On the almost sure (a.s.) central limit theorem for random variables with infinite variance

We give criteria for a sequence (X _n ) of i.i.d.r.v.'s to satisfy the a.s. central limit theorem, i.e.,

Stronger Lagrangian bounds by use of slack variables: Applications to machine scheduling problems

Lagrangian relaxation is a powerful bounding technique that has been applied successfully to manyNP-hard combinatorial optimization problems. The basic idea is to see anNP-hard problem as an easy-to-solve problem complicated by a number of nasty side constraints. We show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds. The trick is widely applicable, but we focus on a broad class of machine scheduling problems for which it is particularly useful. We provide promising computational results for three problems belonging to this class for which Lagrangian bounds have appeared in the literature: the single-machine problem of minimizing total weighted completion time subject to precedence constraints, the two-machine flow-shop problem of minimizing total completion time, and the single-machine problem of minimizing total weighted tardiness.     

Bischler-Napieralski Reaction of 2-(3,4-Dimethoxy-2-nitrophenyl)-N-[2-(3,4-dimethoxyphenyl)ethyl]-N-[(S)-1-phenylethyl] acetamide Accompanied by Elimination of Chiral Auxiliary

Chiral 1-benzyltetrahydroisoquinoline alkaloids can be asymmetrically synthesized via Bischler-Napieralski (B-N) cyclization followed by stereoselective NaBH4 reduction (Polniaszek抯 method) of the N- (2-phenylethyl)-2-phenylacetamides bearing chiral auxiliary such as (S)-1-phenylethyl group on the nitrogen atom1-4. Recently Y. Ohishi and co-workers found an unusual B-N reaction on the carbon at 2-position of the A ring, which bears a bromine atom5, 6. They indicated that the steric ef…     

Peptide backbone reconstruction using dead-end elimination and a knowledge-based forcefield

A novel, yet simple and automated, protocol for reconstruction of complete peptide backbones from C(alpha) coordinates only is described, validated, and benchmarked. The described method collates a set of possible backbone conformations for each set of residue triads from a structural library derived from the PDB. The optimal permutation of these three residue segments of backbone conformations is determined using the dead-end elimination (DEE) algorithm. Putative conformations are evaluated using a pairwise-additive knowledge-based forcefield term and a fragment overlap term. The protocol described in this report is able to restore the full backbone coordinates to within 0.2-0.6 A of the actual crystal structure from C(alpha) coordinates only. In addition, it is insensitive to errors in the input C(alpha) coordinates with RMSDs of 3.0 A, and this is illustrated through application to deliberately distorted C(alpha) traces. The entire process, as described, is rapid, requiring of the order of a few minutes for a typical protein on a typical desktop PC. Approximations enable this to be reduced to a few seconds, although this is at the expense of prediction accuracy. This compares very favorably to previously published methods, being sufficiently fast for general use and being one of the most accurate methods. Because the method is not restricted to the reconstruction from only C(alpha) coordinates, reconstruction based on C(beta) coordinates is also demonstrated.     

Subchronic toxicological effects of aquatic nitrobenzene on Medaka and Chinese rare minnow

Based on the simulative exposure experiments of nitrobenzene to two small experimental fishes, Medaka (Oryzias latipes) and Chinese Rare Minnow (Gobiocypris rarus), it was found that nitrobenzene could decrease in a linear way in the static aquatic system. Both fishes could accumulate dose-related levels of nitrobenzene quickly and eliminate the compound rapidly when they were transferred to clean water. The Chinese rare minnow showed more sensitivity to the acute toxicity exposure of nitrobenzene than Medaka. Typical molecular biomarkers in oxidative defense system including superoxide dismu- tase (SOD), catalase (CAT) showed the chemical induced alterations. The changes of acetylcholi- nesterase (AChE) activities indicated that nitrobenzene might affect the normal neural function. Nitro- benzene exposure could also lead to obvious damaging effects on the target organs, such as gill and liver by hitopathological studies.     

