Extremes of independent chi-square random vectors

We prove that the componentwise maximum of an i.i.d. triangular array of chi-square random vectors converges in distribution, under appropriate assumptions on the dependence within the vectors and after normalization, to the max-stable Hüsler–Reiss distribution. As a by-product we derive a conditional limit result.     

A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

BAMLSS: Bayesian Additive Models for Location,Scale, and Shape (and Beyond)

Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade, it is now possible to tackle complicated inferential problems, for example, with Markov chain Monte Carlo simulation, on virtually any modern computer. This is one of the reasons why Bayesian methods have become increasingly popular, leading to a number of highly specialized and optimized estimation engines and with attention shifting from conditional mean models to probabilistic distributional models capturing location, scale, shape (and other aspects) of the response distribution. To embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits distributions, estimation techniques (posterior mode or posterior mean), and model terms (fixed, random, smooth, spatial,…). It is shown that within this framework implementing algorithms for complex regression problems, as well as the integration of already existing software, is relatively straightforward. The usefulness is emphasized with two complex and computationally demanding application case studies: a large daily precipitation climatology, as well as a Cox model for continuous time with space-time interactions. Supplementary material for this article is available online.     

Systematic Study of the Interaction Between VIV Centres and LnIII Ions in Well Defined {V 2 IV LnIII}{AsIIIW9O33}2 Sandwich-Type Clusters: Part 2

The gadolinium (Gd) member of a new type of heteropolytungstates that contain one lanthanide and two transition metal ions in a triangular arrangement is reported. The compound NaK₆Gd_0.33 [((VO)₂Gd(H₂O)₄K₂(H₂O)₂(Na)(H₂O)₂)(α-B-AsW₉O₃₃)₂]·24H₂O (1) was prepared from acidified aqueous solutions of Na₂WO₄·2H₂O, As₂O₃ and VOSO₄·5H₂O to which Gd³⁺ ions were added. The single crystal X-ray structure analysis (monoclinic, space group P2₁/m) shows that the anion consists of two [α-B-As^IIIW₉O₃₃]^9? trilacunary Keggin-type units linked by two VO²⁺, one Gd³⁺ as well as weakly by two K⁺ and one Na⁺ ions, resulting in a sandwich-type structure with idealized C _2v symmetry. The problem of positioning crystal lattice and special polyoxometalate sites with different cations is discussed also in connection with supramolecular chemistry aspects and as an option for further research. A fit of the magnetic susceptibility yielded exchange coupling constants of J _VV = ?2.55 cm^?1 (anti-ferromagnetic) between the vanadium ions and J _GdV = 0.6 cm^?1 (ferromagnetic) between the Gd and each of the two vanadium ions. The complete magnetochemical analysis also revealed a partial occupancy of the Na⁺ sites in the counter-cation–water system by Gd³⁺ ions (0.33 Gd³⁺ ions in total).     

Chiral Fluorinated α‐Sulfonyl Carbanions: Enantioselective Synthesis and Electrophilic Capture,Racemization Dynamics,and Structure

