scholarly journals Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Frank Morgan

AbstractWe give an example of a smooth surface of revolution for which all circles about the origin are strictly stable for fixed area but small isoperimetric regions are nearly round discs away from the origin.

Author(s):  
D.J. Eaglesham

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs


Author(s):  
B.V.V. Prasad ◽  
E. Marietta ◽  
J.W. Burns ◽  
M.K. Estes ◽  
W. Chiu

Rotaviruses are spherical, double-shelled particles. They have been identified as a major cause of infantile gastroenteritis worldwide. In our earlier studies we determined the three-dimensional structures of double-and single-shelled simian rotavirus embedded in vitreous ice using electron cryomicroscopy and image processing techniques to a resolution of 40Å. A distinctive feature of the rotavirus structure is the presence of 132 large channels spanning across both the shells at all 5- and 6-coordinated positions of a T=13ℓ icosahedral lattice. The outer shell has 60 spikes emanating from its relatively smooth surface. The inner shell, in contrast, exhibits a bristly surface made of 260 morphological units at all local and strict 3-fold axes (Fig.l).The outer shell of rotavirus is made up of two proteins, VP4 and VP7. VP7, a glycoprotein and a neutralization antigen, is the major component. VP4 has been implicated in several important functions such as cell penetration, hemagglutination, neutralization and virulence. From our earlier studies we had proposed that the spikes correspond to VP4 and the rest of the surface is composed of VP7. Our recent structural studies, using the same techniques, with monoclonal antibodies specific to VP4 have established that surface spikes are made up of VP4.


2020 ◽  
Vol 48 (3) ◽  
pp. 1243-1253 ◽  
Author(s):  
Sukriti Kapoor ◽  
Sachin Kotak

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.


2011 ◽  
Author(s):  
Kimberley D. Orsten ◽  
Mary C. Portillo ◽  
James R. Pomerantz
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