Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

Amination of enzymes to improve biocatalyst performance: coupling genetic modification and physicochemical tools

Improvement of the features of an enzyme is in many instances a pre-requisite for the industrial implementation of these exceedingly interesting biocatalysts. To reach this goal, the researcher may utilize different tools. For example, amination of the enzyme surface produces an alteration of the isoelectric point of the protein along with its chemical reactivity (primary amino groups are the most widely used to obtain the reaction of the enzyme with surfaces, chemical modifiers, etc.) and even its “in vivo” behavior. This review will show some examples of chemical (mainly modifying the carboxylic groups using the carbodiimide route), physical (using polycationic polymers like polyethyleneimine) and genetic amination of the enzyme surface. Special emphasis will be put on cases where the amination is performed to improve subsequent protein modifications. Thus, amination has been used to increase the intensity of the enzyme/support multipoint covalent attachment, to improve the interaction with cation exchanger supports or polymers, or to promote the formation of crosslinkings (both intra-molecular and in the production of crosslinked enzyme aggregates). In other cases, amination has been used to directly modulate the enzyme properties (both in immobilized or free form). Amination of the enzyme surface may also pursue other goals not related to biocatalysis. For example, it has been used to improve the raising of antibodies against different compounds (both increasing the number of haptamers per enzyme and the immunogenicity of the composite) or the ability to penetrate cell membranes. Thus, amination may be a very powerful tool to improve the use of enzymes and proteins in many different areas and a great expansion of its usage may be expected in the near future.

Physico-chemical characterization of metal-doped bone chars and their adsorption behavior for water defluoridation

New bone chars for fluoride adsorption from drinking water have been synthetized via metallic doping using aluminum and iron salts. A detailed statistical analysis of the metal doping process using the signal-to-noise ratios from Taguchi's experimental designs and its impact on the fluoride adsorption properties of modified bone chars have been performed. The best conditions, including the proper metallic salt, for metal doping were identified to improve the fluoride uptakes of modified bone chars. Results showed that the fluoride adsorption properties of bone chars can be enhanced up to 600% using aluminum sulfate for the surface modification. This aluminum-based adsorbent showed an adsorption capacity of 31 mg/g, which outperformed the fluoride uptakes reported for several adsorbents. Surface interactions involved in the defluoridation process were established using FTIR, DRX and XPS analysis. Defluoridation using the metal-doped bone chars occurred via an ion exchange process between fluoride ions and the hydroxyl groups on the adsorbent surface, whereas the Al(OH)xFy, FexFy, and CaF2 interactions could play also an important role in the removal process. These metal-doped adsorbents anticipate a promising behavior in water treatment, especially in developing countries where the efficiency – cost tradeoff is crucial for implementing new defluoridation technologies.