Temperley-Lieb planar algebra modules arising from the ADE planar algebras

A Hilbert module over a planar algebra P is essentially a Hilbert module over a canonically defined algebra spanned by the annular tangles in P. It follows that any planar algebra Q containing P is a module over P, and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar algebra with the same modulus. We describe a positivity result that allows us to describe irreducible Temperley-Lieb planar algebra modules, and apply the result to decompose the planar algebras determined by the Coxeter graphs A_n (n?3), D_n (n?4), E₆, E₇, and E₈.     

Molality as a unit of measure for expressing 1H MRS brain metabolite concentrations in vivo

Absolute concentrations of cerebral metabolite in in vivo 1H magnetic resonance spectroscopy studies (1H-MRS) are widely reported in molar units as moles per liter of tissue, or in molal units as moles per kilogram of tissue. Such measurements require external referencing or assumptions as to local water content. To reduce the scan time, avoid assumptions that may be invalid under specific pathologies, and provide a universally accessible referencing procedure, we suggest that metabolite concentrations from 1H-MRS measurements in vivo be reported in molal units as moles per kilogram of tissue water. Using internal water referencing, a two-compartment water model, a simulated brain spectrum for peak identification, and a spectroscopic bi-exponential spin-spin relaxation segmentation technique, we measured the absolute concentrations for the four common 1H brain metabolites: choline (Cho), myo-inositol (mIno), phosphocreatine + creatine (Cr), and N-acetyl-aspartate (NAA), in the hippocampal region (n = 26) and along the Sylvian fissure (n = 61) of 35 healthy adults. A stimulated echo localization method (20 ms echo time, 10 ms mixing time, 4 s repetition time) yielded metabolite concentrations, uncorrected for metabolite relaxation or contributions from macromolecule resonances, that were expectantly higher than with molar literature values. Along the Sylvian fissure the average concentrations (coefficient of variation (CV)) in mmoles/kg of tissue water were 17.6 (12%) for NAA, 14.2 (9%) for Cr, 3.6 (13%) for Cho, and 13.2 (15%) for mIno. Respective values for the hippocampal region were 15.7 (20%), 14.7 (16%), 4.6 (19%), and 17.7 (26%). The concentrations of the two regions were significantly different (p 相似文献   

An operator-valued Lyapunov theorem

We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak^?-closed convex set of quantum effects (positive operators bounded above by the identity operator) under a sufficient condition on the non-injectivity of integration. To prove the operator-valued version of Lyapunov's theorem, we must first define the notions of essentially bounded, essential support, and essential range for quantum random variables (Borel measurable functions from a set to the bounded linear operators acting on a Hilbert space).     

Uniform-in-Bandwidth Functional Limit Laws

We provide uniform-in-bandwidth functional limit laws for the increments of the empirical and quantile processes. Our theorems, established in the framework of convergence in probability, imply new sharp uniform-in-bandwidth limit laws for functional estimators. In particular, they yield the explicit value of the asymptotic limiting constant for the uniform-in-bandwidth sup-norm of the random error of kernel density estimators. We allow the bandwidth to vary within the complete range for which the estimators are consistent.     

Elliptical magnetic resonance spectroscopic imaging with GRAPPA for imaging brain tumors at 3 T

Magnetic Resonance Spectroscopic Imaging (MRSI) is a technique for imaging spatial variation of metabolites and has been very useful in characterizing biochemical changes associated with disease as well as response to therapy in malignant pathologies. This work presents a self-calibrated undersampling to accelerate 3D elliptical MRSI and an extrapolation-reconstruction algorithm based on the GRAPPA method. The accelerated MRSI technique was tested in three volunteers and five brain tumor patients. Acceleration allowed larger spatial coverage and consequently, less lipid contamination in spectra, compared to fully sampled acquisition within the same scantime. Metabolite concentrations measured from the accelerated acquisitions were in good agreement with measurements obtained from fully sampled MRSI scans.     

