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Journal articles on the topic 'Torus topology'

To see the other types of publications on this topic, follow the link: Torus topology.

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Fabre, Ophélia, Simon Prunet, and Jean-Philippe Uzan. "Detectability of Torus Topology." Proceedings of the International Astronomical Union 10, S306 (May 2014): 139–43. http://dx.doi.org/10.1017/s1743921314010989.

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AbstractThe global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (DLSS). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 DLSS. CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.

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2

Andujar-Munoz, Francisco J., Juan A. Villar-Ortiz, Jose L. Sanchez, Francisco Jose Alfaro, and Jose Duato. "N-Dimensional Twin Torus Topology." IEEE Transactions on Computers 64, no. 10 (October 1, 2015): 2847–61. http://dx.doi.org/10.1109/tc.2014.2378267.

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3

Bhardwaj, Manish. "C2 Torus New Interconnection Network Topology Based on 2D Torus." American Journal of Networks and Communications 4, no. 3 (2015): 1. http://dx.doi.org/10.11648/j.ajnc.s.2015040301.11.

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4

Menotti, Pietro. "Torus classical conformal blocks." Modern Physics Letters A 33, no. 28 (September 11, 2018): 1850166. http://dx.doi.org/10.1142/s0217732318501663.

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After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus, we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing the classical conformal blocks for the sphere topology to the tours topology. We give the explicit results for the classical blocks up to the third-order in the nome included and compare them with the classical limit of the quantum conformal blocks. The extension to higher orders is straightforward.

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5

Bukhshtaber, V. M., and T. E. Panov. "Torus actions, combinatorial topology, and homological algebra." Russian Mathematical Surveys 55, no. 5 (October 31, 2000): 825–921. http://dx.doi.org/10.1070/rm2000v055n05abeh000320.

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6

Etnyre, John B. "Transversal torus knots." Geometry & Topology 3, no. 1 (September 5, 1999): 253–68. http://dx.doi.org/10.2140/gt.1999.3.253.

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7

Keener, J. P. "Knotted vortex filaments in an ideal fluid." Journal of Fluid Mechanics 211 (February 1990): 629–51. http://dx.doi.org/10.1017/s0022112090001732.

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Knotted closed-curve solutions of the equation of self-induced vortex motion are studied. It is shown that there are invariant torus knots which translate and rotate as rigid bodies. The general motion of ‘small-amplitude’ torus knots and iterated (cabled) torus knots is described and found to be almost periodic in time, and for some, but not all, initial data, the topology of the knot is shown to be invariant.

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8

Chauhan, Prachi, and Manish Bhardwaj. "Analysis the Performance of Interconnection Network Topology C2 Torus Based on Two Dimensional Torus." International Journal of Emerging Research in Management and Technology 6, no. 6 (June 29, 2018): 169. http://dx.doi.org/10.23956/ijermt.v6i6.264.

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Mesh and Torus are most popular interconnection topologies based on 2D-mesh.Comparison between Mesh and Torus will be considered and new interconnection topology will be proposed to provide better performance. The C2Mesh, is an enhanced mesh interconnected network. This paper enhances the torus network based on the theme of C2Mesh. Topological Properties of new network will be analyzed and implemented by simulation. The new routing Algorithm will be designed for new proposed network (C2Torus). This manuscript performs Comparison between C2Torus and C2Mesh.

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9

Bossard, Antoine, and Keiichi Kaneko. "Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks." International Journal of Applied Mathematics and Computer Science 25, no. 4 (December 1, 2015): 723–35. http://dx.doi.org/10.1515/amcs-2015-0052.

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Abstract Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.

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10

Mellit, Anton. "Homology of torus knots." Geometry & Topology 26, no. 1 (April 5, 2022): 47–70. http://dx.doi.org/10.2140/gt.2022.26.47.

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11

Gonzalez, A., M. Valero-Garcia, and L. Diaz de Cerio. "Executing algorithms with hypercube topology on torus multicomputers." IEEE Transactions on Parallel and Distributed Systems 6, no. 8 (1995): 803–14. http://dx.doi.org/10.1109/71.406957.

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12

Duistermaat, J. J., and A. Pelayo. "Topology of symplectic torus actions with symplectic orbits." Revista Matemática Complutense 24, no. 1 (March 13, 2010): 59–81. http://dx.doi.org/10.1007/s13163-010-0028-5.

