Rectangular amplitudes,conformal blocks,and applications to loop models

In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan, et al., Nucl. Phys. B 862 (2012) 553–575]. Here we develop a general formalism of rectangle boundary states using conformal field theory, adapted to describe geometries supporting different boundary conditions. We discuss the computation of rectangular amplitudes and their modular properties, presenting explicit results for the case of free theories. In a second part of the paper we focus on applications to loop models, discussing in details lattice discretizations using both numerical and analytical calculations. These results allow to interpret geometrically conformal blocks, and as an application we derive new probability formulas for self-avoiding walks.     

Estimation of return values of wave height: consequences of missing observations

Extreme-value statistics is often used to estimate so-called return values (actually related to quantiles) for environmental quantities like wind speed or wave height. A basic method for estimation is the method of block maxima which consists in partitioning observations in blocks, where maxima from each block could be considered independent. Typically a block could be chosen as one year. Large portions of missing data could result in problems for estimation and seems to be an issue not highlighted in detail in the literature. The method of block maxima is here applied to real data and a related simulation study was performed, pointing out that substantially low values tend to increase the estimated return values. A plausible explanation is given by studying the redistribution of probability mass and the implications of this for the behaviours of the tails of distributions.     

The Accumulated Persistence Function,a New Useful Functional Summary Statistic for Topological Data Analysis,With a View to Brain Artery Trees and Spatial Point Process Applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples.     

Volatility skews and extensions of the Libor market model

The paper considers extensions of the Libor market model to markets with volatility skews in observable option prices. The family of forward rate processes is expanded to include diffusions with non-linear forward rate dependence, and efficient techniques for calibration to quoted prices of caps and swaptions are discussed. Special emphasis is put on generalized CEV processes for which closed-form expressions for cap and swaption prices are derived. Modifications of the CEV process which exhibit more appealing growth and boundary characteristics are also discussed. The proposed models are investigated numerically through Crank–Nicholson finite difference schemes and Monte Carlo simulations.     

On Frobenius splitting of orbit closures of spherical subgroups in flag varieties

Let H denote a spherical subgroup within a semisimple algebraic group G. In this paper we study the closures of the finitely many H-orbits in the flag variety of G. Using the language of Frobenius splitting we provide a criterion for these closures to have nice geometric and cohomological properties. We then show how the criterion applies to the spherical subgroups of minimal rank studied by N. Ressayre. Finally, we also provide applications of the criterion to orbit closures which are not multiplicity-free in the sense defined by M. Brion.     

Linearly polarized, single-mode spontaneous emission in a photonic nanowire

We introduce dielectric elliptical photonic nanowires to funnel efficiently the spontaneous emission of an embedded emitter into a single optical mode. Inside a wire with a moderate lateral aspect ratio, the electromagnetic environment is largely dominated by a single guided mode, with a linear polarization oriented along the ellipse major axis. The resulting monomode spontaneous emission is maintained over a broad wavelength range, a key asset of this 1D photonic structure. Our theoretical analysis is completed by an experimental study of GaAs elliptical photonic wires with embedded InAs quantum dots. In particular, the fraction of collected photons with the desired linear polarization can exceed 95%.     

A first low‐resolution difference Fourier map of phosphorus in a membrane protein from near‐edge anomalous diffraction

Crystal diffraction of three membrane proteins (cytochrome bc₁ complex, sarcoplasmic reticulum Ca²⁺ ATPase, ADP‐ATP carrier) and of one nucleoprotein complex (leucyl tRNA synthetase bound to tRNAleu, leuRS:tRNAleu) was tested at wavelengths near the X‐ray K‐absorption edge of phosphorus using a new set‐up for soft X‐ray diffraction at the beamline ID01 of the ESRF. The best result was obtained from crystals of Ca²⁺ ATPase [adenosin‐5′‐(β,γ‐methylene) triphosphate complex] which diffracted out to 7 Å resolution. Data were recorded at a wavelength at which the real resonant scattering factor of phosphorus reaches the extreme value of ?20 electron units. The positions of the four triphosphates of the monoclinic unit cell of the ATPase have been obtained from a difference Fourier synthesis based on a limited set of anomalous diffraction data.     

Asymmetric Transfer Hydrogenation of Ketones Catalyzed by Amino Acid Derived Rhodium Complexes: On the Origin of Enantioselectivity and Enantioswitchability

Amino acid based thioamides, hydroxamic acids, and hydrazides have been evaluated as ligands in the rhodium‐catalyzed asymmetric transfer hydrogenation of ketones in 2‐propanol. Catalysts containing thioamide ligands derived from L ‐valine were found to selectively generate the product with an R configuration (95 % ee), whereas the corresponding L ‐valine‐based hydroxamic acids or hydrazides facilitated the formation of the (S)‐alcohols (97 and 91 % ee, respectively). The catalytic reduction was examined by performing a structure–activity correlation investigation with differently functionalized or substituted ligands and the results obtained indicate that the major difference between the thioamide and hydroxamic acid based catalysts is the coordination mode of the ligands. Kinetic experiments were performed and the rate constants for the reduction reactions were determined by using rhodium–arene catalysts derived from amino acid thioamide and hydroxamic acid ligands. The data obtained show that the thioamide‐based catalyst systems demonstrate a pseudo‐first‐order dependence on the substrate, whereas pseudo‐zero‐order dependence was observed for the hydroxamic acid containing catalysts. Furthermore, the kinetic experiments revealed that the rate‐limiting steps of the two catalytic systems differ. From the data obtained in the structure–activity correlation investigation and along with the kinetic investigation it was concluded that the enantioswitchable nature of the catalysts studied originates from different ligand coordination, which affects the rate‐limiting step of the catalytic reduction reaction.     

Large scale biomimetic membrane arrays

To establish planar biomimetic membranes across large scale partition aperture arrays, we created a disposable single-use horizontal chamber design that supports combined optical–electrical measurements. Functional lipid bilayers could easily and efficiently be established across CO₂ laser micro-structured 8?×?8 aperture partition arrays with average aperture diameters of 301?±?5 μm. We addressed the electro-physical properties of the lipid bilayers established across the micro-structured scaffold arrays by controllable reconstitution of biotechnological and physiological relevant membrane peptides and proteins. Next, we tested the scalability of the biomimetic membrane design by establishing lipid bilayers in rectangular 24?×?24 and hexagonal 24?×?27 aperture arrays, respectively. The results presented show that the design is suitable for further developments of sensitive biosensor assays, and furthermore demonstrate that the design can conveniently be scaled up to support planar lipid bilayers in large square-centimeter partition arrays.

[UF6]2−: A Molecular Hexafluorido Actinide(IV) Complex with Compensating Spin and Orbital Magnetic Moments

The first structurally characterized hexafluorido complex of a tetravalent actinide ion, the [UF₆]^2? anion, is reported in the (NEt₄)₂[UF₆]?2 H₂O salt ( 1 ). The weak magnetic response of 1 results from both U^IV spin and orbital contributions, as established by combining X‐ray magnetic circular dichroism (XMCD) spectroscopy and bulk magnetization measurements. The spin and orbital moments are virtually identical in magnitude, but opposite in sign, resulting in an almost perfect cancellation, which is corroborated by ab initio calculations. This work constitutes the first experimental demonstration of a seemingly non‐magnetic molecular actinide complex carrying sizable spin and orbital magnetic moments.