Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties

The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets representing local averages and local differences. Although one-to-one transformations of data sets are possible, the advantage of the wavelet transform is as an approximation scheme for the efficient calculation of thermodynamic and ensemble properties. Even under the most drastic of approximations, the resulting errors in the values obtained for average absolute magnetization, free energy, and heat capacity are on the order of 10%, with a corresponding computational efficiency gain of two orders of magnitude for a system such as a $4\times 4$ Ising lattice. In addition, the errors in the results tend toward zero in the neighborhood of fixed points, as determined by renormalization group theory.Comment: 13 pages plus 7 figures (PNG

Vitamin C inhibits endothelial cell apoptosis in congestive heart failure

Background - Proinflammatory cytokines like tumor necrosis factor- and oxidative stress induce apoptotic cell death in endothelial cells (ECs). Systemic inflammation and increased oxidative stress in congestive heart failure (CHF) coincide with enhanced EC apoptosis and the development of endothelial dysfunction. Therefore, we investigated the effects of antioxidative vitamin C therapy on EC apoptosis in CHF patients. Methods and Results - Vitamin C dose dependently suppressed the induction of EC apoptosis by tumor necrosis factor- and angiotensin II in vitro as assessed by DNA fragmentation, DAPI nuclear staining, and MTT viability assay. The antiapoptotic effect of vitamin C was associated with reduced cytochrome C release from mitochondria and the inhibition of caspase-9 activity. To assess EC protection by vitamin C in CHF patients, we prospectively randomized CHF patients in a double-blind trial to vitamin C treatment versus placebo. Vitamin C administration to CHF patients markedly reduced plasma levels of circulating apoptotic microparticles to 32±8% of baseline levels, whereas placebo had no effect (87±14%, P<0.005). In addition, vitamin C administration suppressed the proapoptotic activity on EC of the serum of CHF patients (P<0.001). Conclusions - Administration of vitamin C to CHF patients suppresses EC apoptosis in vivo, which might contribute to the established functional benefit of vitamin C supplementation on endothelial function

Multiscale 3D Shape Analysis using Spherical Wavelets

©2005 Springer. The original publication is available at www.springerlink.com: http://dx.doi.org/10.1007/11566489_57DOI: 10.1007/11566489_57Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data

Epoxidation of Allylic Alcohols with TiO2-SiO2: Hydroxy-Assisted Mechanism and Dynamic Structural Changes During Reaction

Epoxidation of allylic alcohols and cyclohexene with TBHP and titania-silica aerogels containing 1 and 5 wt% TiO2 has been studied. For the oxidation of geraniol and cyclohexenol, the regio- and diastereoselectivities and kinetic data indicate an OH-assisted mechanism involving a dative bond between the OH group and the Ti site. This mechanism is disabled in the oxidation of cyclooctenol due to steric hindrance. The moderate regio- and diastereoselectivities of the aerogels, compared with those of TS-1 and the homogeneous model Ti(OSiMe3)4, are attributed to the presence of non-isolated Ti sites and to a "silanol-assisted” mechanism, according to which model the allylic alcohol is anchored to a neighboring SiOH group instead of the Ti-peroxo complex. Kinetic analysis of the initial transient period revealed rapid catalyst restructuring during the first few turnovers. A feasible explanation is the breaking of Si-O-Ti linkages of the carefully predried aerogels by water or TBHP, resulting in active Ti sites with remarkably different catalytic propertie

Coadsorption of Cinchona Alkaloids on Supported Palladium: Nonlinear Effects in Asymmetric Hydrogenation and Resistance of Alkaloids Against Hydrogenation

The transient behavior of the adsorption of cinchona alkaloid modifiers on Pd/TiO2 has been investigated in situ during the enantioselective hydrogenation of 4-methoxy-6-methyl-2-pyrone (1). Modifier mixtures consisting of pairs of alkaloids that alone afford the opposite enantiomers in comparable excess were applied to probe the adsorption behavior and possible nonlinear phenomena. Complementary information has been gathered from an indirect UV-vis study of the adsorption and hydrogenation of cinchonidine and quinidine on Pd/TiO2. The striking nonlinear behavior of cinchonidine-quinidine and cinchonine-quinine pairs in the hydrogenation of 1, and in the competitive saturation of the quinoline rings of the alkaloids, is attributed to differences in the adsorption strength and geometry of the alkaloids. The results are in good agreement with our former mechanistic model assuming that the quinoline ring of cinchona alkaloid and 1 adsorb parallel to the Pd surface during the enantiodifferentiating ste

mm-Wave DRW Antenna Phase Centre Determination

This document presents an approach to the phase centre determination of a dielectric rod waveguide (DRW) antenna by means of measurements obtained with a planar measuring system at millimeter wave lengths. Phase centre determination by the least squares fit technique is described in this document for different DRW antennas (silicon and sapphire). Results at different operating frequencies are offered

