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Relevant bibliographies by topics / Torus topology

Academic literature on the topic 'Torus topology'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Journal articles on the topic "Torus topology"

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Torus topology"

1

Ritchey, Katherine. "Computational Topology for Configuration Spaces of Disks in a Torus." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1562945889197152.

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Nguyenhuu, Rick Hung. "Torus embedding and its applications." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1572.

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Barker, Stephen J. "Interchanging Two Notations for Double-torus Links." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/2616.

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Knot theory is a relatively young branch of mathematics, still less than a century old. The development of the Jones polynomial in 1984 led to increased activity in knot theory. Though work is constantly being done in this ﬁeld, notably the classiﬁcation of torus knots, double-torus knots are still lacking such a complete understanding. There exists two notations, those of Rick Norwood and of Peter Hill, that describe knots on the double-torus. The ambition of this thesis is to begin to make the case that it is possible to render these two notations interchangeable. Illustrating this will require examining the two notations and ﬁnding a way to change one into the other, then check if this process is reversible. If not, then proceed to develop a method that works to convert the second notation back to the ﬁrst.

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La, Fleur Stephen J. "Some fundamentals for Nielsen theory on torus configuration spaces." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453597.

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Osborne, Joshua C. P. "Eigenspectra for Correlating Cosmic Microwave Background Temperature Data." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1544180098307733.

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Wyld, Kira A. "Sudoku Variants on the Torus." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/103.

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This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.

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Barbos, Aneta E. [Verfasser]. "Energy decay law in n-dimensional Gowdy spacetimes with torus topology / Aneta Barbos." Berlin : Freie Universität Berlin, 2010. http://d-nb.info/102508800X/34.

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Butler, Joe R. "The Torus Does Not Have a Hyperbolic Structure." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc500333/.

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Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of automorphisms on the covering space is equivalent to the original surface.

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Bellanco, Olivia. "Articulation topologique de la clinique." Thesis, Paris 8, 2018. http://www.theses.fr/2018PA080039.

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Nous retracerons le parcours de la topologie dans l’enseignement lacanien : de la topologie algébrique, nous traiterons des figures topologiques (tore, bande de Mœbius, bouteille de Klein, cross-cap) pour en arriver à la topologie nodale dont le paradigme est le nœud borroméen. Nous considérerons alors les conséquences théoriques qu’elle implique : de l’inconscient freudien ou l’inconscient symbolique nous passerons à l’inconscient réel et l’une-bévue, et du symptôme nous envisagerons le sinthome et sa logique. Nous affinerons ainsi le double rapport du sujet au signifiant et à la jouissance mettant en avant l’importance du corps pris comme vivant. Pour ce faire, nous étudierons plus précisément le rapport du sujet au trou, manque fondamental qui le constitue, à la fois extérieur et intérieur. Nous verrons comment, dans son creux et dans ses bords, le sujet y loge sa singularité, son « x ». Nous l’articulerons à la clinique afin de révéler l’apport qu’elle représente dans la pratique
We will trace the course of topology in Lacan’s teaching: from algebraic topology, where we will deal with topological surfaces (torus, Moebius strip, Klein bottle, cross-cap) we will reach topology whose paradigm is the Borromean knot. We will then consider the theoretical consequences implied: from the Freudian unconscious or symbolic unconscious we will move to the real unconscious and the une-bévue, and from the symptom we will consider the sinthome and its logic. We will refine the dual relationship of the subject to signifier and Jouissance, and highlight the importance of the body as living. To do this, we will study more precisely the relationship of the subject to the hole, a fundamental lack that constitutes him, both exterior and interior. We will see how, in its hollow and its edges, the subject lodges its singularity, its "x". We will link it to clinic to reveal the contribution of topology in practice

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Heathcote, Jonathan David. "Building and operating large-scale SpiNNaker machines." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/building-and-operating-largescale-spinnaker-machines(6151916a-ed71-42e4-97d2-2993a4caf5f6).html.

