Waiting time problems for a two-dimensional pattern

We consider waiting time problems for a two-dimensional pattern in a sequence of i.i.d. random vectors each of whose entries is 0 or 1. We deal with a two-dimensional pattern with a general shape in the two-dimensional lattice which is generated by the above sequence of random vectors. A general method for obtaining the exact distribution of the waiting time for the first occurrence of the pattern in the sequence is presented. The method is an extension of the method of conditional probability generating functions and it is very suitable for computations with computer algebra systems as well as usual numerical computations. Computational results applied to computation of exact system reliability are also given. Department of Statistical Science, School of Mathematical and Physical Science, The Graduate University for Advanced Studies This research was partially supported by the ISM Cooperative Research Program (2002-ISM-CRP-2007).     

On nonparametric tests for symmetry

Summary This paper is concerned with an extension of the problem of testing symmetry about zero of a distribution function. In order to obtain the asymptotic null distribution of test statistics for the problem, a limit theorem is proved, which indeed plays an essential role in the asymptotic theory of testing, problem for symmetry. The Institute of Statistical Mathematics     

Waiting Time Problems in a Two-State Markov Chain

Let F ₀ be the event that l ₀ 0-runs of length k ₀ occur and F ₁ be the event that l ₁ 1-runs of length k ₁ occur in a two-state Markov chain. In this paper using a combinatorial method and the Markov chain imbedding method, we obtained explicit formulas of the probability generating functions of the sooner and later waiting time between F ₀ and F ₁ by the non-overlapping, overlapping and "greater than or equal" enumeration scheme. These formulas are convenient for evaluating the distributions of the sooner and later waiting time problems.     

Synthesis,antimicrobial activity and QSAR studies of 2,5-disubstituted benzoxazoles

In this study, a new series of 2,5-disubstituted benzoxazoles was synthesized and their structures were elucidated by elemental analysis, MASS, ¹H-NMR, ¹³C-NMR and IR spectral data. Newly and previously synthesized 2,5-disubstituted benzoxazole derivatives were evaluated for antibacterial and antifungal activity against standard strains and their drug-resistant isolates. Microbiological results showed that the compounds presented a large spectrum of activity having MIC values of 250–7.8 µg mL^?1 against the tested microorganisms. Among the newly synthesized derivatives 3–22, compound 11 was the most active against Candida krusei out of all; however, it was one dilution less potent than standard drug fluconazole. In addition, all the new and previous compounds were more active than standard drugs ampicillin trihydrate and rifampicin against Pseudomonas aeruginosa and its gentamicin-resistant isolate. The 2D-QSAR (Quantitative Structure–Activity Relationship) analysis of a set of newly and previously synthesized benzoxazoles tested for growth inhibitory activity against methicillin-resistant Staphylococcus aureus (MRSA) was also performed by using multivariable regression analysis. The activity contributions for substituent effects of these compounds were determined from the correlation equation for predictions of the lead optimization.     

Synthesis of Murisolin, (15R, 16R, 19R, 20S)‐Murisolin A,and (15R, 16R, 19S, 20S)‐16,19‐cis‐Murisolin and Their Inhibitory Action with Bovine Heart Mitochondrial Complex I

The asymmetric total synthesis of murisolin, (15R, 16R, 19R, 20S)‐murisolin A, and (15R, 16R, 19S, 20S)‐16,19‐cis‐murisolin was performed by using an epoxy alcohol as a versatile chiral building block for synthesizing the stereoisomers of mono‐THF annonaceous acetogenins. The inhibitory activity of these murisolin compounds was examined with bovine heart mitochondrial complex I, and they showed almost the same activity.     

Carbohydrate recognition of symmetrical tripodal receptor type tris(2-aminoethyl)amine derivatives

Carbohydrate recognition of some bioactive symmetrical tripodal receptor type tris(2-aminoethyl)amine (TAEA) derivatives was investigated. In calorimetric experiments, the highest binding constant (Ka) of compound C (C₃₅H₄₉N₅O₄S) with methyl α-d-mannopyranoside was Ka = 858 M^?1 with 1:1 stoichiometry. Formation of hydrogen bonds in binding between symmetrical tripodal receptor type compound C and sugars was suggested by the large negative values of ?H° (=?34 to ?511 kJ mol^?1). In a comparison of each set of α- and β-anomers of some monosaccharides (methyl α/β-d-galactopyranoside, methyl α/β-d-glucopyranoside, and methyl α/β-l-fucopyranoside), compound C showed that the binding constant of β-anomer was larger than that of the corresponding α-anomer, indicating higher β-anomer selectivity. The calculated energy-minimized structure of the complex of compound C with guest methyl α-d-mannopyranoside is also presented. The experimental results obtained from this work indicated that symmetrical tripodal receptor type TAEA derivative C has a lectin-like carbohydrate recognition property.     

QSNPlite, a software system for quantitative analysis of SNPs based on capillary array SSCP analysis

We present a newly developed software called "QSNPlite" that comprehensively interprets the data of SSCP and sequencing analyses obtained from capillary array electrophoresis systems used in the quantitative characterization of SNPs. QSNPlite assists in the genotyping of individuals with SNPs and in estimating the allele frequencies of SNPs using pooled DNA. We show that this estimation is accurate (mean absolute error, 1.4%) by comparing the results of the pooled analysis using QSNPlite with the true frequencies based on the allele counting after performing individual genotypings. The QSNPlite program runs on Windows XP and can be used to determine the allele frequencies of SNPs among a large number of individuals, such as in association studies of disease-responsible genes using the candidate gene approach.     

Au(I) complexes-catalyzed transfer vinylation of alcohols and carboxylic acids

Au(I) complexes-catalyzed transfer vinylation of alcohols and carboxylic acids has been achieved. The catalyst system consists of 2 mol % AuClPPh₃ and 2 mol % AgOAc. Primary alcohols and secondary alcohols were converted into corresponding vinyl ethers in good yield (64-93%); however, tertiary alcohols showed poor reactivities. Carboxylic acids were also transformed into corresponding vinyl esters in good yield (78-96%).     

Total Synthesis of Pectenotoxin‐2

Pectenotoxin‐2 (PTX2) is a shellfish toxin and has a non‐anomeric spiroacetal, which is not stabilized by an anomeric effect. The selective construction of the non‐anomeric spiroacetal has been a major problem in the synthesis of PTX2. Described herein is the stereoselective total synthesis of PTX2 via the isomerization of anomeric spiroacetal pectenotoxin‐2b (PTX2b). The synthesis of PTX2b was achieved by a simple process including sulfone‐mediated assembly of spirocyclic and bicyclic acetals and subsequent macrocyclization by ring‐closing olefin metathesis. Finally, the selective construction of PTX2 was accomplished by the early termination of a dynamic transition process to equilibrium in the acid‐catalyzed isomerization of anomeric PTX2b. [6,6]‐Spiroacetal pectenotoxin‐2c (PTX2c) was also synthesized from PTX2b. The cytotoxicity assay of the synthetic compounds against HepG2 and Caco2 cancer cells showed a potency of the order: PTX2?PTX2b>PTX2c.