scholarly journals Determining Genus From Sandpile Torsor Algorithms

2021 ◽  
Vol vol. 23 no. 1 (Combinatorics) ◽  
Author(s):  
Alex McDonough
Keyword(s):  
Ribbon Graphs ◽  
Ribbon Structure ◽  
Topological Genus

We provide a pair of ribbon graphs that have the same rotor routing and Bernardi sandpile torsors, but different topological genus. This resolves a question posed by M. Chan [Cha]. We also show that if we are given a graph, but not its ribbon structure, along with the rotor routing sandpile torsors, we are able to determine the ribbon graph's genus. Comment: Reformatted for DMTCS

scholarly journals The mitotic spindle mediates inheritance of the Golgi ribbon structure

2009 ◽  
Vol 184 (3) ◽  
pp. 391-397 ◽  
Author(s):  
Jen-Hsuan Wei ◽  
Joachim Seemann
Keyword(s):  
Mitotic Spindle ◽  
Daughter Cell ◽  
Daughter Cells ◽  
Spindle Poles ◽  
Golgi Membranes ◽  
Ribbon Structure ◽  
Golgi Ribbon

The mammalian Golgi ribbon disassembles during mitosis and reforms in both daughter cells after division. Mitotic Golgi membranes concentrate around the spindle poles, suggesting that the spindle may control Golgi partitioning. To test this, cells were induced to divide asymmetrically with the entire spindle segregated into only one daughter cell. A ribbon reforms in the nucleated karyoplasts, whereas the Golgi stacks in the cytoplasts are scattered. However, the scattered Golgi stacks are polarized and transport cargo. Microinjection of Golgi extract together with tubulin or incorporation of spindle materials rescues Golgi ribbon formation. Therefore, the factors required for postmitotic Golgi ribbon assembly are transferred by the spindle, but the constituents of functional stacks are partitioned independently, suggesting that Golgi inheritance is regulated by two distinct mechanisms.

Formation and structure of polymeric carbons

1972 ◽  
Vol 327 (1571) ◽  
pp. 501-517 ◽  
Keyword(s):  
Glassy Carbon ◽  
Molecular Orientation ◽  
Early Stage ◽  
Structural Difference ◽  
Direct Consequence ◽  
High Resolution Electron Microscopy ◽  
Polymer Chains ◽  
Resolution Electron ◽  
Ribbon Structure ◽  
Phenolic Polymer

Glassy carbon has been prepared in the shape of disk and fibre by direct pyrolysis of a phenolic resin. Carbonization studies indicate that the unique structure of the final glassy carbon is a direct consequence of the production of very stable aromatic ribbon molecules by the coalescence of phenolic polymer chains at an early stage of pyrolysis. It is shown that molecular orientation induced in the initial polymer before pyrolysis is 'memorized’ to some extent after carbonization. Molecular orientation imposed in this type of carbon is not an intrinsic structural feature, but a physical characteristic which can be varied by the formation process or by extension at high temperatures; there is no essential structural difference apart from preferred orientation between polymeric units or microfibrils in well-oriented carbon fibres and isotropic glassy carbon. High resolution electron microscopy confirms this directly. We thus identify a new class of ‘polymeric carbons’, that consist of intertwined microfibrils comprising stacks of narrow graphitic ribbons. The fibrils are held together with covalent interfibrillar links of strength lower than that in the ribbons themselves. A ribbon structure has been proposed previously by Ruland (1971) for the specific case of high modulus carbon fibre. The structure is elaborated and extended here to cover all polymeric carbons and the steps in its development during carbonization are decisively detailed.

Monomer units for the β-bend ribbon structure: MeAib peptides

1992 ◽  
Vol 14 (4) ◽  
pp. 178-184 ◽  
Author(s):  
V. Moretto ◽  
G. Valle ◽  
M. Crisma ◽  
G.M. Bonora ◽  
C. Toniolo
Keyword(s):  
Ribbon Structure

Ribbon graphs and their invaraints derived from quantum groups

1990 ◽  
Vol 127 (1) ◽  
pp. 1-26 ◽  
Author(s):  
N. Y. Reshetikhin ◽  
V. G. Turaev
Keyword(s):  
Quantum Groups ◽  
Ribbon Graphs

Ribbon structure in gold-quartz veins; discussion

1950 ◽  
Vol 45 (2) ◽  
pp. 177-179
Author(s):  
Ellsworth Young Dougherty
Keyword(s):  
Quartz Veins ◽  
Ribbon Structure

Graphs, ribbon graphs, and polynomials

2021 ◽  
pp. 7-16
Author(s):  
Adrian Tanasa
Keyword(s):  
Graph Theory ◽  
Tutte Polynomial ◽  
Graph Polynomials ◽  
Ribbon Graphs

In this chapter we present some notions of graph theory that will be useful in the rest of the book. It is worth emphasizing that graph theorists and theoretical physicists adopt, unfortunately, different terminologies. We present here both terminologies, such that a sort of dictionary between these two communities can be established. We then extend the notion of graph to that of maps (or of ribbon graphs). Moreover, graph polynomials encoding these structures (the Tutte polynomial for graphs and the Bollobás–Riordan polynomial for ribbon graphs) are presented.

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