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13

MARTÍN, J. C., and L. MORA. "Homoclinic bifurcations and the Floquet torus." Ergodic Theory and Dynamical Systems 20, no. 4 (August 2000): 1173–86. http://dx.doi.org/10.1017/s0143385700000638.

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In this paper we show that a $C^r$ diffeomorphism having an invariant Floquet torus which is non-normally hyperbolic can be approximated, in the $C^{r-3}$ topology, by another one which exhibits a homoclinic tangency.

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14

Mladenov, Ivïalo M. "Torus-Like Balloons." Journal of Geometry and Symmetry in Physics 56 (2020): 59–65. http://dx.doi.org/10.7546/jgsp-56-2020-59-65.

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The concepts for inflatable deployable structures have been under development and evaluation for many years. Strangely enough only the Mylar balloon up to now has been described adequately. Here we provide the mathematical model and its analytical solution for the torus-like balloons. Their characteristics and shapes are described explicitly in terms of elliptic integrals. The obtained results are commented shortly and the possible directions for the related studies in the future are outlined.

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15

Bossard, Antoine, and Keiichi Kaneko. "Torus Pairwise Disjoint-Path Routing." Sensors 18, no. 11 (November 13, 2018): 3912. http://dx.doi.org/10.3390/s18113912.

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Modern supercomputers include hundreds of thousands of processors and they are thus massively parallel systems. The interconnection network of a system is in charge of mutually connecting these processors. Recently, the torus has become a very popular interconnection network topology. For example, the Fujitsu K, IBM Blue Gene/L, IBM Blue Gene/P, and Cray Titan supercomputers all rely on this topology. The pairwise disjoint-path routing problem in a torus network is addressed in this paper. This fundamental problem consists of the selection of mutually vertex disjoint paths between given vertex pairs. Proposing a solution to this problem has critical implications, such as increased system dependability and more efficient data transfers, and provides concrete implementation of green and sustainable computing as well as security, privacy, and trust, for instance, for the Internet of Things (IoT). Then, the correctness and complexities of the proposed routing algorithm are formally established. Precisely, in an n-dimensional k-ary torus ( n < k , k ≥ 5 ), the proposed algorithm connects c ( c ≤ n ) vertex pairs with mutually vertex-disjoint paths of lengths at most 2 k ( c − 1 ) + n ⌊ k / 2 ⌋ , and the worst-case time complexity of the algorithm is O ( n c 4 ) . Finally, empirical evaluation of the proposed algorithm is conducted in order to inspect its practical behavior.

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16

Kloeckner, Benoît, and Stéphane Sabourau. "Mixed sectional-Ricci curvature obstructions on tori." Journal of Topology and Analysis 12, no. 03 (October 23, 2018): 713–34. http://dx.doi.org/10.1142/s1793525319500626.

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We establish new obstruction results to the existence of Riemannian metrics on tori satisfying mixed bounds on both their sectional and Ricci curvatures. More precisely, from Lohkamp’s theorem, every torus of dimension at least three admits Riemannian metrics with negative Ricci curvature. We show that the sectional curvature of these metrics cannot be bounded from above by an arbitrarily small positive constant. In particular, if the Ricci curvature of a Riemannian torus is negative, bounded away from zero, then there exist some planar directions in this torus where the sectional curvature is positive, bounded away from zero. All constants are explicit and depend only on the dimension of the torus.

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17

Ni, Yi, and Xingru Zhang. "Characterizing slopes for torus knots." Algebraic & Geometric Topology 14, no. 3 (April 7, 2014): 1249–74. http://dx.doi.org/10.2140/agt.2014.14.1249.

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18

Teragaito, Masakazu. "Crosscap numbers of torus knots." Topology and its Applications 138, no. 1-3 (March 2004): 219–38. http://dx.doi.org/10.1016/j.topol.2003.08.004.

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19

Stošić, Marko. "Khovanov homology of torus links." Topology and its Applications 156, no. 3 (January 2009): 533–41. http://dx.doi.org/10.1016/j.topol.2008.08.004.

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20

Calegari, Danny. "Real Places and Torus Bundles." Geometriae Dedicata 118, no. 1 (March 2006): 209–27. http://dx.doi.org/10.1007/s10711-005-9037-9.

