Stability of monolayers and bilayers in a copolymer-homopolymer blend model

We study the stability of layered structures in a variational model for diblock copolymer- homopolymer blends. The main step consists of calculating the first and second derivative of a sharp-interface Ohta-Kawasaki energy for straight mono- and bilayers. By developing the interface perturbations in a Fourier series we fully characterise the stability of the structures in terms of the energy parameters. In the course of our computations we also give the Green’s function for the Laplacian on a periodic strip and explain the heuristic method by which we found it

The H^{-1}-norm of tubular neighbourhoods of curves

We study the H-1-norm of the function 1 on tubular neighbourhoods of curves in R2. We take the limit of small thickness e, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit e ¿ 0, containing contributions from the length of the curve (at order e3), the ends (e4), and the curvature (e5). The second result is a G-convergence result, in which the central curve may vary along the sequence e ¿ 0. We prove that a rescaled version of the H-1-norm, which focuses on the e5 curvature term, G-converges to the L2-norm of curvature. In addition, sequences along which the rescaled norm is bounded are compact in the W1, 2-topology. Our main tools are the maximum principle for elliptic equations and the use of appropriate trial functions in the variational characterization of the H-1-norm. For the G-convergence result we use the theory of systems of curves without transverse crossings to handle potential intersections in the limit

Graph Clustering, Variational Image Segmentation Methods and Hough Transform Scale Detection for Object Measurement in Images

© 2016, Springer Science+Business Media New York. We consider the problem of scale detection in images where a region of interest is present together with a measurement tool (e.g. a ruler). For the segmentation part, we focus on the graph-based method presented in Bertozzi and Flenner (Multiscale Model Simul 10(3):1090–1118, 2012) which reinterprets classical continuous Ginzburg–Landau minimisation models in a totally discrete framework. To overcome the numerical difficulties due to the large size of the images considered, we use matrix completion and splitting techniques. The scale on the measurement tool is detected via a Hough transform-based algorithm. The method is then applied to some measurement tasks arising in real-world applications such as zoology, medicine and archaeology

Some studies on the deformation of the membrane in an RF MEMS switch

Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state

Uncertainty quantification in graph-based classification of high dimensional data

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we introduce, develop algorithms for, and investigate the properties of, a variety of Bayesian models for the task of binary classification; via the posterior distribution on the classification labels, these methods automatically give measures of uncertainty. The methods are all based around the graph formulation of semi-supervised learning. We provide a unified framework which brings together a variety of methods which have been introduced in different communities within the mathematical sciences. We study probit classification in the graph-based setting, generalize the level-set method for Bayesian inverse problems to the classification setting, and generalize the Ginzburg-Landau optimization-based classifier to a Bayesian setting; we also show that the probit and level set approaches are natural relaxations of the harmonic function approach introduced in [Zhu et al 2003]. We introduce efficient numerical methods, suited to large data-sets, for both MCMC-based sampling as well as gradient-based MAP estimation. Through numerical experiments we study classification accuracy and uncertainty quantification for our models; these experiments showcase a suite of datasets commonly used to evaluate graph-based semi-supervised learning algorithms.Comment: 33 pages, 14 figure

Water mass analysis along 22°N in the subtropical North Atlantic for the JC150 cruise (GEOTRACES, GApr08)

This study presents a water mass analysis along the JC150 section in the subtropical North Atlantic, based on hydrographic and nutrient data, by combining an extended optimum multiparameter analysis (OMPA) with a Lagrangian particle tracking experiment (LPTE). This combination, which was proposed for the first time, aided in better constraining the OMPA end-member choice and providing information about their trajectories. It also enabled tracing the water mass origins in surface layers, which cannot be achieved with an OMPA. The surface layers were occupied by a shallow type of Eastern South Atlantic Central Water (ESACW) with traces of the Amazon plume in the west. Western North Atlantic Central Water dominates from 100 to 500 m, while the 13°C ESACW contribution occurs marginally deeper (500–900 m). At approximately 700 m, Antarctic Intermediate Water (AAIW) dominates the west of the Mid-Atlantic Ridge (MAR), while Mediterranean Water dominates the east with a small but non-negligible contribution down to 3500 m. Below AAIW, Upper Circumpolar Deep Water (UCDW) is observed throughout section (900–1250 m). Labrador Sea Water (LSW) is found centered at 1500 m, where the LPTE highlights an eastern LSW route from the eastern North Atlantic to the eastern subtropical Atlantic, which was not previously reported. North East Atlantic Deep Water (encompassing a contribution of Iceland-Scotland Overflow Water) is centered at ~2500 m, while North West Atlantic Bottom Water (NWABW, encompassing a contribution of Denmark Strait Overflow Water) is principally localized in the west of the MAR in the range of 3500–5000 m. NWABW is also present in significant proportions (>25%) in the east of the MAR, suggesting a crossing of the MAR possibly through the Kane fracture zone. This feature has not been investigated so far. Finally, Antarctic Bottom Water is present in deep waters throughout the section, mainly in the west of the MAR. Source waters have been characterized from GEOTRACES sections, which enables estimations of trace elements and isotope transport within water masses in the subtropical North Atlantic

An MBO scheme for minimizing the graph Ohta-Kawasaki functional

We study a graph based version of the Ohta-Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph based problems inspired by partial differential equations (PDEs) and varational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph based problems to pattern forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman-Bence-Osher (MBO) scheme for minimizing the graph Ohta-Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme Γ-converge to the Ohta-Kawasaki functional (which includes the standard graph based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta-Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta-Kawasaki functional with a mass constraint

Does Reviewing Lead to Better Learning and Decision Making? Answers from a Randomized Stock Market Experiment

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Clustering of classical swine fever virus isolates by codon pair bias

<p>Abstract</p> <p>Background</p> <p>The genetic code consists of non-random usage of synonymous codons for the same amino acids, termed codon bias or codon usage. Codon juxtaposition is also non-random, referred to as codon context bias or codon pair bias. The codon and codon pair bias vary among different organisms, as well as with viruses. Reasons for these differences are not completely understood. For classical swine fever virus (CSFV), it was suggested that the synonymous codon usage does not significantly influence virulence, but the relationship between variations in codon pair usage and CSFV virulence is unknown. Virulence can be related to the fitness of a virus: Differences in codon pair usage influence genome translation efficiency, which may in turn relate to the fitness of a virus. Accordingly, the potential of the codon pair bias for clustering CSFV isolates into classes of different virulence was investigated.</p> <p>Results</p> <p>The complete genomic sequences encoding the viral polyprotein of 52 different CSFV isolates were analyzed. This included 49 sequences from the GenBank database (NCBI) and three newly sequenced genomes. The codon usage did not differ among isolates of different virulence or genotype. In contrast, a clustering of isolates based on their codon pair bias was observed, clearly discriminating highly virulent isolates and vaccine strains on one side from moderately virulent strains on the other side. However, phylogenetic trees based on the codon pair bias and on the primary nucleotide sequence resulted in a very similar genotype distribution.</p> <p>Conclusion</p> <p>Clustering of CSFV genomes based on their codon pair bias correlate with the genotype rather than with the virulence of the isolates.</p