Note on Logarithmic Switchback Terms in Regular and Singular Perturbation Expansions

The occurrence of logarithmic switchback is studied for ordinary differential equations containing a parameter k which is allowed to take any value in a continuum of real numbers and with boundary conditions imposed at x = ε and x = ∞. Classical theory tells us that if the equation has a regular singular point at the origin there is a family of solutions which varies continuously with k, and the expansion around the origin has log x terms for a discrete set of values of k. It is shown here how nonlinearity enlarges this set so that it may even be dense in some interval of the real numbers. A log x term in the expansion in x leads to expansion coefficients containing log ε (switchback) in the perturbation expansion. If for a given value of k logarithmic terms in x and ε occur they may be obtained by continuity from neighboring values of k. Switchback terms occurred conspicuously in singular-perturbation solutions of problems posed for semi-infinite domain x ≥ ε. This connection is historical rather than logical. In particular we study here switchback terms for a specific example using methods of both singular and regular perturbations

The Penetration of a Finger into a Viscous Fluid in a Channel and Tube

The steady-state shape of a finger penetrating into a region filled with a viscous fluid is examined. The two-dimensional and axisymmetric problems are solved using Stokes equations for low Reynolds number flow. To solve the equations, an assumption for the shape of the finger is made and the normal-stress boundary condition is dropped. The remaining equations are solved numerically by covering the domain with a composite mesh composed of a curvilinear grid which follows the curved interface, and a rectilinear grid parallel to the straight boundaries. The shape of the finger is then altered to satisfy the normal-stress boundary condition by using a nonlinear least squares iteration method. The results are compared with the singular perturbation solution of Bretherton (J. Fluid Mech., 10 (1961), pp. 166–188). When the axisymmetric finger moves through a tube, a fraction $m$ of the viscous fluid is left behind on the walls of the tube. The fraction $m$ was measured experimentally by Taylor (J. Fluid Mech., 10 (1961), pp. 161–165) as a function of the dimensionless parameter µU/T. The numerical results are compared with the experimental results of Taylor

Prewetting transition on a weakly disordered substrate : evidence for a creeping film dynamics

We present the first microscopic images of the prewetting transition of a liquid film on a solid surface. Pictures of the local coverage map of a helium film on a cesium metal surface are taken while the temperature is raised through the transition. The film edge is found to advance at constant temperature by successive avalanches in a creep motion with a macroscopic correlation length. The creep velocity varies strongly in a narrow temperature range. The retreat motion is obtained only at much lower temperature, conforming to the strong hysteresis observed for prewetting transition on a disordered surface. Prewetting transition on such disordered surfaces appears to give rise to dynamical phenomena similar to what is observed for domain wall motions in 2D magnets.Comment: 7 pages, 3 figures, to be published in Euro.Phys.Let

Quality control for more reliable integration of deep learning-based image segmentation into medical workflows

Machine learning algorithms underpin modern diagnostic-aiding software, whichhas proved valuable in clinical practice, particularly in radiology. However,inaccuracies, mainly due to the limited availability of clinical samples fortraining these algorithms, hamper their wider applicability, acceptance, andrecognition amongst clinicians. We present an analysis of state-of-the-artautomatic quality control (QC) approaches that can be implemented within thesealgorithms to estimate the certainty of their outputs. We validated the mostpromising approaches on a brain image segmentation task identifying whitematter hyperintensities (WMH) in magnetic resonance imaging data. WMH are acorrelate of small vessel disease common in mid-to-late adulthood and areparticularly challenging to segment due to their varied size, anddistributional patterns. Our results show that the aggregation of uncertaintyand Dice prediction were most effective in failure detection for this task.Both methods independently improved mean Dice from 0.82 to 0.84. Our workreveals how QC methods can help to detect failed segmentation cases andtherefore make automatic segmentation more reliable and suitable for clinicalpractice.<br

Effects of oxidized lipids (4,5 (E)-epoxy-2(E)-heptenal and 4,5 (E)-epoxy-2 (E) -decenal) and lysine reaction products on zinc and calcium utilization: assays in Caco-2 cells

The influence of the presence of brown products from the reaction between two oxidized lipids (4,5 (E)-epoxy-2(E)-heptenal, EH, and 4,5 (E)-epoxy-2 (E)-decenal, ED) and lysine (EH-L and ED-L) on zinc and calcium utilization was studied, and compared with a fructosyl-lysine mixture (F-L). Assays were carried out in Caco-2 cells grown in bicameral chambers. The Zn transported across the cell monolayer was significantly lower in the presence of the EH-L, ED-L and F-L samples, specially with EH-L. Significant decreases in Zn uptake were also observed, with no differences between samples. However, calcium transport was not modified. Thus, the assayed lipid-aminoacid brown products seem to have negative effects on Zn availability, whereas Ca availability appears to be unaffected.Se estudió la influencia de la presencia de productos obtenidos en la reacción de dos lípidos oxidados (4,5(E)-epoxy-2(E)- heptenal, EH, y 4,5(E)-epoxy-2(E)-decenal, ED) con el aminoácido lisina (EH-L y ED-L), sobre la absorción de zinc y calcio, comparándolos frente a una mezcla de fructosil-lisina (F-L). Los ensayos se realizaron con células Caco-2 sembradas en placas bicamerales. La adición de las muestras EH-L, ED-L y F-L al medio de cultivo supuso una reducción significativa en el Zn transportado a través de la monocapa de células, mucho más marcada ante la presencia de EH-L. También se redujo significativamente la captación celular de Zn, sin diferencias entre las distintas muestras ensayadas. Sin embargo, el transporte de Ca no se vio modificado. Por lo tanto, los productos pardos lípido-aminoacídicos ensayados parecen afectar negativamente la disponibilidad del Zn, sin tener efectos notables sobre la del Ca.Peer reviewe