Estimating Invariant Probability Densities for Dynamical Systems

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.     

Molecular dynamics averaging of Xe chemical shifts in liquids

The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.     

Nickel-catalyzed intramolecular C–H arylation using aryl pivalates as electrophiles

This paper describes a method for nickel catalyzed intramolecular C–H arylation using aryl pivalates as electrophiles. The transformation is efficient for the synthesis of diverse electronically and sterically differentiated dibenzofurans. Additionally, the method could be expanded toward the synthesis of carbazoles. Preliminary mechanistic studies of the transformation are also described.     

Constructions for Terraces and R‐Sequencings,Including a Proof That Bailey's Conjecture Holds for Abelian Groups

Every abelian group of even order with a noncyclic Sylow 2‐subgroup is known to be R‐sequenceable except possibly when the Sylow 2‐subgroup has order 8. We construct an R‐sequencing for many groups with elementary abelian Sylow 2‐subgroups of order 8 and use this to show that all such groups of order other than 8 also have terraces. This completes the proof of Bailey's Conjecture in the abelian case: all abelian groups other than the noncyclic elementary abelian 2‐groups have terraces. For odd orders it is known that abelian groups are R‐sequenceable except possibly those with noncyclic Sylow 3‐subgroups. We show how the theory of narcissistic terraces can be exploited to find R‐sequencings for many such groups, including infinitely many groups with each possible of Sylow 3‐subgroup type of exponent at most 3¹² and all groups whose Sylow 3‐subgroups are of the form or .     

Nuclear magnetic shielding and chirality IV. The odd and even character of the shielding response to a chiral potential

We investigate the odd and even character of the shielding response in a chiral molecule (modeled by a Ne8 helix) when subjected to a chiral potential. We establish that the diastereomeric splittings are a measure of odd powers of Vodd. Implications for diastereomeric, splittings of Xe in handed cages with handed tethers are discussed.     

Properties of graphical regression models for multidimensional categorical data

We propose a two-component graphical chain model, the discrete regression distribution, where a set of discrete random variables is modeled as a response to a set of categorical and continuous covariates. The proposed model is useful for modeling a set of discrete variables measured at multiple sites along with a set of continuous and/or discrete covariates. The proposed model allows for joint examination of the dependence structure of the discrete response and observed covariates and also accommodates site-to-site variability. We develop the graphical model properties and theoretical justifications of this model. Our model has several advantages over the traditional logistic normal model used to analyze similar compositional data, including site-specific random effect terms and the incorporation of discrete and continuous covariates.     

The effectiveness of 1H decoupling in the 13C MAS NMR of paramagnetic solids: an experimental case study incorporating copper(II) amino acid complexes

The use of continuous-wave (CW) 1H decoupling has generally provided little improvement in the 13C MAS NMR spectroscopy of paramagnetic organic solids. Recent solid-state 13C NMR studies have demonstrated that at rapid magic-angle spinning rates CW decoupling can result in reductions in signal-to-noise and that 1H decoupling should be omitted when acquiring 13C MAS NMR spectra of paramagnetic solids. However, studies of the effectiveness of modern 1H decoupling sequences are lacking, and the performance of such sequences over a variety of experimental conditions must be investigated before 1H decoupling is discounted altogether. We have studied the performance of several commonly used advanced decoupling pulse sequences, namely the TPPM, SPINAL-64, XiX, and eDROOPY sequences, in 13C MAS NMR experiments performed under four combinations of the magnetic field strength (7.05 or 11.75T), rotor frequency (15 or 30kHz), and 1H rf-field strength (71, 100, or 140kHz). The effectiveness of these sequences has been evaluated by comparing the 13C signal intensity, linewidth at half-height, LWHH, and coherence lifetimes, T2('), of the methine carbon of copper(II) bis(dl-alanine) monohydrate, Cu(ala)(2).H2O, and methylene carbon of copper(II) bis(dl-2-aminobutyrate), Cu(ambut)(2), obtained with the advanced sequences to those obtained without 1H decoupling, with CW decoupling, and for fully deuterium labelled samples. The latter have been used as model compounds with perfect 1H decoupling and provide a measure of the efficiency of the 1H decoupling sequence. Overall, the effectiveness of 1H decoupling depends strongly on the decoupling sequence utilized, the experimental conditions and the sample studied. Of the decoupling sequences studied, the XiX sequence consistently yielded the best results, although any of the advanced decoupling sequences strongly outperformed the CW sequence and provided improvements over no 1H decoupling. Experiments performed at 7.05T demonstrate that the XiX decoupling sequence is the least sensitive to changes in the 1H transmitter frequency and may explain the superior performance of this decoupling sequence. Overall, the most important factor in the effectiveness of 1H decoupling was the carbon type studied, with the methylene carbon of Cu(ambut)(2) being substantially more sensitive to 1H decoupling than the methine carbon of Cu(ala)(2).H2O. An analysis of the various broadening mechanisms contributing to 13C linewidths has been performed in order to rationalize the different sensitivities of the two carbon sites under the four experimental conditions.     

Top-quark pairs at high invariant mass: a model-independent discriminator of new physics at the Large Hadron Collider

We study top-quark pair production to probe new physics at the CERN Large Hadron Collider. We propose reconstruction methods for tt[over] semileptonic events and use them to reconstruct the tt[over] invariant mass. The angular distribution of top quarks in their c.m. frame can determine the spin and production subprocess for each new physics resonance. Forward-backward asymmetry and CP-odd variables can be constructed to further delineate the nature of new physics. We parametrize the new resonances with a few generic parameters and show high invariant mass top pair production may provide an early indicator for new physics beyond the standard model.