On certain surfaces in the Euclidean space E3{\mathbb{E}}^3

In the present paper we classify all surfaces in \E^3 with a canonical principal direction. Examples of these type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space ${\mathbb{E}}^3$ is the catenoid.Comment: 13 Latex page

Modeling the Background for Incremental and Weakly-Supervised Semantic Segmentation

Deep neural networks have enabled major progresses in semantic segmentation. However, even the most advanced neural architectures suffer from important limitations. First, they are vulnerable to catastrophic forgetting, i.e. they perform poorly when they are required to incrementally update their model as new classes are available. Second, they rely on large amount of pixel-level annotations to produce accurate segmentation maps. To tackle these issues, we introduce a novel incremental class learning approach for semantic segmentation taking into account a peculiar aspect of this task: since each training step provides annotation only for a subset of all possible classes, pixels of the background class exhibit a semantic shift. Therefore, we revisit the traditional distillation paradigm by designing novel loss terms which explicitly account for the background shift. Additionally, we introduce a novel strategy to initialize classifiers parameters at each step in order to prevent biased predictions toward the background class. Finally, we demonstrate that our approach can be extended to point- and scribble-based weakly supervised segmentation, modeling the partial annotations to create priors for unlabeled pixels. We demonstrate the effectiveness of our approach with an extensive evaluation on the Pascal-VOC, ADE20K, and Cityscapes datasets, significantly outperforming state-of-the-art methods

Optical Flow on Evolving Surfaces with an Application to the Analysis of 4D Microscopy Data

We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are defined on an evolving surface. Volumetric microscopy images depicting a live zebrafish embryo serve as both biological motivation and test data.Comment: The final publication is available at link.springer.co

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect

On the Interface Formation Model for Dynamic Triple Lines

This paper revisits the theory of Y. Shikhmurzaev on forming interfaces as a continuum thermodynamical model for dynamic triple lines. We start with the derivation of the balances for mass, momentum, energy and entropy in a three-phase fluid system with full interfacial physics, including a brief review of the relevant transport theorems on interfaces and triple lines. Employing the entropy principle in the form given in [Bothe & Dreyer, Acta Mechanica, doi:10.1007/s00707-014-1275-1] but extended to this more general case, we arrive at the entropy production and perform a linear closure, except for a nonlinear closure for the sorption processes. Specialized to the isothermal case, we obtain a thermodynamically consistent mathematical model for dynamic triple lines and show that the total available energy is a strict Lyapunov function for this system

BicaudalD Actively Regulates Microtubule Motor Activity in Lipid Droplet Transport

A great deal of sub-cellular organelle positioning, and essentially all minus-ended organelle transport, depends on cytoplasmic dynein, but how dynein's function is regulated is not well understood. BicD is established to play a critical role in mediating dynein function-loss of BicD results in improperly localized nuclei, mRNA particles, and a dispersed Golgi apparatus-however exactly what BicD's role is remains unknown. Nonetheless, it is widely believed that BicD may act to tether dynein to cargos. Here we use a combination of biophysical and biochemical studies to investigate BicD's role in lipid droplet transport during Drosophila embryogenesis.Functional loss of BicD impairs the embryo's ability to control the net direction of droplet transport; the developmentally controlled reversal in transport is eliminated. We find that minimal BicD expression (near-BicD(null)) decreases the average run length of both plus and minus end directed microtubule (MT) based transport. A point mutation affecting the BicD N-terminus has very similar effects on transport during cellularization (phase II), but in phase III (gastrulation) motion actually appears better than in the wild-type.In contrast to a simple static tethering model of BicD function, or a role only in initial dynein recruitment to the cargo, our data uncovers a new dynamic role for BicD in actively regulating transport. Lipid droplets move bi-directionally, and our investigations demonstrate that BicD plays a critical-and temporally changing-role in balancing the relative contributions of plus-end and minus-end motors to control the net direction of transport. Our results suggest that while BicD might contribute to recruitment of dynein to the cargo it is not absolutely required for such dynein localization, and it clearly contributes to regulation, helping activation/inactivation of the motors

On equilibrium in non-hydrostatic metamorphic systems

Metamorphic geology has accumulated a huge body of observation on mineral assemblages that reveal strong patterns in occurrence, summarized, for example, in the idea of metamorphic facies. On the realization that such patterns needed a simple explanation, there has been considerable a posteriori success from adopting the idea that equilibrium thermodynamics can be used on mineral assemblages to make sense of the patterns in terms of, for example, the pressure and temperature of formation of mineral assemblages. In doing so, a particularly simple implicit assumption is made, that mineral assemblages operate essentially hydrostatically. Structural geologists have studied the same rocks for different ends, but, remarkably, the phenomena they are interested in depend on non-hydrostatic stress. We look at the effect of such behaviour on mineral equilibria. With adoption of some plausible assumptions about how metamorphism in the crust works, the consequence of minerals being non-hydrostatically stressed is commonly second order in equilibrium calculations

Gebiss: an ImageJ plugin for the specification of ground truth and the performance evaluation of 3D segmentation algorithms.