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SpiNNaker is an unconventional supercomputer architecture designed to simulate up to one billion biologically realistic neurons in real-time. To achieve this goal, SpiNNaker employs a novel network architecture which poses a number of practical problems in scaling up from desktop prototypes to machine room filling installations. SpiNNaker's hexagonal torus network topology has received mostly theoretical treatment in the literature. This thesis tackles some of the challenges encountered when building `real-world' systems. Firstly, a scheme is devised for physically laying out hexagonal torus topologies in machine rooms which avoids long cables; this is demonstrated on a half-million core SpiNNaker prototype. Secondly, to improve the performance of existing routing algorithms, a more efficient process is proposed for finding (logically) short paths through hexagonal torus topologies. This is complemented by a formula which provides routing algorithms with greater flexibility when finding paths, potentially resulting in a more balanced network utilisation. The scale of SpiNNaker's network and the models intended for it also present their own challenges. Placement and routing algorithms are developed which assign processes to nodes and generate paths through SpiNNaker's network. These algorithms minimise congestion and tolerate network faults. The proposed placement algorithm is inspired by techniques used in chip design and is shown to enable larger applications to run on SpiNNaker than the previous state-of-the-art. Likewise the routing algorithm developed is able to tolerate network faults, inevitably present in large-scale systems, with little performance overhead.

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Books on the topic "Torus topology"

1

The topology of torus actions on symplectic manifolds. Basel: Birkhäuser, 1991.

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Audin, Michèle. The Topology of Torus Actions on Symplectic Manifolds. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8.

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Symplectic actions of 2-tori on 4-manifolds. Providence, R.I: American Mathematical Society, 2010.

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Megumi, Harada, ed. Toric topology: International Conference, May 29 - June 3, 2006, Osaka City University, Osaka, Japan. Providence, R.I: American Mathematical Society, 2008.

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Audin, Michèle. Topology of Torus Actions on Symplectic Manifolds. Birkhauser Verlag, 2012.

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6

Torus Actions and Their Applications in Topology and Combinatorics. American Mathematical Society, 2002.

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McDuff, Dusa, and Dietmar Salamon. Symplectic manifolds. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0004.

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The third chapter introduces the basic notions of symplectic topology, such as symplectic forms, symplectomorphisms, and Lagrangian submanifolds. A fundamental classical construction is Moser isotopy, with its various applications such as Darboux’s theorem and the Lagrangian neighbourhood theorem. The chapter now includes a brief discussion of the Chekanov torus and Luttinger surgery. The last section on contact structures has been significantly expanded.

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Farb, Benson, and Dan Margalit. Teichmuller Space. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0011.

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This chapter deals with Teichmüller space Teich(S) of a surface S. It first defines Teichmüller space and a topology on Teich(S) before giving two heuristic counts of its dimension. It then describes explicit coordinates on Teich(Sɡ) coming from certain length and twist parameters for curves in a pair of pants decomposition of Sɡ; these are the Fenchel–Nielsen coordinates on Teich(Sɡ). The chapter also considers the Teichmüller space of the torus and concludes by proving the 9g – 9 theorem, which states that a hyperbolic structure on Sɡ is completely determined by the lengths assigned to 9g – 9 isotopy classes of simple closed curves in Sɡ.

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Bourbaki, N. Éléments de Mathématique: Tous les 28 tomes, y compris le dernier tome Topologie Algébrique Chapitre 1 - 4. Springer, 2016.

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Book chapters on the topic "Torus topology"

1

Goresky, M., and R. MacPherson. "On the topology of algebraic torus actions." In Lecture Notes in Mathematics, 73–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0079233.

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Gu, Huaxi, Qiming Xie, Kun Wang, Jie Zhang, and Yunsong Li. "X-Torus: A Variation of Torus Topology with Lower Diameter and Larger Bisection Width." In Computational Science and Its Applications - ICCSA 2006, 149–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11751649_16.