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21

Hirasa, Tomonori. "Dissecting the torus by immersions." Geometriae Dedicata 145, no. 1 (July 28, 2009): 33–41. http://dx.doi.org/10.1007/s10711-009-9400-3.

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22

Bossard, Antoine. "On Solving the Decycling Problem in a Torus Network." Wireless Communications and Mobile Computing 2021 (April 12, 2021): 1–6. http://dx.doi.org/10.1155/2021/5598173.

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Modern supercomputers are massively parallel systems: they embody thousands of computing nodes and sometimes several millions. The torus topology has proven very popular for the interconnect of these high-performance systems. Notably, this network topology is employed by the supercomputer ranked number one in the world as of November 2020, the supercomputer Fugaku. Given the high number of compute nodes in such systems, efficient parallel processing is critical to maximise the computing performance. It is well known that cycles harm the parallel processing capacity of systems: for instance, deadlocks and starvations are two notorious issues of parallel computing that are directly linked to the presence of cycles. Hence, network decycling is an important issue, and it has been extensively discussed in the literature. We describe in this paper a decycling algorithm for the 3-dimensional k -ary torus topology and compare it with established results, both theoretically and experimentally. (This paper is a revised version of Antoine Bossard (2020)).

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23

S. Bhople, Sonal, and M. A. Gaikwad. "Design of Mesh and Torus Topologies for Network-On-Chip Application." International Journal of Reconfigurable and Embedded Systems (IJRES) 2, no. 2 (July 1, 2013): 76. http://dx.doi.org/10.11591/ijres.v2.i2.pp76-82.

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<p>Network-on-Chip (NoC) is a general purpose on-chip communication concept that offers high throughput, which is the basic requirement to deal with complexity of modern systems. In Network on chip topology design is one of the significant factors that affect the net delay of the system. In this paper mesh topology and torus topology are compared in terms of network delay for a given NOC application using Xillinc 9.1c.</p>

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24

Hamada, Noriyuki, and Kenta Hayano. "Topology of holomorphic Lefschetz pencils on the four-torus." Algebraic & Geometric Topology 18, no. 3 (April 3, 2018): 1515–72. http://dx.doi.org/10.2140/agt.2018.18.1515.

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25

Eingorn, Maxim, Ezgi Canay, Jacob M. Metcalf, Maksym Brilenkov, and Alexander Zhuk. "Effect of the Cubic Torus Topology on Cosmological Perturbations." Universe 7, no. 12 (November 30, 2021): 469. http://dx.doi.org/10.3390/universe7120469.

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We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula, we express the Yukawa potentials via Ewald sums. We show that for the present Universe, both the bare summation of Yukawa potentials and the Yukawa-Ewald sums require smaller numbers of terms to yield the numerical values of the potential and the force up to desired accuracy. Nevertheless, the Yukawa formula is yet preferable owing to its much simpler structure.

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26

YUE, Zu-Hui, You-Jian ZHAO, Jian-Ping WU, and Xiao-Ping ZHANG. "Calculation on the Bisection Width of H-Torus Topology." Journal of Software 20, no. 2 (April 7, 2009): 415–24. http://dx.doi.org/10.3724/sp.j.1001.2009.00415.

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27

., Poornima Kotriki. "FPGA BASED: DESIGN AND IMPLEMENTATION OF NOC TORUS TOPOLOGY." International Journal of Research in Engineering and Technology 03, no. 15 (May 25, 2014): 399–402. http://dx.doi.org/10.15623/ijret.2014.0315079.

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28

Wang, Hao, and Ling Wu. "Design and Simulation of Multicast Communication Model Based on 2D Torus Network on Chip." Advanced Materials Research 630 (December 2012): 276–82. http://dx.doi.org/10.4028/www.scientific.net/amr.630.276.

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In order to avoid the deadlock and high transmission delay of network on chip in multicast communication, this paper put forward a solution of multicast communication model. First, the author carried out a formalized description for the multicast communication model. Secondly, illustrate the deadlock caused by the loop circuit waiting. To solve this problem, the NOC multicast communication model was proposed based on the 2D Torus topology. In addition, this paper also presented an example to validate its correctness. Finally, simulate and apply this model simulation to the NOC of 2D Torus topology structure by the OPNET Modeler. The test results show that this multicast communication model has lower transmission delay and higher throughput volume compared with the unicast routing strategy using XY routing.