Background: Image segmentation is a crucial step in quantitative microscopy that helps to define regions of tissues, cells or subcellular compartments. Depending on the degree of user interactions, segmentation methods can be divided into manual, automated or semi-automated approaches. 3D image stacks usually require automated methods due to their large number of optical sections. However, certain applications benefit from manual or semi-automated approaches. Scenarios include the quantification of 3D images with poor signal-to-noise ratios or the generation of so-called ground truth segmentations that are used to evaluate the accuracy of automated segmentation methods. Results: We have developed Gebiss; an ImageJ plugin for the interactive segmentation, visualisation and quantification of 3D microscopic image stacks. We integrated a variety of existing plugins for threshold-based segmentation and volume visualisation. Conclusions: We demonstrate the application of Gebiss to the segmentation of nuclei in live Drosophila embryos and the quantification of neurodegeneration in Drosophila larval brains. Gebiss was developed as a cross-platform ImageJ plugin and is freely available on the web at http://imaging.bii.a-star.edu.sg/projects/gebiss

Serum MicroRNA-21 as Marker for Necroinflammation in Hepatitis C Patients with and without Hepatocellular Carcinoma

Background: MicroRNA-21 (miR-21) is up-regulated in tumor tissue of patients with malignant diseases, including hepatocellular carcinoma (HCC). Elevated concentrations of miR-21 have also been found in sera or plasma from patients with malignancies, rendering it an interesting candidate as serum/plasma marker for malignancies. Here we correlated serum miR-21 levels with clinical parameters in patients with different stages of chronic hepatitis C virus infection (CHC) and CHC-associated HCC. Methodology/Principal Findings: 62 CHC patients, 29 patients with CHC and HCC and 19 healthy controls were prospectively enrolled. RNA was extracted from the sera and miR-21 as well as miR-16 levels were analyzed by quantitative real-time PCR; miR-21 levels (normalized by miR-16) were correlated with standard liver parameters, histological grading and staging of CHC. The data show that serum levels of miR-21 were elevated in patients with CHC compared to healthy controls (P<0.001); there was no difference between serum miR-21 in patients with CHC and CHC-associated HCC. Serum miR-21 levels correlated with histological activity index (HAI) in the liver (r = −0.494, P = 0.00002), alanine aminotransferase (ALT) (r = −0.309, P = 0.007), aspartate aminotransferase (r = −0.495, P = 0.000007), bilirubin (r = −0.362, P = 0.002), international normalized ratio (r = −0.338, P = 0.034) and γ-glutamyltransferase (r = −0.244, P = 0.034). Multivariate analysis revealed that ALT and miR-21 serum levels were independently associated with HAI. At a cut-off dCT of 1.96, miR-21 discriminated between minimal and mild-severe necroinflammation (AUC = 0.758) with a sensitivity of 53.3% and a specificity of 95.2%. Conclusions/Significance: The serum miR-21 level is a marker for necroinflammatory activity, but does not differ between patients with HCV and HCV-induced HCC

Dengue Virus Capsid Protein Usurps Lipid Droplets for Viral Particle Formation

Dengue virus is responsible for the highest rates of disease and mortality among the members of the Flavivirus genus. Dengue epidemics are still occurring around the world, indicating an urgent need of prophylactic vaccines and antivirals. In recent years, a great deal has been learned about the mechanisms of dengue virus genome amplification. However, little is known about the process by which the capsid protein recruits the viral genome during encapsidation. Here, we found that the mature capsid protein in the cytoplasm of dengue virus infected cells accumulates on the surface of ER-derived organelles named lipid droplets. Mutagenesis analysis using infectious dengue virus clones has identified specific hydrophobic amino acids, located in the center of the capsid protein, as key elements for lipid droplet association. Substitutions of amino acid L50 or L54 in the capsid protein disrupted lipid droplet targeting and impaired viral particle formation. We also report that dengue virus infection increases the number of lipid droplets per cell, suggesting a link between lipid droplet metabolism and viral replication. In this regard, we found that pharmacological manipulation of the amount of lipid droplets in the cell can be a means to control dengue virus replication. In addition, we developed a novel genetic system to dissociate cis-acting RNA replication elements from the capsid coding sequence. Using this system, we found that mislocalization of a mutated capsid protein decreased viral RNA amplification. We propose that lipid droplets play multiple roles during the viral life cycle; they could sequester the viral capsid protein early during infection and provide a scaffold for genome encapsidation