver staining, where increased temperatures cause a high background stain. Silver staining using acidic silver nitrate solution is preferred, due to easy preparation and good storage stability of the reagents. This method also causes little precipitation of silver on the walls of the reaction chamber. Silver staining is accomplished within one hour. Staining with PhastGel Blue is accomplished within 30 min.     

In(OH)BDC.0.75BDCH2 (BDC = Benzenedicarboxylate), a hybrid inorganic-organic vernier structure

The compound In(OH)BDC.0.75BDCH2 (BDC = benzenedicarboxylate), 1, has been synthesized and characterized by single-crystal X-ray diffraction. The structure comprises two distinct sublattices formed by a covalently linked In(OH)BDC lattice and ordered chains of hydrogen-bonded H2BDC molecules and can be described as a hybrid inorganic coordination polymer-organic vernier structure. Each InO6 octahedron of the octahedral chain has a length of 3.6 A along the chain axis, whereas each H2BDC molecule has a length of 9.6 A along the guest column axis. Therefore, a unit of eight InO6 octahedra of the octahedral chain is just in registry with three H2BDC molecules of the guest column giving a repeat unit of 28.76 A along the channel axis direction.     

Perfecting imperfect "monolayers": removal of siloxane multilayers by CO2 snow treatment

Self-assembled monolayers (SAMs) of N-(3-triethoxysilylpropyl)-4-hydroxybutyramide were prepared on silicon oxide on silicon (Si/SiO(2)). Initial silane adsorption and high-temperature annealing led to a stable base monolayer with many large over-lying islands of disordered multilayers as a result of the non-self-limited growth process. The disordered multilayers were hydrolyzed and subsequently removed by CO(2) snow treatment. The resulting films were one monolayer thick as measured by ellipsometry. Atomic force microscopy, attenuated total reflection Fourier transform infrared spectroscopy, and contact angle analysis showed that the films were composed of monolayers with full and uniform surface coverage rather than nonuniform coverage by islands or patches of multilayers. Monolayers of octadecyltrichlorosilane were also prepared by multilayer removal via CO(2) treatment, showing the general applicability of the technique toward siloxane SAMs. We believe that CO(2) is an excellent solvent for weakly bound and hydrolyzed molecules that compose multilayers, and this ability to prepare near-perfect monolayer films from imperfect ones allows for less stringent formation conditions.