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29

Gerig, Chris. "Lagrangian torus invariants using $ECH = SWF$." Journal of Symplectic Geometry 19, no. 4 (2021): 959–92. http://dx.doi.org/10.4310/jsg.2021.v19.n4.a3.

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30

Montero, Antonio. "Regular polyhedra in the 3-torus." Advances in Geometry 18, no. 4 (October 25, 2018): 431–50. http://dx.doi.org/10.1515/advgeom-2018-0017.

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Abstract We discuss the classification of rank 3 lattices preserved by finite orthogonal groups and derive from it the classification of regular polyhedra in the 3-dimensional torus. This classification is closely related to the classification of regular polyhedra in 3-space.

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31

Keen, Linda, and Caroline Series. "Pleating invariants for punctured torus groups." Topology 43, no. 2 (March 2004): 447–91. http://dx.doi.org/10.1016/s0040-9383(03)00052-1.

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32

Marché, Julien. "On Kontsevich integral of torus knots." Topology and its Applications 143, no. 1-3 (August 2004): 15–26. http://dx.doi.org/10.1016/j.topol.2004.01.006.

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33

Moriah, Yoav, and Eric Sedgwick. "Heegaard splittings of twisted torus knots." Topology and its Applications 156, no. 5 (February 2009): 885–96. http://dx.doi.org/10.1016/j.topol.2008.11.003.

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34

Isozaki, Hiroshi, and Evgeny L. Korotyaev. "Inverse Spectral Theory for Perturbed Torus." Journal of Geometric Analysis 30, no. 4 (July 31, 2019): 4427–52. http://dx.doi.org/10.1007/s12220-019-00248-6.

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35

Civan, Yusuf. "Bott Towers, Crosspolytopes and Torus Actions." Geometriae Dedicata 113, no. 1 (June 2005): 55–74. http://dx.doi.org/10.1007/s10711-005-1725-y.

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36

Dalbelo, T. M., and N. G. Grulha. "The Euler obstruction and torus action." Geometriae Dedicata 175, no. 1 (January 24, 2014): 373–83. http://dx.doi.org/10.1007/s10711-014-9952-8.

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37

Usimov, Igor, and S. M. Ageev. "The locked cohomology of the torus." Topology and its Applications 221 (April 2017): 156–66. http://dx.doi.org/10.1016/j.topol.2017.02.033.

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38

Demailly, Jean-Pierre, Jun-Muk Hwang, and Thomas Peternell. "Compact Manifolds Covered by a Torus." Journal of Geometric Analysis 18, no. 2 (February 29, 2008): 324–40. http://dx.doi.org/10.1007/s12220-008-9017-z.

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39

Horowitz, Charles, Karin Usadi Katz, and Mikhail G. Katz. "Loewner’s Torus Inequality with Isosystolic Defect." Journal of Geometric Analysis 19, no. 4 (June 19, 2009): 796–808. http://dx.doi.org/10.1007/s12220-009-9090-y.

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40

Raissy, Jasmin. "Torus Actions in the Normalization Problem." Journal of Geometric Analysis 20, no. 2 (September 23, 2009): 472–524. http://dx.doi.org/10.1007/s12220-009-9108-5.

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41

BUNKE, ULRICH, and THOMAS SCHICK. "ON THE TOPOLOGY OF T-DUALITY." Reviews in Mathematical Physics 17, no. 01 (February 2005): 77–112. http://dx.doi.org/10.1142/s0129055x05002315.

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We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a classifying space for such pairs and show that it admits a selfmap which implements a T-duality transformation. We give a simple derivation of a T-duality isomorphism for certain twisted cohomology theories. We conclude with some explicit computations of twisted K-theory groups and discuss an example of iterated T-duality for higher-dimensional torus bundles.

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42

Morris, Sidney A. "The Tubby Torus as a Quotient Group." Axioms 9, no. 1 (January 20, 2020): 11. http://dx.doi.org/10.3390/axioms9010011.

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Let E be any metrizable nuclear locally convex space and E ^ the Pontryagin dual group of E. Then the topological group E ^ has the tubby torus (that is, the countably infinite product of copies of the circle group) as a quotient group if and only if E does not have the weak topology. This extends results in the literature related to the Banach–Mazur separable quotient problem.

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43

Diks, Krzysztof, Evangelos Kranakis, and Andrzej Pelc. "Broadcasting in Unlabeled Tori." Parallel Processing Letters 08, no. 02 (June 1998): 177–88. http://dx.doi.org/10.1142/s0129626498000195.

