Organocatalytic Enantioselective Higher‐Order Cycloadditions of In Situ Generated Amino Isobenzofulvenes

The [8+2] cycloaddition of indene‐2‐carbaldehydes and nitro olefins is described to provide benzonorbornene scaffolds in a highly peri‐, diastereo‐, and enantioselective fashion in the presence of a C₂‐symmetric aminocatalyst. This reaction, which proceeds through a transient semi‐aromatic amino isobenzofulvene, represents the first example of catalytic formation and transformation of these species. Quantum chemical calculations suggest a kinetically controlled stepwise mechanism where the stereochemistry is determined in the first bond‐forming event. Beyond the useful [8+2] cycloadducts, [10+4] cycloadducts have been identified in silico as potential off‐pathway intermediates.     

An efficient synthesis of a potent PPARpan agonist

An efficient synthesis of 2-{4-[({4-{[4-(4-methoxyphenyl)piperazin-1-yl]methyl}-2-[4-(trifluoromethyl)phenyl]-1,3-thiazol-5-yl}methyl)thio]phenoxy}-2-methylpropanoic acid (1), a potent PPARpan agonist, is described. The seven-step synthesis, which afforded 1 in 30% overall yield, includes a highly regioselective carbon-sulfur bond formation via coupling of a bishydroxymethylthiazole (3) with 4-hydroxythiophenol, displacement of the remaining alcohol through a three-step telescoped sequence involving an efficient cleavage of an aryl mesylate, and an efficient and practical method of introducing an isobutyric acid fragment.     

On the Least Median Square Problem

We consider the exact and approximate computational complexity of the multivariate least median-of-squares (LMS) linear regression estimator. The LMS estimator is among the most widely used robust linear statistical estimators. Given a set of n points in and a parameter k, the problem is equivalent to computing the narrowest slab bounded by two parallel hyperplanes that contains k of the points. We present algorithms for the exact and approximate versions of the multivariate LMS problem. We also provide nearly matching lower bounds for these problems. These lower bounds hold under the assumptions that k is Ω(n) and that deciding whether n given points in are affinely non-degenerate requires Ω(n^d) time.     

Carbanionic rearrangements of halomethylenecyclobutanes. Stereochemistry of the migrating group

The unusual base-induced ring-enlargement of halomethylenecyclobutanes to 1-halocyclopentenes was examined with unsymmetrical and (13)C-labeled substrates to study regio- and stereochemical characteristics. Migration of a ring carbon atom (single migration) or simultaneous migration of a ring carbon atom and the halide (double migration) gives the ring-enlarged products. (13)C-labeling experiments established that both rearrangements occur with retention of configuration at the migrating center. These systems are suggested as models for the Fritsch-Buttenberg-Wiechell (FBW) rearrangement.     

Nice Point Sets Can Have Nasty Delaunay Triangulations

   Abstract. We consider the complexity of Delaunay triangulations of sets of points in R ³ under certain practical geometric constraints. The spread of a set of points is the ratio between the longest and shortest pairwise distances. We show that in the worst case, the Delaunay triangulation of n points in R ³ with spread Δ has complexity Ω(min{ Δ³, nΔ, n² }) and O(min{ Δ⁴, n ² }). For the case