Enantiomerically pure triflones R¹CH(R²)SO₂CF₃ have been synthesized starting from the corresponding chiral alcohols via thiols and trifluoromethylsulfanes. Key steps of the syntheses of the sulfanes are the photochemical trifluoromethylation of the thiols with CF₃Hal (Hal=halide) or substitution of alkoxyphosphinediamines with CF₃SSCF₃. The deprotonation of RCH(Me)SO₂CF₃ (R=CH₂Ph, iHex) with nBuLi with the formation of salts [RC(Me)? SO₂CF₃]Li and their electrophilic capture both occurred with high enantioselectivities. Displacement of the SO₂CF₃ group of (S)‐MeOCH₂C(Me)(CH₂Ph)SO₂CF₃ (95 % ee) by an ethyl group through the reaction with AlEt₃ gave alkane MeOCH₂C(Me)(CH₂Ph)Et of 96 % ee. Racemization of salts [R¹C(R²)SO₂CF₃]Li follows first‐order kinetics and is mainly an enthalpic process with small negative activation entropy as revealed by polarimetry and dynamic NMR (DNMR) spectroscopy. This is in accordance with a C_α? S bond rotation as the rate‐determining step. Lithium α‐(S)‐trifluoromethyl‐ and α‐(S)‐nonafluorobutylsulfonyl carbanion salts have a much higher racemization barrier than the corresponding α‐(S)‐tert‐butylsulfonyl carbanion salts. Whereas [PhCH₂C(Me)SO₂tBu]Li/DMPU (DMPU = dimethylpropylurea) has a half‐life of racemization at ?105 °C of 2.4 h, that of [PhCH₂C(Me)SO₂CF₃]Li at ?78 °C is 30 d. DNMR spectroscopy of amides (PhCH₂)₂NSO₂CF₃ and (PhCH₂)N(Ph)SO₂CF₃ gave N? S rotational barriers that seem to be distinctly higher than those of nonfluorinated sulfonamides. NMR spectroscopy of [PhCH₂C(Ph)SO₂R]M (M=Li, K, NBu₄; R=CF₃, tBu) shows for both salts a confinement of the negative charge mainly to the C_α atom and a significant benzylic stabilization that is weaker in the trifluoromethylsulfonyl carbanion. According to crystal structure analyses, the carbanions of salts {[PhCH₂C(Ph)SO₂CF₃]Li? L }₂ ( L =2 THF, tetramethylethylenediamine (TMEDA)) and [PhCH₂C(Ph)SO₂CF₃]NBu₄ have the typical chiral C_α? S conformation of α‐sulfonyl carbanions, planar C_α atoms, and short C_α? S bonds. Ab initio calculations of [MeC(Ph)SO₂tBu]^? and [MeC(Ph)SO₂CF₃]^? showed for the fluorinated carbanion stronger n_C→σ* and n_O→σ* interactions and a weaker benzylic stabilization. According to natural bond orbital (NBO) calculations of [R¹C(R²)SO₂R]^? (R=tBu, CF₃) the n_C→σ*_{S? R} interaction is much stronger for R=CF₃. Ab initio calculations gave for [MeC(Ph)SO₂tBu]Li ? 2 Me₂O an O,Li,C_α contact ion pair (CIP) and for [MeC(Ph)SO₂CF₃]Li ? 2 Me₂O an O,Li,O CIP. According to cryoscopy, [PhCH₂C(Ph)SO₂CF₃]Li, [iHexC(Me)SO₂CF₃]Li, and [PhCH₂C(Ph)SO₂CF₃]NBu₄ predominantly form monomers in tetrahydrofuran (THF) at ?108 °C. The NMR spectroscopic data of salts [R¹(R²)SO₂R³]Li (R³=tBu, CF₃) indicate that the dominating monomeric CIPs are devoid of C_α? Li bonds.     

Structure‐Based Optimization of the Terminal Tripeptide in Glycopeptide Dendrimer Inhibitors of Pseudomonas aeruginosa Biofilms Targeting LecA

The galactopeptide dendrimer GalAG2 ((β‐Gal‐OC₆H₄CO‐Lys‐Pro‐Leu)₄(Lys‐Phe‐Lys‐Ile)₂Lys‐His‐Ile‐NH₂) binds strongly to the Pseudomonas aeruginosa (PA) lectin LecA, and it inhibits PA biofilms, as well as disperses already established ones. By starting with the crystal structure of the terminal tripeptide moiety GalA‐KPL in complex with LecA, a computational mutagenesis study was carried out on the galactotripeptide to optimize the peptide–lectin interactions. 25 mutants were experimentally evaluated by a hemagglutination inhibition assay, 17 by isothermal titration calorimetry, and 3 by X‐ray crystallography. Two of these tripeptides, GalA‐KPY (dissociation constant (K_D)=2.7 μM ) and GalA‐KRL (K_D=2.7 μM ), are among the most potent monovalent LecA ligands reported to date. Dendrimers based on these tripeptide ligands showed improved PA biofilm inhibition and dispersal compared to those of GalAG2 , particularly G2KPY ((β‐Gal‐OC₆H₄CO‐Lys‐Pro‐Tyr)₄(Lys‐Phe‐Lys‐Ile)₂Lys‐His‐Ile‐NH₂). The possibility to retain and even improve the biofilm inhibition in several analogues of GalAG2 suggests that it should be possible to fine‐tune this dendrimer towards therapeutic use by adjusting the pharmacokinetic parameters in addition to the biofilm inhibition through amino acid substitutions.     

Development of a Metal‐Ion‐Mediated Base Pair for Electron Transfer in DNA

A new C‐nucleoside structurally based on the hydroxyquinoline ligand was synthesized that is able to form stable pairs in DNA in both the absence and the presence of metal ions. The interactions between the metal centers in adjacent Cu^II‐mediated base pairs in DNA were probed by electron paramagnetic resonance (EPR) spectroscopy. The metal–metal distance falls into the range of previously reported values. Fluorescence studies with a donor–DNA–acceptor system indicate that photoinduced charge‐transfer processes across these metal‐ion‐mediated base pairs in DNA occur more efficiently than over natural base pairs.