Probing the Catalytically Active Species in POM-Catalysed DNA-Model Hydrolysis**

Phosphoester hydrolysis is an important chemical step in DNA repair. One archetypal molecular model of phosphoesters is para-nitrophenylphosphate (pNPP). It has been shown previously that the presence of molecular metal oxide [Mo₇O₂₄]⁶⁻ may catalyse the hydrolysis of pNPP through the partial decomposition of polyoxomolybdate framework resulting in a [(PO₄)₂Mo₅O₁₅]⁶⁻ product. Real-time monitoring of the catalytic system using electrospray ionisation mass spectrometry (ESI-MS) provided a glance into the species present in the reaction mixture and identification of potential catalytic candidates. Following up on the obtained spectrometric data, Density Functional Theory (DFT) calculations were carried out to characterise the hypothetical intermediate [Mo₅O₁₅(pNPP)₂(H₂O)₆]⁶⁻ that would be required to form under the hypothesised transformation. Surprisingly, our results point to the dimeric [Mo₂O₈]⁴⁻ anion resulting from the decomposition of [Mo₇O₂₄]⁶⁻ as the active catalytic species involved in the hydrolysis of pNPP rather than the originally assumed {Mo₅O₁₅} species. A similar study was carried out involving the same species but substituting Mo by W. The mechanism involving W species showed a higher barrier and less stable products in agreement with the non-catalytic effect found in experimental results.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Operator Splitting Multiscale Finite Volume Element Method for Two-Phase Flow with Capillary Pressure

A numerical method used for solving a two-phase flow problem as found in typical oil recovery is investigated in the setting of physics-based two-level operator splitting. The governing equations involve an elliptic differential equation coupled with a parabolic convection-dominated equation which poses a severe restriction for obtaining fully implicit numerical solutions. Furthermore, strong heterogeneity of the porous medium over many length scales adds to the complications for effectively solving the system. One viable approach is to split the system into three sub-systems: the elliptic, the hyperbolic, and the parabolic equation, respectively. In doing so, we allow for the use of appropriate numerical discretization for each type of equation and the careful exchange of information between them. We propose to use the multiscale finite volume element method (MsFVEM) for the elliptic and parabolic equations, and a nonoscillatory difference scheme for the hyperbolic equation. Performance of this procedure is confirmed through several numerical experiments.     

Quantum Light-Front Wave Function in a Scalar Yukawa Model

The valence component of the light-front wave function of a quantum of a scalar field is studied within a bosonic model. The light-front time projection of the inhomogeneous Bethe-Salpeter equation for the vertex function in the covariant ladder approximation is given. The valence wave function and distribution are obtained from the numerical solution of the light-front equation for the vertex with different values of the time-like off-shell momentum carried by the quantum.     

A new oxovanadium(IV)–cucurbit[6]uril complex: Properties and potential for confined heterogeneous catalytic oxidation reactions

This work presents a new oxovanadium(IV)–cucurbit[6]uril complex, which combines the catalytic properties of the metal ion with the size-excluding properties of the macrocycle cavity. In this coordination compound, the VO²⁺${\text{VO}}^{2+}$ ions are coordinated to the oxygen atoms located at the rim of the macrocycle in slightly distorted square-pyramidal configurations, which are in fact _C2v$C_{2v}$ symmetries. This combination results in a size-selective heterogeneous catalyst, which is able to oxidize linear alkanes like n-pentane at room temperature, but not styrene, cyclohexane or z-cyclooctene, which are too big to enter the cucurbit[6]uril cavity. The results presented here contribute to understanding the mechanism of alkane catalytic oxidation by oxovanadium(IV) complexes.     

Non-Positive Curvature and Global Invertibility of Maps

Let F:M→N be a C ¹ map between Riemannian manifolds of the same dimension, M complete, N Cartan–Hadamard. We show that F is a C ¹ diffeomorphism if inf _x∈M |d(B _ζ °F)(x)|>0 for all ζ∈N(∞) and Busemann functions B _ζ . This generalizes the Cartan–Hadamard theorem and the Hadamard invertibility criterion, which requires inf _x∈M ∥DF(x)^?1∥^?1=inf _ζ∈N(∞)inf _x∈M |d(B _ζ °F)(x)|>0. Our proofs use a version of the shooting method for two-point boundary value problems. These ideas lead to new results about the size of the critical set of a function f∈C ²(? ⁿ ,?): a) If \(\inf_{x\in \mathbb{R}^{n}}|\operatorname{Hess} f(x)v|>0\) for all v≠0 then the function f has precisely one critical point. (b) If g∈C ²(? ⁿ ,?) is the C ¹ local uniform limit of functions as in a), and \(\operatorname{Hess} g(x)\) is nowhere singular, then g has at most one critical point. The totality of functions described in (b) properly contains the class consisting of all C ² strictly convex functions defined on ? ⁿ .     

Semi-Parametric Probability-Weighted Moments Estimation Revisited

In this paper, for heavy-tailed models and through the use of probability weighted moments based on the largest observations, we deal essentially with the semi-parametric estimation of the Value-at-Risk at a level p, the size of the loss occurred with a small probability p, as well as the dual problem of estimation of the probability of exceedance of a high level x. These estimation procedures depend crucially on the estimation of the extreme value index, the primary parameter in Statistics of Extremes, also done on the basis of the same weighted moments. Under regular variation conditions on the right-tail of the underlying distribution function F, we prove the consistency and asymptotic normality of the estimators under consideration in this paper, through the usual link of their asymptotic behaviour to the one of the extreme value index estimator they are based on. The performance of these estimators, for finite samples, is illustrated through Monte-Carlo simulations. An adaptive choice of thresholds is put forward. Applications to a real data set in the field of insurance as well as to simulated data are also provided.     

Renormalization in few-body nuclear physics

Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). They express the renormalization group invariance of quantum mechanics. The present approach for the renormalization scheme relies on a subtracted T-matrix equation.     

Production of the Bengamide Class of Marine Natural Products in Myxobacteria: Biosynthesis and Structure–Activity Relationships

The bengamides, sponge‐derived natural products that have been characterized as inhibitors of methionine aminopeptidases (MetAPs), have been intensively investigated as anticancer compounds. We embarked on a multidisciplinary project to supply bengamides by fermentation of the terrestrial myxobacterium M. virescens, decipher their biosynthesis, and optimize their properties as drug leads. The characterization of the biosynthetic pathway revealed that bacterial resistance to bengamides is conferred by Leu 154 of the myxobacterial MetAP protein, and enabled transfer of the entire gene cluster into the more suitable production host M. xanthus DK1622. A combination of semisynthesis of microbially derived bengamides and total synthesis resulted in an optimized derivative that combined high cellular potency in the nanomolar range with high metabolic stability, which translated to an improved half‐life in mice and antitumor efficacy in a melanoma mouse model.