An interpretation of structural sorting diagrams for AB type compounds using molecular orbital ideas

The factors governing the structure adopted by a particular AB compound are investigated by deriving two parameters reflecting aspects of the interaction between A and B, using simple molecular orbital ideas, which can be quantified by use of atomic parameters derived from pseudopotential theory. A plot of the values of these two parameters, for a large database of compounds, produces a remarkable topological clustering of AB compounds with the same structure. This structural sorting can also be effected for nonoctet AB compounds if the number of electrons is taken into account. These parameters are related to other indices, R_σ, R_π, previously used by Bloch, Zunger, Phillips et al. to construct structural sorting diagrams. Hence we find a justification for the success of such displays, and shed light on the reasons underpinning structural preference, in terms of the number of valence electrons, and the relative positions of the energy levels of the constituent atoms. There appear to be strong similarities between the electronic reasons behind atomic site preferences in molecules and this site preference or coordination number problem in solids.     

The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)-f(y)|? 2 if xand y are adjacent vertices and |f(x)-f(y)|?1 if xand y are at distance two. The goal is to determine the λ-number of G, which is defined as the minimum span over all L(2,1)-labelings of G, or equivalently, the smallest number k such that G has an L(2,1)-labeling using integers from {0,1,…,k}. Recent work has focused on determining the λ-number of generalized Petersen graphs (GPGs) of order n. This paper provides exact values for the λ-numbers of GPGs of orders 5, 7, and 8, closing all remaining open cases for orders at most 8. It is also shown that there are no GPGs of order 4, 5, 8, or 11 with λ-number exactly equal to the known lower bound of 5, however, a construction is provided to obtain examples of GPGs with λ-number 5 for all other orders. This paper also provides an upper bound for the number of distinct isomorphism classes for GPGs of any given order. Finally, the exact values for the λ-number of n-stars, a subclass of the GPGs inspired by the classical Petersen graph, are also determined. These generalized stars have a useful representation on Möebius strips, which is fundamental in verifying our results.     

Organization in lipid membranes containing cholesterol

A fundamental attribute of raft formation in cell membranes is lateral separation of lipids into coexisting liquid phases. Using fluorescence microscopy, we observe spontaneous lateral separation in free-floating giant unilamellar vesicles. We record coexisting liquid domains over a range of composition and temperature significantly wider than previously reported. Furthermore, we establish correlations between miscibility in bilayers and in monolayers. For example, the same lipid mixtures that produce liquid domains in bilayer membranes produce two upper miscibility critical points in the phase diagrams of monolayers.     

Load balancing via random local search in closed and open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach themselves to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner. We first analyze the natural Random Local Search (RLS) strategy. Under this strategy, after sampling a new server randomly, clients only switch to it if their service rate is improved. In closed systems, where the client population is fixed, we derive tight estimates of the time it takes under RLS strategy to balance the load across servers. We then study open systems where clients arrive according to a random process and leave the system upon service completion. In this scenario, we analyze how client migrations within the system interact with the system dynamics induced by client arrivals and departures. We compare the load-aware RLS strategy to a load-oblivious strategy in which clients just randomly switch server without accounting for the server loads. Surprisingly, we show that both load-oblivious and load-aware strategies stabilize the system whenever this is at all possible. We use large-system asymptotics to characterize system performance, and augment this with simulations, which suggest that the average client sojourn time under the load-oblivious strategy is not considerably reduced when clients apply smarter load-aware strategies.     

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.