Backtracking Adaptive Search: Distribution of Number of Iterations to Convergence

Backtracking adaptive search is a simplified stochastic optimiza-tion procedure which permits the acceptance of worsening objective function values. It generalizes the hesitant adaptive search, which in turn is a gener-alization of the pure adaptive search. In this paper, we use ideas from the theory of stochastic processes to determine the full distribution of the number of iterations to convergence for the backtracking adaptive search.Communicated by P. M. PardalosThe authors thank theMarsden Fund of the Royal Society of New Zealand for support of this research. The fourth author was supported by a Bright Future Scholarship administered by the Foundation for Research, Science and Technology.     

Biomimetic synthesis of (±)-aculeatin D

A practical, efficient and diastereoselective synthesis of the cytotoxic and antiprotozoal compound aculeatin D (1) is described, employing a biomimetic oxidative cyclisation cascade reaction to generate the tricyclic system of the natural product. The synthesis proceeds in ten steps from commercially available 1-tetradecanol.     

Generating functions and the performance of backtracking adaptive search

Backtracking adaptive search is a simplified stochastic optimisation procedure which permits the acceptance of worsening objective function values. Key properties of backtracking adaptive search are defined and obtained using generating functions. Examples are given to illustrate the use of this methodology.      

Cascade reactions in total synthesis

The design and implementation of cascade reactions is a challenging facet of organic chemistry, yet one that can impart striking novelty, elegance, and efficiency to synthetic strategies. The application of cascade reactions to natural products synthesis represents a particularly demanding task, but the results can be both stunning and instructive. This Review highlights selected examples of cascade reactions in total synthesis, with particular emphasis on recent applications therein. The examples discussed herein illustrate the power of these processes in the construction of complex molecules and underscore their future potential in chemical synthesis.     

Enhanced radical scavenging activity of polyhydroxylated C<Subscript>60</Subscript> functionalized cellulose nanocrystals

A first demonstration of conjugated polyhydroxylated fullerene (C₆₀(OH)₃₀) on the surface of cellulose nanocrystals (CNC)s is reported. These nanohybrids display favourable antioxidant performance and are an attractive alternative to derivatized fullerene nanocages reported previously. UV–Vis measurements indicated that the C₆₀(OH)₃₀-CNC system scavenged 2,2-diphenyl-1-picrylhydrazyl (DPPH) free radicals to a greater degree than C₆₀(OH)₃₀ alone, due to the nucleation of C₆₀(OH)₃₀ on the surface of CNC and high colloidal stability of the engineered nanohybrid. A mechanism for the 2-stage process of the radical reaction with C₆₀(OH)₃₀-CNC is proposed, and modelled by pseudo-first order kinetics. Successful grafting of C₆₀(OH)₃₀ on CNC was confirmed by FTIR, while TEM revealed the morphology of the system with a grafting degree of 20.8 % C₆₀(OH)₃₀. Zeta potential measurements of C₆₀(OH)₃₀-CNC in aqueous solution showed a high stability in the pH range 4.0-8.0, indicating functionality of the CNC based antioxidant system as a biocompatible and sustainable protocol with potential for use in personal care applications.     

Approximation of the distribution of convergence times for stochastic global optimisation

How long should we run a stochastic global optimisation algorithm such as simulated annealing? How should we tune such an algorithm? This paper proposes an approach to the study of these questions through successive approximation of a generic stochastic global optimisation algorithm with a sequence of stochastic processes, culminating in a backtracking adaptive search process. Our emerging understanding of backtracking adaptive search can thus be used to study the original algorithm. The first approximation, the averaged range process, has the same expected number of iterations to convergence as the original process.     

Metathesis reactions in total synthesis

With the exception of palladium-catalyzed cross-couplings, no other group of reactions has had such a profound impact on the formation of carbon-carbon bonds and the art of total synthesis in the last quarter of a century than the metathesis reactions of olefins, enynes, and alkynes. Herein, we highlight a number of selected examples of total syntheses in which such processes played a crucial role and which imparted to these endeavors certain elements of novelty, elegance, and efficiency. Judging from their short but impressive history, the influence of these reactions in chemical synthesis is destined to increase.     

Recent advances in biomimetic natural product synthesis

This review highlights some of the most elegant and instructive biomimetic syntheses of natural products over the last few years, providing an updated overview of this area of research.