Burstiness and fractional diffusion on complex networks

Many dynamical processes on real world networks display complex temporal patterns as, forinstance, a fat-tailed distribution of inter-events times, leading to heterogeneouswaiting times between events. In this work, we focus on distributions whose averageinter-event time diverges, and study its impact on the dynamics of random walkers onnetworks. The process can naturally be described, in the long time limit, in terms ofRiemann-Liouville fractional derivatives. We show that all the dynamical modes possess, inthe asymptotic regime, the same power law relaxation, which implies that the dynamics doesnot exhibit time-scale separation between modes, and that no mode can be neglected versusanother one, even for long times. Our results are then confirmed by numericalsimulations.     

Ultra-rapid separation of an angiotensin mixture in nanochannels using shear-driven chromatography

The present paper reports on the separation of a mixture of fluorescein isothiocyanate-labeled angiotensin I and II peptides in a shear-driven nanochannel with a C18-coating and using an eluent consisting of 5% acetonitrile in 0.02 M aqueous phosphate buffer at pH 6.5. The flat-rectangular nanochannel in fused silica consisted of an etched structure in combination with a flat moving wall. The very fast separation kinetics that can be achieved in a nanochannel allowed to separate the angiotensin peptides in less then 0.2 s in a distance of only 1.8 mm. Plate heights as small as 0.4 microm were calculated after substraction of the injection effect.     

CO2 Hydroboration: Impact of the Boryl Moieties on the Reactivity of Four Bis(boryl)acetal Compounds toward 2,6-Diisopropylaniline

The hydroboration of CO₂ into bis(boryl)acetal (BBA) compounds is an important transformation, since it enabled to selectively reduce CO₂ by 4e^- and to subsequently use the BBA compounds as C₁ and C_n sources. However, the influence of the nature of the boryl moieties on the reactivity of BBA compounds has not been evaluated so far. In the present study, four BBA compounds – including two new ones – were reacted with 2,6-diisopropylaniline to afford the expected imine. Significant differences in the rate of the reaction from minutes to weeks have been observed depending on the BBA used, showing the importance of the nature of the boryl moieties. Theoretical investigations enabled to propose a mechanism involving the addition of the aniline to the BBA as the rate-determining step and to determine that the steric hindrance of the BBA compounds is the main factor driving the rate of this condensation reaction.     

Kinetic stability of complex molecular clusters

This investigation is concerned with modeling the evaporation, or decay, of n-nonane molecular clusters. We use a unique cluster decay model that was first developed to estimate the decay time scale of argon clusters using molecular-dynamics simulations. In this study we seek to enhance the model so that it represents a more complex cluster decay dynamic, suitable for n-nonane clusters. Experimental measurements of nucleation rates of n-nonane droplets have been used to deduce the rate at which a molecule escapes from the cluster. Typically for an n-nonane cluster containing 40 molecules, at an experimental temperature of 225 K, the empirical decay time, which is the inverse of the decay rate, is estimated to be 50 ns. For this time scale, the direct observation of n-nonane cluster decay from a molecular-dynamics trajectory is not feasible, since decay events are so rare. However, the cluster decay model uses a combination of molecular dynamics and stochastic dynamics in order to resolve the problem associated with long decay time scales. The model is based on a Langevin treatment that views cluster decay as single-particle escape from a confining potential of mean force. It is used to predict kinetic decay times of n-nonane clusters. We discover this result differs significantly from a classically derived decay time scale determined from a continuum thermodynamic treatment of the population balance equations of clusters. However, the dynamically generated results obtained from the kinetic decay model compare more favorably than the classical results with the empirical decay times that are deduced from experimental measurements of n-nonane clusters.     

Natural products as an inspiration in the diversity-oriented synthesis of bioactive compound libraries

The purpose of diversity-oriented synthesis is to drive the discovery of small molecules with previously unknown biological functions. Natural products necessarily populate biologically relevant chemical space, since they bind both their biosynthetic enzymes and their target macromolecules. Natural product families are, therefore, libraries of pre-validated, functionally diverse structures in which individual compounds selectively modulate unrelated macromolecular targets. This review describes examples of diversity-oriented syntheses which have, to some extent, been inspired by the structures of natural products. Particular emphasis is placed on innovations that allow the synthesis of compound libraries that, like natural products, are skeletally diverse. Mimicking the broad structural features of natural products may allow the discovery of compounds that modulate the functions of macromolecules for which ligands are not known. The ability of innovations in diversity-oriented synthesis to deliver such compounds is critically assessed.