Uncommon suffix tries

Common assumptions on the source producing the words inserted in a suffix trie with n leaves lead to a height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of n and another one whose saturation level is negligible with respect to . Both are built from VLMC (Variable Length Markov Chain) probabilistic sources and are easily extended to families of tries having the same properties. The first example corresponds to a “logarithmic infinite comb” and enjoys a non uniform polynomial mixing. The second one corresponds to a “factorial infinite comb” for which mixing is uniform and exponential. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 117–141, 2015     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

Estimation of rating classes and default probabilities in credit risk models with dependencies

Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.     

Synthesis of 3-iodothiophenes via iodocyclization of (Z)-thiobutenynes

A simple synthesis of 3-iodothiophenes was demonstrated using a wide range of (Z)-thioenynes. The key step in the iodocyclofunctionalization was the selective reduction of the triple bond in (Z)-thioenynes by the addition of iodine as an electrophilic agent. The 3-iodothiophenes were obtained in good to excellent yields of 61–92%. The 3-iodothiophenes were used as substrates in Sonogashira cross-coupling reactions to obtain thiophene acetylenes.     

Stereoselective total synthesis of penaresidin A starting from d-galactal

A stereoselective total synthesis of penaresidin A has been accomplished involving Sharpless asymmetric epoxidation, regioselective ring-opening of epoxide, azetidine formation via S_N2 reaction, Jung’s protocol, and Julia–Kocienski olefination. This approach has successfully demonstrated the synthetic utility of d-galactal in the construction of azetidine core of the natural product.     

Asymptotically optimal neighbour sum distinguishing colourings of graphs

Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C₅. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015     

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.     

Computation of electronic structure and magnetic properties of strongly correlated materials with LDA+DMFT method

In this review, we describe general ideas of the LDA+DMFT method which merges dynamical mean-field theory (DMFT) and density functional theory (in particular the local density approximation (LDA)). Nowadays, the LDA+DMFT computational scheme is the most powerful numerical tool for studying physical properties of real materials and chemical compounds. It incorporates the advantage of DMFT to treat the full range of local dynamical Coulomb correlations and the ability of band methods to describe material-specific band dispersion caused by the lattice periodicity. We briefly discuss underlying physical ideas of LDA+DMFT and its mathematical implementation. Then different algorithms applied to solution of the DMFT impurity problem are briefly described. We then give examples of successful applications of the LDA+DMFT method to study spectral and magnetic properties of recently synthesized compounds like pnictide superconductors as well as classic charge-transfer systems NiO and MnO.     

Strong Coupling and Laser Action of Ladder‐Type Oligo(p‐phenylene)s in a Microcavity

We investigate the coupling of ladder‐type quarterphenyl to the photon modes of a dielectric ZrO_x/SiO_x microcavity at ultraviolet wavelengths. For a relatively long cavity (≈10 μm) with high‐reflectivity mirrors (0.998), optically pumped laser action is demonstrated in the weak‐coupling regime. We observe single‐mode operation with a threshold of 0.4 mJ cm^?2. Strong coupling is achieved by using a short λ/2 cavity. We find pronounced anti‐crossing features of the molecular (0,0) and (0,1) vibronic transitions and the cavity mode in angle‐dependent reflectivity measurements providing Rabi splittings of (90±10) meV. All these features occur spectrally resonant to the exciton transition of ZnO demonstrating the potential of ladder‐type oligo(p‐phenylene)s for the construction of inorganic/organic hybrid microcavities.     

Pyridinylidenaminophosphines: Facile Access to Highly Electron-Rich Phosphines

Electron-rich tertiary phosphines are valuable species in chemical synthesis. However, their broad application as ligands in catalysis and reagents in stoichiometric reactions is often limited by their costly synthesis. Herein, we report the synthesis and properties of a series of phosphines with 1-alkylpyridin-4-ylidenamino and 1-alkylpyridin-2-ylidenamino substituents that are accessible in a very short and scalable route starting from commercially available aminopyridines and chlorophosphines. The determination of the Tolman electronic parameter (TEP) value reveals that the electron donor ability can be tuned by the substituent pattern at the aminopyridine backbone and it can exceed that of common alkylphosphines and N-heterocyclic carbenes. The potential of the new phosphines as strong nucleophiles in phosphine-mediated transformations is demonstrated by the formation of Lewis base adducts with CO₂ and CS₂. In addition, the coordination chemistry of the new phosphines towards Cu^I, Au^I, and Pd^II metal centers has been explored, and a convenient procedure to introduce the most basic phosphine into metal complexes starting from air-stable phosphonium salt is described.