Estimating the spectral measure of an extreme value distribution

Let (X₁, Y₁), (X₂, Y₂),…, (X_n, Y_n) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.     

A new lot sizing and scheduling heuristic for multi-site biopharmaceutical production

Biopharmaceutical manufacturing requires high investments and long-term production planning. For large biopharmaceutical companies, planning typically involves multiple products and several production facilities. Production is usually done in batches with a substantial set-up cost and time for switching between products. The goal is to satisfy demand while minimising manufacturing, set-up and inventory costs. The resulting production planning problem is thus a variant of the capacitated lot-sizing and scheduling problem, and a complex combinatorial optimisation problem. Inspired by genetic algorithm approaches to job shop scheduling, this paper proposes a tailored construction heuristic that schedules demands of multiple products sequentially across several facilities to build a multi-year production plan (solution). The sequence in which the construction heuristic schedules the different demands is optimised by a genetic algorithm. We demonstrate the effectiveness of the approach on a biopharmaceutical lot sizing problem and compare it with a mathematical programming model from the literature. We show that the genetic algorithm can outperform the mathematical programming model for certain scenarios because the discretisation of time in mathematical programming artificially restricts the solution space.     

Transpeptidase-mediated incorporation of D-amino acids into bacterial peptidoglycan

The β-lactams are the most important class of antibiotics in clinical use. Their lethal targets are the transpeptidase domains of penicillin binding proteins (PBPs), which catalyze the cross-linking of bacterial peptidoglycan (PG) during cell wall synthesis. The transpeptidation reaction occurs in two steps, the first being formation of a covalent enzyme intermediate and the second involving attack of an amine on this intermediate. Here we use defined PG substrates to dissect the individual steps catalyzed by a purified E. coli transpeptidase. We demonstrate that this transpeptidase accepts a set of structurally diverse D-amino acid substrates and incorporates them into PG fragments. These results provide new information on donor and acceptor requirements as well as a mechanistic basis for previous observations that noncanonical D-amino acids can be introduced into the bacterial cell wall.     

Synthesis and characterization of (smif)2M(n) (n = 0, M = V, Cr, Mn, Fe, Co, Ni, Ru; n = +1, M = Cr, Mn, Co, Rh, Ir; smif =1,3-di-(2-pyridyl)-2-azaallyl)

A series of Werner complexes featuring the tridentate ligand smif, that is, 1,3-di-(2-pyridyl)-2-azaallyl, have been prepared. Syntheses of (smif)(2)M (1-M; M = Cr, Fe) were accomplished via treatment of M(NSiMe(3))(2)(THF)(n) (M = Cr, n = 2; Fe, n = 1) with 2 equiv of (smif)H (1,3-di-(2-pyridyl)-2-azapropene); ortho-methylated ((o)Mesmif)(2)Fe (2-Fe) and ((o)Me(2)smif)(2)Fe (3-Fe) were similarly prepared. Metatheses of MX(2) variants with 2 equiv of Li(smif) or Na(smif) generated 1-M (M = Cr, Mn, Fe, Co, Ni, Zn, Ru). Metathesis of VCl(3)(THF)(3) with 2 Li(smif) with a reducing equiv of Na/Hg present afforded 1-V, while 2 Na(smif) and IrCl(3)(THF)(3) in the presence of NaBPh(4) gave [(smif)(2)Ir]BPh(4) (1(+)-Ir). Electrochemical experiments led to the oxidation of 1-M (M = Cr, Mn, Co) by AgOTf to produce [(smif)(2)M]OTf (1(+)-M), and treatment of Rh(2)(O(2)CCF(3))(4) with 4 equiv Na(smif) and 2 AgOTf gave 1(+)-Rh. Characterizations by NMR, EPR, and UV-vis spectroscopies, SQUID magnetometry, X-ray crystallography, and DFT calculations are presented. Intraligand (IL) transitions derived from promotion of electrons from the unique CNC(nb) (nonbonding) orbitals of the smif backbone to ligand π*-type orbitals are intense (ε ≈ 10,000-60,000 M(-1)cm(-1)), dominate the UV-visible spectra, and give crystals a metallic-looking appearance. High energy K-edge spectroscopy was used to show that the smif in 1-Cr is redox noninnocent, and its electron configuration is best described as (smif(-))(smif(2-))Cr(III); an unusual S = 1 EPR spectrum (X-band) was obtained for 1-Cr.     

Synthesis of 2',3'-dideoxynucleoside phosphoesters using H-phosphonate chemistry on soluble polymer support

Phosphorylation of ddC and 3TC was efficiently performed on soluble poly(ethylene glycol) support. The corresponding 5'-monophosphate derivatives were obtained by oxidation of the support bound 5'-H-phosphonate intermediates. Then, di- and triphosphorylations were carried out using a carbonyldiimidazole activation step followed by nucleophilic substitution with suitable phosphate salts. Trivalent phosphorus chemistry appeared as a good alternative for monophosphate synthesis of acid-sensitive 2',3'-dideoxynucleosides.     

