A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Design-based random permutation models with auxiliary information

We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.

Insights into Phosphate Cooperativity and Influence of Substrate Modifications on Binding and Catalysis of Hexameric Purine Nucleoside Phosphorylases

The hexameric purine nucleoside phosphorylase from Bacillus subtilis (BsPNP233) displays great potential to produce nucleoside analogues in industry and can be exploited in the development of new anti-tumor gene therapies. In order to provide structural basis for enzyme and substrates rational optimization, aiming at those applications, the present work shows a thorough and detailed structural description of the binding mode of substrates and nucleoside analogues to the active site of the hexameric BsPNP233. Here we report the crystal structure of BsPNP233 in the apo form and in complex with 11 ligands, including clinically relevant compounds. The crystal structure of six ligands (adenine, 2'deoxyguanosine, aciclovir, ganciclovir, 8-bromoguanosine, 6-chloroguanosine) in complex with a hexameric PNP are presented for the first time. Our data showed that free bases adopt alternative conformations in the BsPNP233 active site and indicated that binding of the co-substrate (2'deoxy) ribose 1-phosphate might contribute for stabilizing the bases in a favorable orientation for catalysis. The BsPNP233-adenosine complex revealed that a hydrogen bond between the 5' hydroxyl group of adenosine and Arg(43*) side chain contributes for the ribosyl radical to adopt an unusual C3'-endo conformation. The structures with 6-chloroguanosine and 8-bromoguanosine pointed out that the Cl-6 and Br-8 substrate modifications seem to be detrimental for catalysis and can be explored in the design of inhibitors for hexameric PNPs from pathogens. Our data also corroborated the competitive inhibition mechanism of hexameric PNPs by tubercidin and suggested that the acyclic nucleoside ganciclovir is a better inhibitor for hexameric PNPs than aciclovir. Furthermore, comparative structural analyses indicated that the replacement of Ser(90) by a threonine in the B. cereus hexameric adenosine phosphorylase (Thr(91)) is responsible for the lack of negative cooperativity of phosphate binding in this enzyme.

ABSENCE OF STABILIZATION POINT OF THE SPECIES ACCUMULATION CURVE IN TROPICAL FORESTS

The definition of the sample size is a major problem in studies of phytosociology. The species accumulation curve is used to define the sampling sufficiency, but this method presents some limitations such as the absence of a stabilization point that can be objectively determined and the arbitrariness of the order of sampling units in the curve. A solution to this problem is the use of randomization procedures, e. g. permutation, for obtaining a mean species accumulation curve and empiric confidence intervals. However, the randomization process emphasizes the asymptotical character of the curve. Moreover, the inexistence of an inflection point in the curve makes it impossible to define objectively the point of optimum sample size.

A Simple Method to Evaluate, Correlate and Predict Boiling and Flash Points of Alkynes

Boiling points (T-B) of acyclic alkynes are predicted from their boiling point numbers (Y-BP) with the relationship T-B(K) = -16.802Y(BP)(2/3) + 337.377Y(BP)(1/3) - 437.883. In turn, Y-BP values are calculated from structure using the equation Y-BP = 1.726 + A(i) + 2.779C + 1.716M(3) + 1.564M + 4.204E(3) + 3.905E + 5.007P - 0.329D + 0.241G + 0.479V + 0.967T + 0.574S. Here A(i) depends on the substitution pattern of the alkyne and the remainder of the equation is the same as that reported earlier for alkanes. For a data set consisting of 76 acyclic alkynes, the correlation of predicted and literature T-B values had an average absolute deviation of 1.46 K, and the R-2 of the correlation was 0.999. In addition, the calculated Y-BP values can be used to predict the flash points of alkynes.

Exploring the intrinsic polar [4?+?2+] cycloaddition reactivity of gaseous carbosulfonium and carboxonium ions

Gas-phase reactions of model carbosulfonium ions (CH3-S+?=?CH2; CH3CH2-S+?=?CH2 and Ph-S+?=?CH2) and an O-analogue carboxonium ion (CH3-O+?=?CH2) with acyclic (isoprene, 1,3-butadiene, methyl vinyl ketone) and cyclic (1,3-cyclohexadiene, thiophene, furan) conjugated dienes were systematically investigated by pentaquadrupole mass spectrometry. As corroborated by B3LYP/6-311?G(d,p) calculations, the carbosulfonium ions first react at large extents with the dienes forming adducts via simple addition. The nascent adducts, depending on their stability and internal energy, react further via two competitive channels: (1) in reactions with acyclic dienes via cyclization that yields formally [4?+?2+] cycloadducts, or (2) in reactions with the cyclic dienes via dissociation by HSR loss that yields methylenation (net CH+ transfer) products. In great contrast to its S-analogues, CH3-O+?=?CH2 (as well as C2H5-O+?=?CH2 and Ph-O+?=?CH2 in reactions with isoprene) forms little or no adduct and proton transfer is the dominant reaction channel. Isomerization to more acidic protonated aldehydes in the course of reaction seems to be the most plausible cause of the contrasting reactivity of carboxonium ions. The CH2?=?CH-O+?=?CH2 ion forms an abundant [4?+?2+] cycloadduct with isoprene, but similar to the behavior of such alpha,beta-unsaturated carboxonium ions in solution, seems to occur across the C?=?C bond. Copyright (c) 2012 John Wiley & Sons, Ltd.

A simple method to evaluate, correlate and predict boiling and flash points of alkynes

Boiling points (T B) of acyclic alkynes are predicted from their boiling point numbers (Y BP) with the relationship T B(K) = -16.802Y BP2/3 + 337.377Y BP1/3 - 437.883. In turn, Y BP values are calculated from structure using the equation Y BP = 1.726 + Ai + 2.779C + 1.716M3 + 1.564M + 4.204E3 + 3.905E + 5.007P - 0.329D + 0.241G + 0.479V + 0.967T + 0.574S. Here Ai depends on the substitution pattern of the alkyne and the remainder of the equation is the same as that reported earlier for alkanes. For a data set consisting of 76 acyclic alkynes, the correlation of predicted and literature T B values had an average absolute deviation of 1.46 K, and the R² of the correlation was 0.999. In addition, the calculated Y BP values can be used to predict the flash points of alkynes.