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We consider broadcasting a message from one node to all other nodes of an asynchronous totally unlabeled torus: neither nodes nor links have a priori assigned labels but they know the topology and the size of the torus. Nodes can send messages of arbitrary size and we are interested in minimizing the total number of messages. A naive broadcasting algorithm in a n × n totally unlabeled torus uses 3n2 + 1 messages, while the obvious lower bound is n2 - 1. The main result of this paper is a broadcasting algorithm using 2n2 + O(n) messages. We also give a lower bound of 1.04n2 - O(n) messages. This is the first result on message complexity of broadcasting in totally unlabeled networks.

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44

Punhani, Akash, Pardeep Kumar, and Nitin Nitin. "A Modified Diagonal Mesh Shuffle Exchange Interconnection Network." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 2 (April 1, 2017): 1042. http://dx.doi.org/10.11591/ijece.v7i2.pp1042-1050.

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Interconnection network is an important part of the digital system. The interconnection mainly describes the topology of the network along with the routing algorithm and flow control mechanism. The topology of the network plays an important role on the performance of the system. Mesh interconnection network was the simplest topology, but has the limited bisection bandwidth on the other hand torus and diagonal mesh was having long links. The Modified diagonal mesh network tried to replace the torodial links but was having more average path length so in proposed topology we have tried to improve the average distance using shuffle exchange network over the boundary node. In this paper, we propose the architecture of Modified Diagonal Mesh Shuffle Exchange Interconnection Network. This Modified Diagonal Mesh Shuffle Exchange Interconnection network have been compared with four popular topologies that are simple 2D Mesh, 2D Torus, Diagonal Mesh and Modified Diagonal Mesh Interconnection Network on the four traffic patterns such as Bit Complement traffic, Neighbor traffic, Tornado traffic and Uniform traffic are used for comparisonand performance analysis. We have performed the analysis with a 5% and 10% of hotspot on the Uniform Traffic. The simulation results shows that the proposed topology is performed better on bit complement traffic and can also handle the other traffic up to certain level.

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45

Heil, Wolfgang, and Pedja Raspopović. "Dehn fillings of Klein bottle bundles." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (September 1992): 255–70. http://dx.doi.org/10.1017/s0305004100070948.

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An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.

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46

DE MARCO, GIANLUCA, and ADELE A. RESCIGNO. "TIGHTER TIME BOUNDS ON BROADCASTING IN TORUS NETWORKS IN PRESENCE OF DYNAMIC FAULTS." Parallel Processing Letters 10, no. 01 (March 2000): 39–49. http://dx.doi.org/10.1142/s0129626400000068.

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We consider the problem of broadcasting in a network G under the hypothesis that each vertex can inform in one unit of time all of its neighbours and that any number of message transmissions, less than the edge-connectivity of G, may fail during each time unit. In particular, we study broadcasting in the n-dimensional k-ary torus, a popular topology for link connections in communication networks. We prove that under the above strong fault-assumption, if k is even and polynomially limited in n, and n is sufficient large, broadcasting in the n-dimensional k-ary torus can be accomplished in time [Formula: see text], where [Formula: see text] is the diameter of the n-dimensional k-ary torus.

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47

Ginzburg, Viktor L. "Book Review: The topology of torus actions on symplectic manifolds." Bulletin of the American Mathematical Society 27, no. 2 (October 1, 1992): 315–21. http://dx.doi.org/10.1090/s0273-0979-1992-00315-4.

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48

Gratus, J. "A noncommutative geometric analysis of a sphere–torus topology change." Journal of Geometry and Physics 49, no. 2 (February 2004): 156–75. http://dx.doi.org/10.1016/s0393-0440(03)00072-x.

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49

Wu, Jingjin, Xuanxing Xiong, Eduardo Berrocal, Jia Wang, and Zhiling Lan. "Topology mapping of irregular parallel applications on torus-connected supercomputers." Journal of Supercomputing 73, no. 4 (October 26, 2016): 1691–714. http://dx.doi.org/10.1007/s11227-016-1876-7.

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50

Matkovič, Irena. "Non-loose negative torus knots." Quantum Topology 13, no. 4 (January 26, 2023): 669–89. http://dx.doi.org/10.4171/qt/169.

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