Generalized Isotonic Regression

We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ?₂-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the l₂ algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials.     

Electrochemical Hydroxylation of Arenes Catalyzed by a Keggin Polyoxometalate with a Cobalt(IV) Heteroatom

The sustainable, selective direct hydroxylation of arenes, such as benzene to phenol, is an important research challenge. An electrocatalytic transformation using formic acid to oxidize benzene and its halogenated derivatives to selectively yield aryl formates, which are easily hydrolyzed by water to yield the corresponding phenols, is presented. The formylation reaction occurs on a Pt anode in the presence of [Co^IIIW₁₂O₄₀]^5? as a catalyst and lithium formate as an electrolyte via formation of a formyloxyl radical as the reactive species, which was trapped by a BMPO spin trap and identified by EPR. Hydrogen was formed at the Pt cathode. The sum transformation is ArH+H₂O→ArOH+H₂. Non‐optimized reaction conditions showed a Faradaic efficiency of 75 % and selective formation of the mono‐oxidized product in a 35 % yield. Decomposition of formic acid into CO₂ and H₂ is a side‐reaction.     

Development of a capillary electrophoresis-based assay of sirtuin enzymes

Sirtuins are a family of nicotinamide adenine dinucleotide (NAD(+))-dependent enzymes catalyzing the deacetylation of acetyl-lysine residues of histones and other proteins. Three 9-fluorenylmethoxycarbonyl (Fmoc)-labeled peptide substrates derived from the amino acid sequence of p53, i.e. Fmoc-KK(Ac)-NH(2), Fmoc-KK(Ac)L-NH(2) and Fmoc-RHKK(Ac)-NH(2), were synthesized and evaluated as substrates of the human isoenzyme SIRT1. The acetylated and respective deacetylated peptides as well as nicotinamide as the reaction product of nicotinamide adenine dinucleotide were separated by capillary electrophoresis in a fused-silica capillary using 200 mM phosphate-Tris buffer, pH 2.7. Sodium hydroxide-mediated sample stacking was performed in order to overcome peak asymmetry due to the high salt and acid content of the sample as well as to enhance UV detection sensitivity. The assay was subsequently validated. Upon incubation of the acetylated peptides for 60 min in the presence of 2.5 U of SIRT1 at least 87% of the peptides was deacetylated, indicating that the new derivatives are efficient substrates of the enzyme.     

Oxidative C-C bond cleavage of primary alcohols and vicinal diols catalyzed by H5PV2Mo10O40 by an electron transfer and oxygen transfer reaction mechanism

Primary alcohols such as 1-butanol were oxidized by the H5PV2Mo10O40 polyoxometalate in an atypical manner. Instead of C-H bond activation leading to the formation of butanal and butanoic acid, C-C bond cleavage took place leading to the formation of propanal and formaldehyde as initial products. The latter reacted with the excess 1-butanol present to yield butylformate and butylpropanate in additional oxidative transformations. Kinetic studies including measurement of kinetic isotope effects, labeling studies with 18O labeled H5PV2Mo10O40, and observation of a prerate determining step intermediate by 13C NMR leads to the formulation of a reaction mechanism based on electron transfer from the substrate to the polyoxometalate and oxygen transfer from the reduced polyoxometalate to the organic substrate. It was also shown that vicinal diols such as 1,2-ethanediol apparently react by a similar reaction mechanism.     

Linear Openness of the Composition of Set-Valued Maps and Applications to Variational Systems

In this paper we study the linear openness of the composition of set-valued maps carried out thanks to applications of Nadler’s fixed point theorem and Lim’s lemma. As a byproduct, we obtain the Lipschitz property of the solution map of a generalized parametric equation and of parametric approximate variational inequalities, as well.     

