Surface diffusion flow near spheres

We consider closed immersed hypersurfaces evolving by surface diffusion flow, and perform an analysis based on local and global integral estimates. First we show that a properly immersed stationary (ΔH ≡ 0) hypersurface in ${\mathbb{R}^3}$ or ${\mathbb{R}^4}$ with restricted growth of the curvature at infinity and small total tracefree curvature must be an embedded union of umbilic hypersurfaces. Then we prove for surfaces that if the L ² norm of the tracefree curvature is globally initially small it is monotonic nonincreasing along the flow. We also derive pointwise estimates for all derivatives of the curvature assuming that its L ² norm is locally small. Using these results we show that if a singularity develops the curvature must concentrate in a definite manner, and prove that a blowup under suitable conditions converges to a nonumbilic embedded stationary surface. We obtain our main result as a consequence: the surface diffusion flow of a surface initially close to a sphere in L ² is a family of embeddings, exists for all time, and exponentially converges to a round sphere.     

Integer programming methods for normalisation and variable selection in mathematical programming discriminant analysis models

Mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requirement can cause difficulties, and unlike statistical discriminant analysis, variables cannot be selected in a computationally efficient way with mathematical programming discriminant analysis models. Two new integer programming normalisations are proposed in this paper. In the first, binary variables are used to represent the constant term, but with this normalisation functions with a zero constant term cannot be generated and the variable coefficients are not invariant under origin shifts. These limitations are overcome by using integer programming methods to constrain the sum of the absolute values of the variable coefficients to a constant. These new normalisations are extended to allow variable selection with mathematical programming discriminant analysis models. The use of these new applications of integer programming is illustrated using published data.     

An Asynchronous Distributed Expectation Maximization Algorithm for Massive Data: The DEM Algorithm

The family of expectation--maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called workers and managers for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a γ-fraction of the workers, where γ is a fixed constant in (0, 1]. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings. Supplementary material for this article is available online.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

Robust spatially resolved pressure measurements using MRI with novel buoyant advection-free preparations of stable microbubbles in polysaccharide gels

MRI of fluids containing lipid coated microbubbles has been shown to be an effective tool for measuring the local fluid pressure. However, the intrinsically buoyant nature of these microbubbles precludes lengthy measurements due to their vertical migration under gravity and pressure-induced coalescence. A novel preparation is presented which is shown to minimize both these effects for at least 25 min. By using a 2% polysaccharide gel base with a small concentration of glycerol and 1,2-distearoyl-sn-glycero-3-phosphocholine coated gas microbubbles, MR measurements are made for pressures between 0.95 and 1.44 bar. The signal drifts due to migration and amalgamation are shown to be minimized for such an experiment whilst yielding very high NMR sensitivities up to 38% signal change per bar.     

Polar Plot Representation for Frequency-Domain Analysis of Fluorescence Lifetimes

We present applications of polar plots for analyzing fluorescence lifetime data acquired in the frequency domain. This graphical, analytical method is especially useful for rapid FLIM measurements. The usual method for sorting out and determining the underlying lifetime components from a complex fluorescence signal is to carry out the measurement at multiple frequencies. When it is not possible to measure at more than one frequency, such as rapid lifetime imaging, specific features of the polar plot analysis yield valuable information, and provide a diagnostic visualization of the participating fluorescent species underlying a complex lifetime distributions. Data are presented where this polar plot presentation is useful to derive valuable, unique information about the underlying component distributions. We also discuss artifacts of photolysis and how this method can also be applied to samples where each fluorescence species shows a continuous distribution of lifetimes. Polar plots of frequency-domain data are commonly used for analysis of dielectric relaxation experiments (Cole–Cole plots), which have proved to be exceptionally useful in that field for decades. We compare this analytical tool that is well developed and extensively used in dielectric relaxation and chemical kinetics to fluorescence measurements.     

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Discrimination of components in atherosclerotic plaques from human carotid endarterectomy specimens by magnetic resonance imaging ex vivo

Specific MRI techniques have been used to determine the dimensional and compositional properties of atherosclerotic lesions in carotid endarterectomy tissues. A quantitative comparison of areas of specific features in typical tissue segments was performed using MR images and histologic images. The mean difference for the measurements by the two methods was 4.5% for the total vessel, 5.3% for the internal carotid artery lumen, and 5.0% for the external carotid lumen. For other less abundant components, the mean difference was 14.2%. For direct characterization, individual tissue components were isolated by microdissection and their T1 and T2 relaxation times measured. Highly calcified areas typically had rather short T1 (452-837 ms) and short T2 (10.4-18.4 ms). In contrast, regions enriched in lipid had much longer T1 (1,380-1,480 ms) and longer T2 (35.3-49.0 ms). Other components such as thrombus had intermediate T1 (1,180 ms) and short T2 (15.4 ms). T2 parametric imaging was used as a complementary approach for segmentation and quantitation of tissue components. In fresh tissue, several different components exhibited different T2 ranges: calcified/solid lipid (13-18 ms). cellular/ECM (9-30 ms), fluid lipid (35-40 ms): fibrous (50-60 ms). These results demonstrate the utility of MRI for identifying and quantifying specific components of atherosclerotic plaque ex vivo, and suggest its value for these measurements in vivo as well.     

Resonance excitation and dynamic collision-induced dissociation in quadrupole ion traps using higher-order excitation frequencies

Fragmentation of the pentapeptide leucine enkephalin (YGGFL) is accomplished via higher-order resonances combined with simultaneous analysis of low-mass product ions. Two methods of achieving excitation are explored: (1) 0.5 ms resonant excitation at the omega and at Omega-omega secular frequencies of ion motion (where Omega is the radio-frequency (rf) drive frequency) in a manner similar to both pulsed q collision-induced dissociation (PQD) and high amplitude short time excitation (HASTE), and (2) 0.5 ms pulse of the omega or at Omega-omega excitation frequencies when the secular frequency of the ions is quickly swept across resonance conditions (pulsed q dynamic CID, PqDCID). In both methods of excitation, the rf amplitude on the ring electrode is rapidly decreased after excitation, therefore enabling analysis of low-mass product ions. Maximum fragmentation efficiencies of approximately 20% can be obtained with pulsed CID with both regular and high-order frequency excitation, while pulsed DCID offers maximum efficiencies of approximately 12%. All the excitation methods studied offer increased internal energy depositions when compared to conventional CID, as measured by the a4/b4 product ion ratios of leucine enkephalin. These ratios were as high as 13:1 for pulsed CID and 8:1 for PqDCID. Successful mass analysis of the low-mass ions is observed with both pulsed CID and PqDCID. The combined benefit of high internal energy deposition and wider dynamic mass range offers the possibility of increased sequence coverage and the identification of unique internal fragments or high-energy product ions which may provide complementary information to biological applications of conventional CID. This is the first report on deliberate fragmentation of precursor ions at a higher-order component of the ion secular frequency combined with a successful mass analysis of the low-mass ions through pulsed CID and PqDCID.