News Update on Topology Research: Nov – 2019

Modeling Internet topology

The topology of a network, or a gaggle of networks like the net, features a sturdy relating several management and performance problems. smart models of the topological structure of a network area unit essential for developing and analyzing internetworking technology. this text discusses however graph-based models will be wont to represent the topology of huge networks, significantly aspects of neighbourhood and hierarchy gift within the net. 2 implementations that generate networks whose topology resembles that of typical internetworks area unit delineated , beside in public obtainable ASCII text file. [1]

The HMMTOP transmembrane topology prediction server

The HMMTOP transmembrane topology prediction server predicts each the localization of volute transmembrane segments and also the topology of transmembrane proteins. Recently, many enhancements are introduced to the first technique. Now, the user is allowed to submit further data regarding phase localization to reinforce the prediction power. this feature improves the prediction accuracy also as helps the interpretation of experimental results, i.e. in epitope insertion experiments. [2]

Topology representing networks

A Hebbian adaptation rule with winner-take-all like competition is introduced. it’s shown that this competitive Hebbian rule forms supposed Delaunay triangulations, that play a very important role in machine pure mathematics for with efficiency determination proximity issues. Given a collection of neural units i, i = 1,…, N, the colligation weights of which might be understood as pointers Badger State, i = 1,…, N in RD, the competitive Hebbian rule ends up in a property structure between the units i that corresponds to the Delaunay triangulation of the set of pointers Badger State. Such competitive Hebbian rule develops connections (Cij > 0) between neural units i, j with neighboring receptive fields (Voronoi polygons) Vi, Vj, whereas between all alternative units i, j no connections evolve (Cij = 0). Combined Badger Stateth a procedure that distributes the pointers wi over a given feature manifold M, for instance, a submanifold M ⊂ RD, the competitive Hebbian rule provides a unique approach to the matter of constructing topology conserving feature maps and representing in an elaborate way structured manifolds. [3]

Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals

Wave housing and manipulation are at the guts of recent integrated photonics and acoustics. Grand challenges emerge on increasing the combination density and reducing the wave leakage/noises thanks to fabrication imperfections, particularly for waveguides and cavities at subwavelength scales. The rising of sturdy wave dynamics supported topological mechanisms offers attainable solutions. Ideally, in an exceedingly three-dimensional (3D) topological integrated chip, there are synchronous  sturdy two-dimensional (2D) interfaces, one-dimensional (1D) waveguides and zero-dimensional (0D) cavities. Here, we have a tendency to report the experimental discovery of such a dimensional hierarchy of the topologically-protected 2nd surface states, 1D hinge states and 0D corner states in an exceedingly single 3D system. [4]

Geometry and Topology-based Segmentation of 2-Manifold Triangular Meshes in R3

This manuscript reports a geometrical and a topological strategies to phase a closed triangular 2-manifold mesh M ⊂ R3. The mesh M doesn’t self-intersect) and has no border (i.e. watertight. Geometrical and topological segmentation strategies need a Boundary illustration (BRep) from M. Building the BRep for M uniforms constellation orientations, and makes express triangle and edge – counter edge closeness. within the context of Reverse Engineering, the sub-meshes created by the segmentation ar after wont to match constant quantity surfaces, that ar successively cut by the sub-mesh boundaries (forming FACEs). A Full constant quantity Boundary illustration needs a seamless set of FACEs, to create watertight SHELLs. The fitting of constant quantity surfaces to the triangular sub-meshes (i.e. sub-mesh parameterization) needs quasi-developable sub-meshes.As a result, our geometric segmentation places two neighboring triangles within the same sub-mesh if their dihedral angle is π ± η for tiny|alittle|atiny low} η (angle between their triangle traditional vectors could be a small η angle). [5]

Reference

[1] Calvert, K.L., Doar, M.B. and Zegura, E.W., 1997. Modeling internet topology. IEEE Communications magazine, 35(6), (Web Link)

[2] Tusnady, G.E. and Simon, I., 2001. The HMMTOP transmembrane topology prediction server. Bioinformatics, 17(9), (Web Link)

[3] Martinetz, T. and Schulten, K., 1994. Topology representing networks. Neural Networks, 7(3), (Web Link)

[4] Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals
Xiujuan Zhang, Bi-Ye Xie, Hong-Fei Wang, Xiangyuan Xu, Yuan Tian, Jian-Hua Jiang, Ming-Hui Lu & Yan-Feng Chen
Nature Communications volume 10, Article number: 5331 (2019) (Web Link)

[5] Orozco, S., Formella, A., Cadavid, C. A., Ruiz – Salguero, O. and Osorno, M. (2017) “Geometry and Topology-based Segmentation of 2-Manifold Triangular Meshes in R3”, Current Journal of Applied Science and Technology, 21(1), (Web Link)

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