Finding the projection of a point onto the intersection of convex sets via projections onto half-spaces

We present a modification of Dykstra's algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a half-space or onto the intersection of two half-spaces. Convergence of the algorithm is established and special choices of the half-spaces are proposed.The option to project onto half-spaces instead of general convex sets makes the algorithm more practical. The fact that the half-spaces are quite general enables us to apply the algorithm in a variety of cases and to generalize a number of known projection algorithms.The problem of projecting a point onto the intersection of closed convex sets receives considerable attention in many areas of mathematics and physics as well as in other fields of science and engineering such as image reconstruction from projections.In this work we propose a new class of algorithms which allow projection onto certain super half-spaces, i.e., half-spaces which contain the convex sets. Each one of the algorithms that we present gives the user freedom to choose the specific super half-space from a family of such half-spaces. Since projecting a point onto a half-space is an easy task to perform, the new algorithms may be more useful in practical situations in which the construction of the super half-spaces themselves is not too difficult.     

Adjustable robust solutions of uncertain linear programs

We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (``non-adjustable variables'), while the other part are variables that can be chosen after the realization (``adjustable variables'). We extend the Robust Optimization methodology ([1, 3-6, 9, 13, 14]) to this situation by introducing the Adjustable Robust Counterpart (ARC) associated with an LP of the above structure. Often the ARC is significantly less conservative than the usual Robust Counterpart (RC), however, in most cases the ARC is computationally intractable (NP-hard). This difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data. The ensuing Affinely Adjustable Robust Counterpart (AARC) problem is then shown to be, in certain important cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multi-stage inventory management problem.Research was partially supported by the Israeli Ministry of Science grant #0200-1-98, the Israel Science Foundation founded by The Israel Academy of Sciences and Humanities, grant #683/99-10.0, and the Fund for Promotion of Research at the Technion.     

Direct Conversion of Alcohols into Alkenes by Dehydrogenative Coupling with Hydrazine/Hydrazone Catalyzed by Manganese

We have developed unprecedented methods for the direct transformation of primary alcohols to alkenes in the presence of hydrazine, and for the synthesis of mixed alkenes by the reaction of alcohols with hydrazones. The reactions are catalyzed by a manganese pincer complex and proceed in absence of added base or hydrogen acceptors, liberating dihydrogen, dinitrogen, and water as the only byproducts. The proposed mechanism, based on preparation of proposed intermediates and control experiments, suggests that the transformation occurs through metal–ligand cooperative N?H activation of a hydrazone intermediate.     

In-house reference materials of mometasone furoate with traceable assay certified values

Characterization of in-house reference materials (IHRMs) with traceable property values for the mometasone furoate assay is discussed. The traceability of the value carried by the IHRM has been established to the value carried by a higher metrological status United States Pharmacopoeia Reference Standard (USP RS). A comparative approach is used to overcome systematic errors in measurement results, specific to the measurement method and/or to the laboratory developing the IHRM. The traceability chain was realized by the simultaneous analysis of the IHRM and the USP RS test portions under the same conditions.     

Assessment of the parallelization approach of d2_cluster for high-performance sequence clustering

The exponential increase in expressed sequence tag (EST) sequence data amplifies the computational cost of clustering sequences such that new algorithms are required to analyze data at a greater rate. We have parallelized d2_cluster on a SGI Origin 2000 multiprocessor and observed a speedup of approximately 100x on 126 processors when processing a 15,876 EST dataset. The parallelized d2_cluster code is obtainable from the SANBI website (http://www.sanbi.ac.za/CODES).     

Unusual aggregates from the oxidation of alkene self-assembled monolayers: a previously unrecognized mechanism for SAM ozonolysis?

Self-assembled monolayers (SAMs) of vinyl-terminated 3- and 8-carbon compounds were generated on Si substrates and reacted at room temperature with approximately 1 ppm gaseous O(3). A combination of atomic force microscopy (AFM), scanning electron microscopy (SEM), Auger electron spectroscopy (AES) and time-of-flight secondary ion mass spectrometry (TOF-SIMS) was used to study the surface composition and morphology after oxidation. A distribution of large ( approximately 0.1-10 microm) organic aggregates was formed, while the surrounding substrate became depleted of carbon compared to the unreacted SAM. This highly unusual result establishes that the mechanism of ozonolysis of alkene SAMs must have a channel that is unique compared to that in the gas phase or in solution, and may involve polymerization induced by the Criegee intermediate (CI). Oxidation at 60% RH led to the formation of a number of smaller aggregates, suggesting water intercepted the CI in competition with aggregate formation. The uptake of water, measured using transmission FTIR, was not increased upon oxidation of these films. In conjunction with literature reports of polymer formation from VOC-NO(x) photooxidations, these results suggest that formation of aggregates and polymers in the atmosphere is much more widespread than previously thought. The implications for the ozonolysis of alkenes on surfaces, for the transformation of organics in the atmosphere, and for the reactions and stability of unsaturated SAMs, are discussed.     

Real‐Time In‐Situ Monitoring of a Tunable Pentapeptide Gel–Crystal Transition

Supramolecular gels often become destabilized by the transition of the gelator into a more stable crystalline phase, but often the long timescale and sporadic localization of the crystalline phase preclude a persistent observation of this process. We present a pentapeptide gel–crystal phase transition amenable for continuous visualization and quantification by common microscopic methods, allowing the extraction of kinetics and visualization of the dynamics of the transition. Using optical microscopy and microrheology, we show that the transition is a sporadic event in which gel dissolution is associated with microcrystalline growth that follows a sigmoidal rate profile. The two phases are based on β‐sheets of similar yet distinct configuration. We also demonstrate that the transition kinetics and crystal morphology can be modulated by extrinsic factors, including temperature, solvent composition, and mechanical perturbation. This work introduces an accessible model system and methodology for studying phase transitions in supramolecular gels.     

Light‐triggered stabilization of microgel aggregates

Supramolecular assembly holds great potential in many technological applications. Such structures, however, tend to destabilize in dynamic environments due to weak interactions between their constituent entities. We report on a highly modular and biofriendly chemistry for the stabilization of supramolecular microgel aggregates. Upon irradiation, these structures undergo intermolecular cross‐linking, providing an efficient mechanism for stabilization.