A map on the space of rational functions

We describe dynamical properties of a map $\mathfrak{F}$ defined on the space of rational functions. The fixed points of $\mathfrak{F}$ are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

The influence of surface stress on the equilibrium shape of strained quantum dots

The equilibrium shapes of InAs quantum dots (i.e., dislocation-free, strained islands with sizes >= 10,000 atoms) grown on a GaAs (001) substrate are studied using a hybrid approach which combines density functional theory (DFT) calculations of microscopic parameters, surface energies, and surface stresses with elasticity theory for the long-range strain fields and strain relaxations. In particular we report DFT calculations of the surface stresses and analyze the influence of the strain on the surface energies of the various facets of the quantum dot. The surface stresses have been neglected in previous studies. Furthermore, the influence of edge energies on the island shapes is briefly discussed. From the knowledge of the equilibrium shape of these islands, we address the question whether experimentally observed quantum dots correspond to thermal equilibrium structures or if they are a result of the growth kinetics.Comment: 7 pages, 8 figures, submitted to Phys. Rev. B (February 2, 1998). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Rhomboid family member 2 regulates cytoskeletal stress-associated Keratin 16.

Keratin 16 (K16) is a cytoskeletal scaffolding protein highly expressed at pressure-bearing sites of the mammalian footpad. It can be induced in hyperproliferative states such as wound healing, inflammation and cancer. Here we show that the inactive rhomboid protease RHBDF2 (iRHOM2) regulates thickening of the footpad epidermis through its interaction with K16. K16 expression is absent in the thinned footpads of irhom2-/- mice compared with irhom2+/+mice, due to reduced keratinocyte proliferation. Gain-of-function mutations in iRHOM2 underlie Tylosis with oesophageal cancer (TOC), characterized by palmoplantar thickening, upregulate K16 with robust downregulation of its type II keratin binding partner, K6. By orchestrating the remodelling and turnover of K16, and uncoupling it from K6, iRHOM2 regulates the epithelial response to physical stress. These findings contribute to our understanding of the molecular mechanisms underlying hyperproliferation of the palmoplantar epidermis in both physiological and disease states, and how this 'stress' keratin is regulated

Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy

We study the energetics of island formation in Stranski-Krastanow growth within a parameter-free approach. It is shown that an optimum island size exists for a given coverage and island density if changes in the wetting layer morphology after the 3D transition are properly taken into account. Our approach reproduces well the experimental island size dependence on coverage, and indicates that the critical layer thickness depends on growth conditions. The present study provides a new explanation for the (frequently found) rather narrow size distribution of self-assembled coherent islands.Comment: 4 pages, 5 figures, In print, Phys. Rev. Lett. Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Equilibrium shapes and energies of coherent strained InP islands

The equilibrium shapes and energies of coherent strained InP islands grown on GaP have been investigated with a hybrid approach that has been previously applied to InAs islands on GaAs. This combines calculations of the surface energies by density functional theory and the bulk deformation energies by continuum elasticity theory. The calculated equilibrium shapes for different chemical environments exhibit the {101}, {111}, {\=1\=1\=1} facets and a (001) top surface. They compare quite well with recent atomic-force microscopy data. Thus in the InP/GaInP-system a considerable equilibration of the individual islands with respect to their shapes can be achieved. We discuss the implications of our results for the Ostwald ripening of the coherent InP islands. In addition we compare strain fields in uncapped and capped islands.Comment: 10 pages including 6 figures. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image

We describe the first method to automatically estimate the 3D pose of the human body as well as its 3D shape from a single unconstrained image. We estimate a full 3D mesh and show that 2D joints alone carry a surprising amount of information about body shape. The problem is challenging because of the complexity of the human body, articulation, occlusion, clothing, lighting, and the inherent ambiguity in inferring 3D from 2D. To solve this, we first use a recently published CNN-based method, DeepCut, to predict (bottom-up) the 2D body joint locations. We then fit (top-down) a recently published statistical body shape model, called SMPL, to the 2D joints. We do so by minimizing an objective function that penalizes the error between the projected 3D model joints and detected 2D joints. Because SMPL captures correlations in human shape across the population, we are able to robustly fit it to very little data. We further leverage the 3D model to prevent solutions that cause interpenetration. We evaluate our method, SMPLify, on the Leeds Sports, HumanEva, and Human3.6M datasets, showing superior pose accuracy with respect to the state of the art.Comment: To appear in ECCV 201

Spin states of zigzag-edged Mobius graphene nanoribbons from first principles

Mobius graphene nanoribbons have only one edge topologically. How the magnetic structures, previously associated with the two edges of zigzag-edged flat nanoribbons or cyclic nanorings, would change for their Mobius counterparts is an intriguing question. Using spin-polarized density functional theory, we shed light on this question. We examine spin states of zigzag-edged Mobius graphene nanoribbons (ZMGNRs) with different widths and lengths. We find a triplet ground state for a Mobius cyclacene, while the corresponding two-edged cyclacene has an open-shell singlet ground state. For wider ZMGNRs, the total magnetization of the ground state is found to increase with the ribbon length. For example, a quintet ground state is found for a ZMGNR. Local magnetic moments on the edge carbon atoms form domains of majority and minor spins along the edge. Spins at the domain boundaries are found to be frustrated. Our findings show that the Mobius topology (i.e., only one edge) causes ZMGNRs to favor one spin over the other, leading to a ground state with non-zero total magnetization.Comment: 17 pages, 4 figure