Quantitative Regular Expressions for Arrhythmia Detection Algorithms

Motivated by the problem of verifying the correctness of arrhythmia-detection algorithms, we present a formalization of these algorithms in the language of Quantitative Regular Expressions. QREs are a flexible formal language for specifying complex numerical queries over data streams, with provable runtime and memory consumption guarantees. The medical-device algorithms of interest include peak detection (where a peak in a cardiac signal indicates a heartbeat) and various discriminators, each of which uses a feature of the cardiac signal to distinguish fatal from non-fatal arrhythmias. Expressing these algorithms' desired output in current temporal logics, and implementing them via monitor synthesis, is cumbersome, error-prone, computationally expensive, and sometimes infeasible. In contrast, we show that a range of peak detectors (in both the time and wavelet domains) and various discriminators at the heart of today's arrhythmia-detection devices are easily expressible in QREs. The fact that one formalism (QREs) is used to describe the desired end-to-end operation of an arrhythmia detector opens the way to formal analysis and rigorous testing of these detectors' correctness and performance. Such analysis could alleviate the regulatory burden on device developers when modifying their algorithms. The performance of the peak-detection QREs is demonstrated by running them on real patient data, on which they yield results on par with those provided by a cardiologist.Comment: CMSB 2017: 15th Conference on Computational Methods for Systems Biolog

Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition

In this paper, the adaptive chirplet decomposition combined with the Wigner-Ville transform and the empirical mode decomposition combined with the Hilbert transform are employed to process various non-stationary signals (strong ground motions and structural responses). The efficacy of these two adaptive techniques for capturing the temporal evolution of the frequency content of specific seismic signals is assessed. In this respect, two near-field and two far-field seismic accelerograms are analyzed. Further, a similar analysis is performed for records pertaining to the response of a 20-story steel frame benchmark building excited by one of the four accelerograms scaled by appropriate factors to simulate undamaged and severely damaged conditions for the structure. It is shown that the derived joint time–frequency representations of the response time histories capture quite effectively the influence of non-linearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event; in this context, tracing the mean instantaneous frequency of records of critical structural responses is adopted. The study suggests, overall, that the aforementioned techniques are quite viable tools for detecting and monitoring damage to constructed facilities exposed to seismic excitations

Quasi-local evolution of cosmic gravitational clustering in the weakly non-linear regime

We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel'dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the relation between the evolved DWT mode and the initial perturbations in the weakly non-linear regime is quasi-local. That is, the evolved density perturbations are mainly determined by the initial perturbations localized in the same spatial range. Furthermore, we show that the evolved mode is monotonically related to the initial perturbed mode. Thus large (small) perturbed modes statistically correspond to the large (small) initial perturbed modes. We test this prediction by using QSO Ly$\alpha$ absorption samples. The results show that the weakly non-linear features for both the transmitted flux and identified forest lines are quasi-localized. The locality and monotonic properties provide a solid basis for a DWT scale-by-scale Gaussianization reconstruction algorithm proposed by Feng & Fang (Feng & Fang, 2000) for data in the weakly non-linear regime. With the Zel'dovich solution, we find also that the major non-Gaussianity caused by the weakly non-linear evolution is local scale-scale correlations. Therefore, to have a precise recovery of the initial Gaussian mass field, it is essential to remove the scale-scale correlations.Comment: 22 pages, 13 figures. Accepted for publication in the Astrophysical Journa

A Stochastic Description for Extremal Dynamics

We show that extremal dynamics is very well modelled by the "Linear Fractional Stable Motion" (LFSM), a stochastic process entirely defined by two exponents that take into account spatio-temporal correlations in the distribution of active sites. We demonstrate this numerically and analytically using well-known properties of the LFSM. Further, we use this correspondence to write an exact expressions for an n-point correlation function as well as an equation of fractional order for interface growth in extremal dynamics.Comment: 4 pages LaTex, 3 figures .ep