Pattern recognition strategies for molecular surfaces. I. Pattern generation using fuzzy set theory

A new method for the characterization of molecules based on the model approach of molecular surfaces is presented. We use the topographical properties of the surface as well as the electrostatic potential, the local lipophilicity/hydrophilicity, and the hydrogen bond density on the surface for characterization. The definition and the calculation method for these properties are reviewed shortly. The surface is segmented into overlapping patches with similar molecular properties. These patches can be used to represent the characteristic local features of the molecule in a way that is beyond the atomistic resolution but can nevertheless be applied for the analysis of partial similarities of different molecules as well as for the identification of molecular complementarity in a very general sense. The patch representation can be used for different applications, which will be demonstrated in subsequent articles.     

A method for near-infrared spectral calibration of complex plant samples with wavelet transform and elimination of uninformative variables

An algorithm is proposed for extracting relevant information from near-infrared (NIR) spectra for multivariate calibration of routine components in complex plant samples. The algorithm is a combination of wavelet transform (WT) data compression and a procedure for uninformative variable elimination (UVE). After compression of the NIR spectra by WT, the UVE approach is used to eliminate the irrelevant wavelet coefficients. Finally, a calibration model is built from the retained wavelet coefficients to enable prediction. Because irrelevant information can be removed from the spectra used for multivariate calibration, the model based on the extracted relevant features is better than those obtained with full-spectrum data. Both prediction precision and calculation speed are improved.     

Theoretical study of the internal elimination reactions of xanthate precursors

The gas‐phase internal elimination (E_i) reaction of ethyl xanthate (CH₃‐CH₂‐S‐CS‐O‐CH₃) has been investigated by means of Hartree–Fock, second‐order Møller–Plesset, and density functional theory (DFT) using the Becke three‐parameter Lee–Yang–Parr (B3LYP) functional and the modified Perdew–Wang one‐parameter model for kinetics (MPW1K). Considerable differences between the ground‐ and transition‐state geometries and the calculated activation energies are observed from one approach to the other, which justifies first a careful calibration of the methods against the results of benchmark CCSD(T) calculations. Compared with these, DFT calculations along with the MPW1K functional are found to be an appropriate choice for describing the E_i reaction of xanthate precursors. The precursor conformation and the transition states involved in the internal conversion of xanthate precursors of cyano derivatives of ethylene, and of cis‐ and trans‐stilbene, are then characterized in detail by means of this functional. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 2023–2031, 2003     

Validation and application of a method for the determination of nicotine and five major metabolites in smokers' urine by solid-phase extraction and liquid chromatography-tandem mass spectrometry

An SPE-LC-MS/MS method was developed, validated and applied to the determination of nicotine and five major metabolites in human urine: cotinine, trans-3'-hydroxycotinine, nicotine-N-glucuronide, cotinine-N-glucuronide and trans-3'-hydroxycotinine-O-glucuronide. A 500 microL urine sample was pH-adjusted with phosphate buffer (1.5 mL) containing nicotine-methyl-d3, cotinine-methyl-d3 and trans-3'-hydroxycotinine-methyl-d3 internal standards. For the unconjugated metabolites, an aliquot (800 microL) of the buffered solution was applied to a 30 mg Oasis HLB-SPE column, rinsed with 2% NH4OH/H2O (3.0 mL) and H2O (3.0 mL) and eluted with methanol (500 microL). The eluate was analyzed isocratically (100% methanol) by LC-MS/MS on a diol column (50 x 2.1 mm). For the total metabolites, a beta-glucuronidase/buffer preparation (100 microL) was added to the remaining buffered solution and incubated at 37 degrees C (20 h). An aliquot (800 microL) of the enzymatically treated buffered solution was extracted and analyzed in the same manner. The conjugated metabolites were determined indirectly by subtraction. The quantitation range of the method (ng/mL) was 14-10,320 for nicotine, 15-9800 for cotinine and 32-19,220 for trans-3'-hydroxycotinine. The validated method was used to observe diurnal variations from a smoker's spot urine samples, elimination half-lives from a smoker's 24 h urine samples and metabolite distribution profiles in the spot and 24 h urine samples.     

Some basic properties of the correlation matrices

On the basis of the properties of correlation matrices, it is shown here that the set of all the first‐order transition reduced density matrices of a system provide complete information about that system. Also, the interrelation between the properties of the correlation matrix and the 2‐RDM N‐representability conditions is studied. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002