Human reaction to vibrations from blasting activity – Norwegian exposure–effect relationships

Rock blasting may cause disturbances, fear, and annoyance in residential and community areas affected by such activities. These community reactions can be quite strong, even when the blasting activities and the resulting vibrations are unlikely to cause physical damage to building foundations or buildings. A socio-vibrational survey was undertaken to assess residential reactions to blasting activities. Vibration velocities were obtained for 520 respondent dwellings located in seven study areas, and compared to the residents’ assessments of environment quality. Even at low vibration values, many people report annoyance. Exposure–effect relationships with acceptable statistical error bands were obtained. The level of annoyance from long-term blasting activities (quarry blasting) was not higher than from finite periods of more intense blasting activities (road and rail tunnels). Providing information in advance of the blasting activities, can reduce community reactions. Self-reported sensitivity to vibrations was associated with significantly increased annoyance. Sensitivity to vibrations was uncorrelated with exposure to vibrations. Sensitivity to noise and sensitivity to vibration were moderately correlated.     

Model colloidal fluid with competing interactions: bulk and interfacial properties

Using a simple mean field density functional theory (DFT), the authors investigate the structure and phase behavior of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter sigma, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. The authors analyze the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from DFT with those from the self-consistent Ornstein-Zernike approximation (SCOZA). In both theories the authors find rich crossover behavior, whereby the ultimate decay of correlation functions changes from monotonic to long wavelength damped oscillatory decay on crossing certain lines in the phase diagram or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters the authors find, within the DFT, a lambda line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a lambda line. The propensity towards clustering of particles, which is reflected by the presence of a long wavelength (>sigma) slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but nonzero wave numbers, is enhanced in states near the lambda line. The authors present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby lambda transition gives rise to pronounced long wavelength oscillations in the one-body density profiles at both types of interface.     

Asymptotic Convergence of Conjugate Gradient Methods for the Partial Symmetric Eigenproblem

Recently an efficient method (DACG) for the partial solution of the symmetric generalized eigenproblem A x = δB x has been developed, based on the conjugate gradient (CG) minimization of the Rayleigh quotient over successive deflated subspaces of decreasing size. The present paper provides a numerical analysis of the asymptotic convergence rate ρ_j of DACG in the calculation of the eigenpair λ_j, u _j, when the scheme is preconditioned with A⁻¹. It is shown that, when the search direction are A-conjugate, ρ_j is well approximated by 4/ξ_j, where ξ_j is the Hessian condition number of a Rayleigh quotient defined in appropriate oblique complements of the space spanned by the leftmost eigenvectors u ₁, u ₂,…, u _j−1 already calculated. It is also shown that 1/ξ_j is equal to the relative separation between the eigenvalue λ_j currently sought and the next higher one λ_j+1 and the next higher one λ_{j + 1}. A modification of DACG (MDACG) is studied, which involves a new set of CG search directions which are made M-conjugate, with M-conjugate, with M-conjugate, with M a matrix approximating the Hessian. By distinction, MDACG has an asymptotic rate of convergence which appears to be inversely proportional to the square root of ξ_j, in complete agreement with the theoretical results known for the CG solution to linear systems. © 1997 by John Wiley & Sons, Ltd.     

One‐Pot Cascade Transformation of Glucal into Structurally Diverse Drug‐Like Scaffolds

A diversity‐oriented synthesis strategy to produce three types of structurally drug‐like N‐heterocyclic‐fused rings has been developed from abundant biomass‐derived d ‐glucal, aniline and water in a stereoselective manner. The overall transformation which entails a cascade of Ferrier reaction and 4π conrotatory imino‐Nazarov cyclization was performed in one‐pot allowing convenient preparation of scaffolds of high molecular complexity from relatively simple starting materials. While indoline‐fused products were readily accessible using ortho‐unsubstituted secondary anilines as substrates, reactions with ortho‐hydroxyl‐anilines furnished fused 1,4‐benzoxazines instead. In both cases, InBr₃ acted as the Lewis acid catalyst. By altering InBr₃ to Ln(OTf)₃, the indoline‐fused products could be further converted into tetrahydroquinoline‐fused cyclopentenones via ensuing retro‐ene rearrangement.