Practical algorithms for transposition-invariant string-matching

We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transposition-invariant text searching using indel distance. These problems have applications in music comparison and retrieval. We introduce two novel techniques to solve these problems efficiently. The first is based on the branch and bound method, the second on bit-parallelism. Our branch and bound algorithm computes the longest common transposition-invariant subsequence (LCTS) in time O((m²+loglogσ)logσ) in the best case and O((m²+logσ)σ) in the worst case, where m and σ, respectively, are the length of the strings and the size of the alphabet. On the other hand, we show that the same problem can be solved by using bit-parallelism and thus obtain a speedup of O(w/logm) over the classical algorithms, where the computer word has w bits. The advantage of this latter algorithm over the present bit-parallel ones is that it allows the use of more complex distances, including general integer weights. Since our branch and bound method is very flexible, it can be further improved by combining it with other efficient algorithms such as our novel bit-parallel algorithm. We experiment on several combination possibilities and discuss which are the best settings for each of those combinations. Our algorithms are easily extended to other musically relevant cases, such as δ-matching and polyphony (where there are several parallel texts to be considered). We also show how our bit-parallel algorithm is adapted to text searching and illustrate its effectiveness in complex cases where the only known competing method is the use of brute force.     

Acousto-optic mode coupling of partially coherent light in two-mode optical fibers

An acoustic pulse propagating on a two-mode fiber can act as a beam splitter in a scanning interferometer. When this device is employed in white-light interferometry, the effects of distributed coupling and dispersive interferometer arms need to be considered. A theory suitable for treating acousto-optic interaction of partially coherent light in a moving interaction region was developed. It was found that differential optical dispersion should be negligible and the acoustic pulse length short. Also the coherence time should be short but long compared to the intermodal group delay difference over a pulse length. Experiments with long acoustic pulses were performed, and fairly good agreement with theory was obtained.     

α-Halo sulfides in the alkylation of 2-pyrimidinones

When α-halo sulfides are reacted with ambident 2-pyrimidinones, the major product is due to N-alkylation, the minor product to O-alkylation. N-Alkylation is favoured by the presence of a tertiary amine in a solvent of low dielectric constant and also by a change of the α-halo sulfide substituent from chlorine to iodine. Complete selectivity can be achieved. The course of the reaction is rationalized in terms of the HSAB-principle.     

BRCA1 mutation screening using restriction endonuclease fingerprinting-single-strand conformation polymorphism in an automated capillary electrophoresis system

Efficient mutation scanning techniques are needed for the rapid detection of novel disease-associated mutations and rare-sequence variants of putative importance. The large size of the breast cancer 1 gene (BRCA1) and the many mutations found throughout its entire coding sequence make screening for mutations in this gene particularly challenging. We have developed a method for screening exon 11 of the BRCA1 gene based on restriction enzyme digestion of fluorescence-labeled polymerase chain reaction (PCR) products followed by single-strand conformation polymorphism (SSCP) using an automated capillary electrophoresis system, denoted capillary restriction endonuclease fingerprinting (REF)-SSCP electrophoresis. Using this strategy on a control set of samples, we were able to detect 17 of 18 known sequence alterations. The method was then applied to screen 73 Norwegian females with family histories of breast and/or ovarian cancer. A total of 172 sequence alterations were detected, including substitutions, insertions, and deletions. One novel substitution of unknown function was identified. Sequencing of all samples negative in the capillary REF-SSCP system gave no additional mutations confirming the high sensitivity of the described methodology. Capillary REF-SSCP electrophoresis appeared as a technically convenient technique, requiring amplification of fewer PCR fragments than traditional SSCP. The novel strategy allows high-throughput mutation scanning without radioactive labeling and polyacrylamide gel electrophoresis (PAGE).     

Mass spectrometry of onium compounds—XI: Ionization potentials of hydroxy and mercapto pyridines

Ionization potential measurements of the volatile species from the three isomers of the tautomeric hydroxyl and mercapto pyridines show that these are in the hydroxy and mercapto forms rather than appearing as lactams and betaines. The corresponding N-methyl lactams and S- and O-methyl ethers were also studied for comparative purposes.     

Homomorphisms onC ∞ (E) andC ∞-bounding sets

We prove, for the class of real locally convex spacesE that are continuously and linearly injectable into somec ₀(), that every non-zero homomorphism on the algebraC (E) ofC -functions onE is given by a point evaluation at some point ofE. Furthermore, if every real-valuedC -function on the weak topology of a quasi-complete locally convex spaceE is bounded on a subsetA ofE, thenA is relatively weakly compact.     

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. I. Basic considerations and calculational procedure

A simulation method is described for the comparison of a molecular decomposition theory, based on the fundamental RRKM theory, with crossed molecular beam experiments. In the present formulation, the method is applied to the case with long-lived collision complexes surrounded by a centrifugal barrier. The procedure uses Monte Carlo techniques to simulate the formation and decomposition of the complexes, thus effectively solving the high-dimensional integrals resulting but seldom solved in the analytical treatments. Several computational problems, like singularities in the c.m. angular distributions, have been circumvented in this procedure. Angular momentum conservation, the simultaneous interaction of several decomposition channels and strict flux conservation are included in the procedure. Dynamical features can be introduced, as will be shown in forthcoming papers.     

Efficient asymmetric synthesis of an azasugar in water

An extremely efficient asymmetric synthesis of a pyrrolidine azasugar was completed in only four steps in water, without the use of protecting groups and in 60% overall yield from a simple, achiral bis-electrophile.