Infrared-induced reactivity of N2O on small gas-phase rhodium clusters

Far- and mid-infrared multiple photon dissociation spectroscopy has been employed to study both the structure and surface reactivity of isolated cationic rhodium clusters with surface-adsorbed nitrous oxide, Rh(n)N(2)O(+) (n = 4-8). Comparison of experimental spectra recorded using the argon atom tagging method with those calculated using density functional theory (DFT) reveals that the nitrous oxide is molecularly bound on the rhodium cluster via the terminal N-atom. Binding is thought to occur exclusively on atop sites with the rhodium clusters adopting close-packed structures. In related, but conceptually different experiments, infrared pumping of the vibrational modes corresponding with the normal modes of the adsorbed N(2)O has been observed to result in the decomposition of the N(2)O moiety and the production of oxide clusters. This cluster surface chemistry is observed for all cluster sizes studied except for n = 5. Plausible N(2)O decomposition mechanisms are given based on DFT calculations using exchange-correlation functionals. Similar experiments pumping the Rh-O stretch in Rh(n)ON(2)O(+) complexes, on which the same chemistry is observed, confirm the thermal nature of this reaction.     

Rate coefficients and mechanisms of the reaction of cl‐atoms with a series of unsaturated hydrocarbons under atmospheric conditions

Rate coefficients and/or mechanistic information are provided for the reaction of Cl‐atoms with a number of unsaturated species, including isoprene, methacrolein ( MACR ), methyl vinyl ketone ( MVK ), 1,3‐butadiene, trans‐2‐butene, and 1‐butene. The following Cl‐atom rate coefficients were obtained at 298 K near 1 atm total pressure: k(isoprene) = (4.3 ± 0.6) × 10^?10cm³ molecule^?1 s^?1 (independent of pressure from 6.2 to 760 Torr); k( MVK ) = (2.2 ± 0.3) × 10^?10 cm³ molecule^?1 s^?1; k( MACR ) = (2.4 ± 0.3) × 10^?10 cm³ molecule^?1 s^?1; k(trans‐2‐butene) = (4.0 ± 0.5) × 10^?10 cm³ molecule^?1 s^?1; k(1‐butene) = (3.0 ± 0.4) × 10^?10 cm³ molecule^?1 s^?1. Products observed in the Cl‐atom‐initiated oxidation of the unsaturated species at 298 K in 1 atm air are as follows (with % molar yields in parentheses): CH₂O (9.5 ± 1.0%), HCOCl (5.1 ± 0.7%), and 1‐chloro‐3‐methyl‐3‐buten‐2‐one (CMBO, not quantified) from isoprene; chloroacetaldehyde (75 ± 8%), CO₂ (58 ± 5%), CH₂O (47 ± 7%), CH₃OH (8%), HCOCl (7 ± 1%), and peracetic acid (6%) from MVK ; CO (52 ± 4%), chloroacetone (42 ± 5%), CO₂ (23 ± 2%), CH₂O (18 ± 2%), and HCOCl (5%) from MACR ; CH₂O (7 ± 1%), HCOCl (3%), acrolein (≈3%), and 4‐chlorocrotonaldehyde (CCA, not quantified) from 1,3‐butadiene; CH₃CHO (22 ± 3%), CO₂ (13 ± 2%), 3‐chloro‐2‐butanone (13 ± 4%), CH₂O (7.6 ± 1.1%), and CH₃OH (1.8 ± 0.6%) from trans‐2‐butene; and chloroacetaldehyde (20 ± 3%), CH₂O (7 ± 1%), CO₂ (4 ± 1%), and HCOCl (4 ± 1%) from 1‐butene. Product yields from both trans‐2‐butene and 1‐butene were found to be O₂‐dependent. In the case of trans‐2‐butene, the observed O₂‐dependence is the result of a competition between unimolecular decomposition of the CH₃CH(Cl)? CH(O?)? CH₃ radical and its reaction with O₂, with k_decomp/k_O2 = (1.6 ± 0.4) × 10¹⁹ molecule cm^?3. The activation energy for decomposition is estimated at 11.5 ± 1.5 kcal mol^?1. The variation of the product yields with O₂ in the case of 1‐butene results from similar competitive reaction pathways for the two β‐chlorobutoxy radicals involved in the oxidation, ClCH₂CH(O?)CH₂CH₃ and ?OCH₂CHClCH₂CH₃. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 334–353, 2003     

On the smallest maximal increment of partial sums of i.i.d. random variables

Summary. We study the almost sure limiting behavior of the smallest maximal increment of partial sums of independent identically distributed random variables for a variety of increment sizes , where is a sequence of integers satisfying , and going to infinity at various rates. Our aim is to obtain universal results on such behavior under little or no assumptions on the underlying distribution function. Received: 30 August 1995 / In revised form: 27 September 1996     

Selective flourinations with 1-flouro-2-pyridone

1-Fluoro-2-pyridone has been used to fluorinata selectively enamines and Grignard reagents under mild conditions.