Min-cut clustering

We describe a decomposition framework and a column generation scheme for solving a min-cut clustering problem. The subproblem to generate additional columns is itself an NP-hard mixed integer programming problem. We discuss strong valid inequalities for the subproblem and describe some efficient solution strategies. Computational results on compiler construction problems are reported.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.This research was supported by NSF grants DMS-8719128 and DDM-9115768, and by an IBM grant to the Computational Optimization Center, Georgia Institute of Technology.     

New generation of nucleophilic glycine equivalents

A new generation of nucleophilic glycine equivalents, designed to contain a functional framework, that allows control over the physical properties as well as the reactivity, is described. The reactivity of these nucleophilic glycine equivalents have been compared to previously described examples with the application of various transformations such as alkyl halide alkylations, Michael additions, and aldol condensations.     

Thermal Stability and Degradation Mechanism for Two Main-Chain Liquid Crystal Polyesters a TG-MS Study

The thermal stabilities of two thermotropic liquid crystal polyesters were analysed by means of thermogravimetric analysis (TG), as a function of the chemical structure of the aliphatic spacer between the aromatic-triad mesogenic units. TG was combined with mass spectrometry to confirm that the degradation mechanism previously observed in a Fourier transform infrared study of the degrading polymers follows a β-cis-elimination process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asymmetric Binary Covering Codes

An asymmetric binary covering code of length n and radius R is a subset of the n-cube Q_n such that every vector xQ_n can be obtained from some vector c by changing at most R 1's of c to 0's, where R is as small as possible. K⁺(n,R) is defined as the smallest size of such a code. We show K⁺(n,R)Θ(2ⁿ/n^R) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. We show K⁺(n,n− )= +1 for constant coradius iff n ( +1)/2. These two results are extended to near-constant R and , respectively. Various bounds on K⁺ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code ([n,R]⁺-code) is determined to be min{0,n−R}. We conclude by discussing open problems and techniques to compute explicit values for K⁺, giving a table of best-known bounds.     

Closed Trapped Surfaces in Cosmology

The existence of closed trapped surfaces need not imply a cosmological singularity when the spatial hypersurfaces are compact. This is illustrated by a variety of examples, in particular de Sitter spacetime admits many closed trapped surfaces and obeys the null convergence condition but is non-singular in the k = +1 frame.     

The synthesis of functionalised chiral bicyclic lactam and lactone N-oxides using a tandem Cope elimination/reverse Cope elimination protocol

Functionalised hydroxylamine derivatives of (S)-proline and (R)-pipecolic acid have been prepared using a Cope elimination. These undergo reverse Cope elimination onto a pendant double bond to give bicyclic lactam and lactone N-oxides containing three contiguous chiral centres, this extends the scope and applicability of the reverse Cope elimination in the synthesis of heterocyclic systems by incorporation of the lactone and lactam structural motifs.