1,3-Dilithio-2-(diphenylmethylene)propane

The reaction of 2,2-diphenylmethylenecyclopropane (5) with an excess of lithium and a catalytic amount of DTBB (4 mol %) in THF at −78 °C leads to the formation of dilithiated species 6-8 by reductive opening of the cyclopropane ring. Further reaction of these intermediates with different electrophiles [E = H₂O, D₂O, CH₂CMeCH₂Cl, Me₃SiCl, Me₃SiCH₂Cl, t-BuCHO, Me₂CO, Et₂CO, n-Pr₂CO, i-Pr₂CO, t-Bu₂CO, (CH₂)₅CO, Ph₂CO and adamantanone] is highly regioselective, yielding exclusively the corresponding products 9, after hydrolysis with water. However, when 3-chloro-2-(chloromethyl)propene (14) is used as a dielectrophile, the cyclisation to give a six-membered ring takes place through intermediate 6, giving compound 16 as the only reaction product.     

Multifaceted palladium catalysts towards the tandem diboration-arylation reactions of alkenes

Novel Pd(2) (6+) compounds have been synthesized in high yield. These compounds and their Pd(2) (4+) counterparts as synthetic precursors mediate the diboration of vinylarenes and aliphatic 1-alkenes, and under mild and basic reaction conditions they produce a variety of 1,2-diboronate esters with excellent conversions and chemoselectivities. The presence of bis(catecholato)diboron (B(2)cat(2)) favours the reduction of Pd(III) to Pd(II), while the catalytic precursor of Pd(II) is transformed into Pd(0)-nanoparticles. An "in situ" catalytic tandem reaction has been designed to transform the diboronate intermediates into the monoarylated product, which after oxidative workup, provides the carbohydroxylated adduct. Eventually, the same catalyst performs both sequences with total conversion from the alkene.     

The non-random walk of stock prices: the long-term correlation between signs and sizes

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.     

Estimating the absolute flux distribution for a synchrotron X‐ray beam using ionization‐chamber measurements with various filters

It is shown that an extensive set of accurate ionization‐chamber measurements with a primary polychromatic synchrotron X‐ray beam transmitted through various filter combinations/thicknesses can be used to quite effectively estimate the absolute flux distribution. The basic technique is simple but the `inversion' of the raw data to extract the flux distribution is a fundamentally ill‐posed problem. It is demonstrated, using data collected at the Imaging and Medical Beamline (IMBL) of the Australian Synchrotron, that the absolute flux can be quickly and reliably estimated if a suitable choice of filters is made. Results are presented as a function of the magnetic field (from 1.40 to 4.00 T) of the superconducting multi‐pole wiggler insertion device installed at IMBL. A non‐linear least‐squares refinement of the data is used to estimate the incident flux distribution and then comparison is made with calculations from the programs SPECTRA, XOP and spec.exe. The technique described is important not only in estimating flux itself but also for a variety of other, derived, X‐ray properties such as beam quality, power density and absorbed‐dose rate. The applicability of the technique with a monochromatic X‐ray beam for which there is significant harmonic contamination is also demonstrated. Whilst absolute results can also be derived in this monochromatic beam case, relative (integrated) flux values are sufficient for our primary aim of establishing reliable determinations of the percentages of the various harmonic components.     

Generation of hierarchically correlated multivariate symbolic sequences

We introduce a method to generate multivariate series of symbols from a finite alphabet with a given hierarchical structure of similarities based on the Hamming distance. The target hierarchical structure of similarities is arbitrary, for instance the one obtained by some hierarchical clustering method applied to an empirical matrix of similarities. The method that we present here is based on a generating mechanism that does not make use of mutation rate, which is widely used in phylogenetic analysis. Here we use the proposed simulation method to investigate the relationship between the bootstrap value associated with a node of a phylogeny and the probability of finding that node in the true phylogeny. The results of this analysis are compared with those obtained in the literature according to an evolutionary model with a per-symbol constant mutation rate. We observe that the relationship between the bootstrap value of a node and the probability of the corresponding clade being correct is sensitive to both the length of data series and the length of the branch connecting the node to its closest ancestor in the phylogenetic tree, whereas such a relationship is only slightly affected by the topology of the true phylogeny and by the absolute value of similarity.     

Identifiability of the MAP 2/G/1 queueing system

In this paper, we study how the lack of a unique representation for the two-state Markovian arrival process (MAP ₂) can influence statistical estimation for the MAP ₂/G/1 queueing system. In particular, given two equivalent representations of the same MAP ₂, we find that the steady-state distributions of the queuing system can be identified.