Central Limit Theorems for the Shrinking Target Problem

Suppose B _i :=B(p,r _i ) are nested balls of radius r _i about a point p in a dynamical system (T,X,μ). The question of whether T ⁱ x∈B _i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if $E_{n}:=\sum_{i=1}^{n} \mu(B_{i})$ diverges then there is a quantitative rate of entry and $\lim_{n\to\infty} \frac{1}{E_{n}} \sum_{j=1}^{n} 1_{B_{i}} (T^{i} x) \to1$ for μ a.e. x∈X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form $\lim_{ n\to\infty} \frac{1}{a_{n}} \sum_{i=1}^{n} [1_{B_{i}} (T^{i} x)-\mu(B_{i})] \to N(0,1)$ (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are $a^{2}_{n} \sim E [\sum_{i=1}^{n} 1_{B_{i}} (T^{i} x)-\mu(B_{i})]^{2}$ . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.     

A Coumarin Triflate Reagent Enables One-Step Synthesis of Photo-Caged Lipid Metabolites for Studying Cell Signaling

Photorelease of caged compounds is among the most powerful experimental approaches for studying cellular functions on fast timescales. However, its full potential has yet to be exploited, as the number of caged small molecules available for cell biological studies has been limited by synthetic challenges. Addressing this problem, a straightforward, one-step procedure for efficiently synthesizing caged compounds was developed. An in situ generated benzylic coumarin triflate reagent was used to specifically functionalize carboxylate and phosphate moieties in the presence of free hydroxy groups, generating various caged lipid metabolites, including a number of GPCR ligands. By combining the photo-caged ligands with the respective receptors, an easily implementable experimental platform for the optical control and analysis of GPCR-mediated signal transduction in living cells was developed. Ultimately, the described synthetic strategy allows rapid generation of photo-caged small molecules and thus greatly facilitates the analysis of their biological roles in live cell microscopy assays.     

Observation of entanglement between two light beams spanning an octave in optical frequency

We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.     

Enantioselective Access to 1H‐Isoindoles with Quaternary Stereogenic Centers by Palladium(0)‐Catalyzed C−H Functionalization

A catalytic enantioselective method for the synthesis of chiral 1H‐isoindoles bearing quaternary stereogenic centers is reported. Powered by readily accessible phosphordiamidite ligands, the presented palladium(0)‐catalyzed C?H functionalization uses trifluoroacetimidoyl chlorides as electrophilic components. It delivers previously inaccessible perfluoroalkylated 1H‐isoindoles in high yields and enantioselectivities. The subsequent diastereoselective addition of nucleophiles provides access to densely substituted and sterically hindered isoindolines.     

Structural and functional changes in the membrane and membrane skeleton of red blood cells induced by peroxynitrite

The changes in passive ion permeability of the red blood cell membrane after peroxynitrite action (3 microM-3 mM) have been studied by biophysical (using radioisotopes of rubidium, sodium and sulphur (sulphate)) and electrophysiological methods. The enhancement of passive membrane permeability to cations (potassium and sodium ions) and the inhibition of anion flux through the anion exchanger in peroxynitrite-treated red blood cells were revealed. In patch-clamp experiments the whole-cell conductance after peroxynitrite (80 muM) treatment of red blood cells increased 3-3.5-fold with a shift in the reversal potential from -7.0+/-1.5 mV to -4.3+/-0.9 mV (n=7, p=0.005). The addition of cobalt and nickel ions to red blood cell suspensions before peroxynitrite treatment had no effect on the peroxynitrite-induced cation flux but zinc ions in the same condition decreased cation flux about 2-fold. Using atomic force microscopy methods we revealed an increase in red blood cell membrane stiffness and the membrane skeleton complexity after peroxynitrite action. We conclude that the peroxynitrite-induced water and ion imbalance and reorganization in membrane structure lead to crenation of red blood cells.     

Detailed assignment of the magnetic circular dichroism and UV-vis spectra of five-coordinate high-spin ferric [Fe(TPP)(Cl)

High-spin (hs) ferric heme centers occur in the catalytic or redox cycles of many metalloproteins and exhibit very complicated magnetic circular dichroism (MCD) and UV-vis absorption spectra. Therefore, detailed assignments of the MCD spectra of these species are missing. In this study, the electronic spectra (MCD and UV-vis) of the five-coordinate hs ferric model complex [Fe(TPP)(Cl)] are analyzed and assigned for the first time. A correlated fit of the absorption and low-temperature MCD spectra of [Fe(TPP)(Cl)] lead to the identification of at least 20 different electronic transitions. The assignments of these spectra are based on the following: (a) variable temperature and variable field saturation data, (b) time-dependent density functional theory calculations, (c) MCD pseudo A-terms, and (d) correlation to resonance Raman (rRaman) data to validate the assignments. From these results, a number of puzzling questions about the electronic spectra of [Fe(TPP)(Cl)] are answered. The Soret band in [Fe(TPP)(Cl)] is split into three components because one of its components is mixed with the porphyrin A2u72-->Eg82/83 (pi-->pi*) transition. The broad, intense absorption feature at higher energy from the Soret band is due to one of the Soret components and a mixed sigma and pi chloro to iron CT transition. The high-temperature MCD data allow for the identification of the Q v band at 20 202 cm(-1), which corresponds to the C-term feature at 20 150 cm(-1). Q is not observed but can be localized by correlation to rRaman data published before. Finally, the low energy absorption band around 650 nm is assigned to two P-->Fe charge transfer transitions, one being the long sought after A1u(HOMO)-->d pi transition.     

Enantioselective Access to Spirocyclic Sultams by Chiral Cpx–Rhodium(III)‐Catalyzed Annulations

Chiral spirocyclic sultams are a valuable compound class in organic and medicinal chemistry. A rapid entry to this structural motif involves a [3+2] annulation of an N‐sulfonyl ketimine and an alkyne. Although the directing‐group properties of the imino group for C?H activation have been exploited, the developments of related asymmetric variants have remained very challenging. The use of rhodium(III) complexes equipped with a suitable atropchiral cyclopentadienyl ligand, in conjunction with a carboxylic acid additive, enables an enantioselective and high yielding access to such spirocyclic sultams.     

Metal-free entry to phosphonylated isoindoles by a cascade of 5-exo-dig cyclization, a [1,3]-alkyl shift, and aromatization under microwave heating

[reaction: see text] When o-ethynylbenzyl alpha-aminophosphonates are heated under microwave conditions, a rearrangement occurs which results in the formation of phosphonylated isoindoles. The rearrangement consists of a 5-exo-dig cyclization followed by a [1,3]-alkyl shift and finally aromatization.     

FeIII(tmdta)]--twist-boat/half-chair conformer ratio reliably deduced from DFT-calculated Raman spectra

The equilibrium between the twist-boat (tb) and half-chair (hc) conformers of the central diamine chelate ring of [Fe(III)(tmdta)]- in solids and aqueous solution has been studied by Raman spectroscopy, supported by calculated Raman spectra using Density Functional Theory.