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Takahashi, Ryo, and Ken-ichi Kitayama. "Torus-Topology Data Center Networks with Hybrid Optoelectronic Routers." In Optical Switching in Next Generation Data Centers, 129–45. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61052-8_7.

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Audin, Michèle. "Introduction." In The Topology of Torus Actions on Symplectic Manifolds, 7–11. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_1.

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Audin, Michèle. "Smooth Lie group actions on manifolds." In The Topology of Torus Actions on Symplectic Manifolds, 13–35. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_2.

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Audin, Michèle. "Symplectic geometry." In The Topology of Torus Actions on Symplectic Manifolds, 37–59. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_3.

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Audin, Michèle. "Morse theory for hamiltonians." In The Topology of Torus Actions on Symplectic Manifolds, 61–74. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_4.

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Audin, Michèle. "About manifolds of this dimension." In The Topology of Torus Actions on Symplectic Manifolds, 75–111. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_5.

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Audin, Michèle. "Equivariant cohomology and the Duistermaat-Heckman theorems." In The Topology of Torus Actions on Symplectic Manifolds, 113–49. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_6.

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Audin, Michèle. "Toric manifolds." In The Topology of Torus Actions on Symplectic Manifolds, 151–76. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7221-8_7.

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Conference papers on the topic "Torus topology"

1

IWAKIRI, Masahide. "QUANDLE COCYCLE INVARIANTS OF TORUS LINKS." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0008.

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Lusala, Angelo Kuti, Philippe Manet, Bertrand Rousseau, and Jean-Didier Legat. "NoC Implementation in FPGA using Torus Topology." In 2007 International Conference on Field Programmable Logic and Applications. IEEE, 2007. http://dx.doi.org/10.1109/fpl.2007.4380767.

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Tripathy, Laxmi Nath, and Chitta Ranjan Tripathy. "A torus connected ring: A new interconnection topology." In 2017 International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC). IEEE, 2017. http://dx.doi.org/10.1109/i-smac.2017.8058335.

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Madhubala, T., P. Karthika, and S. Sobana. "A competent performance estimation of king torus topology." In 2017 International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC). IEEE, 2017. http://dx.doi.org/10.1109/i-smac.2017.8058342.

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"CCTorus: A New Torus Topology for Interconnection Networks." In International Conference on Advanced Computational Technologies and Creative Media. International Institute of Engineers, 2014. http://dx.doi.org/10.15242/iie.e0814512.

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Tarkov, Mikhail S. "Mapping semigroup array operations onto multicomputer with torus topology." In the 5th International Confernece. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1968613.1968768.

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Weigang Hou, Lei Guo, Qing Cai, and Lijiao Zhu. "3D Torus ONoC: Topology design, router modeling and adaptive routing algorithm." In 2014 13th International Conference on Optical Communications and Networks (ICOCN). IEEE, 2014. http://dx.doi.org/10.1109/icocn.2014.6987095.

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Yang, Xiaoqiang, Huimin Du, and Jungang Han. "A Node Coding and the Improved Routing Algorithm in Torus Topology." In 2008 International Conference on Computer Science and Information Technology (ICCSIT). IEEE, 2008. http://dx.doi.org/10.1109/iccsit.2008.48.

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Wang, Liang, Leibo Liu, Xiaohang Wang, Jie Han, Chenchen Deng, and Shaojun Wei. "CDRing: Reconfigurable Ring Architecture by Exploiting Cycle Decomposition of Torus Topology." In 2020 57th ACM/IEEE Design Automation Conference (DAC). IEEE, 2020. http://dx.doi.org/10.1109/dac18072.2020.9218647.

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Wang, Hong, Du Xu, Dan Liao, and Lemin Li. "A scheme to construct scalable Packet Switching Fabrics of Torus topology." In 2007 5th International Conference on Communications, Circuits and Systems. IEEE, 2007. http://dx.doi.org/10.1109/icccas.2007.6251614.

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