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Journal articles on the topic 'Calculus of tensors Computer graphics'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Wood, Christopher J., Jacob D. Biamonte, and David G. Cory. "Tensor networks and graphical calculus for open quantum systems." Quantum Information and Computation 15, no. 9&10 (July 2015): 759–811. http://dx.doi.org/10.26421/qic15.9-10-3.

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We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we demonstrate the construction of tensor networks to pictographically represent the Liouville-superoperator, Choi-matrix, process-matrix, Kraus, and system-environment representations for the evolution of quantum states, review how these representations interrelate, and illustrate how graphical manipulations of the tensor networks may be used to concisely transform between them. To further demonstrate the utility of the presented graphical calculus we include several examples where we provide arguably simpler graphical proofs of several useful quantities in quantum information theory including the composition and contraction of multipartite channels, a condition for whether an arbitrary bipartite state may be used for ancilla assisted process tomography, and the derivation of expressions for the average gate fidelity and entanglement fidelity of a channel in terms of each of the different representations of the channel.

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2

Lončarić, Nataša, and Marko Kraljić. "Matrices in computer graphics." Tehnički glasnik 12, no. 2 (June 28, 2018): 120–23. http://dx.doi.org/10.31803/tg-20180119143651.

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In this article, the usage of matrices and matrix operations in computer graphics is shown. A brief overview of geometric transformations in computer graphics is given. The "Matrix - Computer Graphics" application software is created for the representation and easier understanding of relations between geometric transformations and matrix calculus.

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3

Desbrun, Mathieu. "Applied Geometry:Discrete Differential Calculus for Graphics." Computer Graphics Forum 23, no. 3 (September 2004): 269. http://dx.doi.org/10.1111/j.1467-8659.2004.00756.x.

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4

Acar, Umut A., Arthur Charguéraud, Mike Rainey, and Filip Sieczkowski. "Dag-calculus: a calculus for parallel computation." ACM SIGPLAN Notices 51, no. 9 (December 5, 2016): 18–32. http://dx.doi.org/10.1145/3022670.2951946.

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5

Pletinckx, Daniel. "Quaternion calculus as a basic tool in computer graphics." Visual Computer 5, no. 1-2 (January 1989): 2–13. http://dx.doi.org/10.1007/bf01901476.

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6

Bos, Jan. "RasterCalc: Calculus for Operations on Graphics Colour Rasters." Computer Graphics Forum 6, no. 3 (September 1987): 181–93. http://dx.doi.org/10.1111/j.1467-8659.1987.tb00538.x.

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7

Oliveira, Bruno C. d. S., Tom Schrijvers, Wontae Choi, Wonchan Lee, and Kwangkeun Yi. "The implicit calculus." ACM SIGPLAN Notices 47, no. 6 (August 6, 2012): 35–44. http://dx.doi.org/10.1145/2345156.2254070.

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8

Schmitt, Alan, and Jean-Bernard Stefani. "The m-calculus." ACM SIGPLAN Notices 38, no. 1 (January 15, 2003): 50–61. http://dx.doi.org/10.1145/640128.604136.

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9

Ernst, Erik, Klaus Ostermann, and William R. Cook. "A virtual class calculus." ACM SIGPLAN Notices 41, no. 1 (January 12, 2006): 270–82. http://dx.doi.org/10.1145/1111320.1111062.

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10

Hayashi, Koby, Grey Ballard, Yujie Jiang, and Michael J. Tobia. "Shared-memory parallelization of MTTKRP for dense tensors." ACM SIGPLAN Notices 53, no. 1 (March 23, 2018): 393–94. http://dx.doi.org/10.1145/3200691.3178522.

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11

Steidl, G., and T. Teuber. "Diffusion Tensors for Processing Sheared and Rotated Rectangles." IEEE Transactions on Image Processing 18, no. 12 (December 2009): 2640–48. http://dx.doi.org/10.1109/tip.2009.2028934.

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12

Elmas, Tayfun, Shaz Qadeer, and Serdar Tasiran. "A calculus of atomic actions." ACM SIGPLAN Notices 44, no. 1 (January 21, 2009): 2–15. http://dx.doi.org/10.1145/1594834.1480885.

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13

Goyet, Alexis. "The Lambda Lambda-Bar calculus." ACM SIGPLAN Notices 48, no. 1 (January 23, 2013): 155–66. http://dx.doi.org/10.1145/2480359.2429089.

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14

Crary, Karl, and Michael J. Sullivan. "A Calculus for Relaxed Memory." ACM SIGPLAN Notices 50, no. 1 (May 11, 2015): 623–36. http://dx.doi.org/10.1145/2775051.2676984.

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15

Michaylov, Spiro, and Frank Pfenning. "Compiling the polymorphic λ-calculus." ACM SIGPLAN Notices 26, no. 9 (September 1991): 285–96. http://dx.doi.org/10.1145/115866.115896.

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16

Park, Sungwoo. "A calculus for probabilistic languages." ACM SIGPLAN Notices 38, no. 3 (March 18, 2003): 38–49. http://dx.doi.org/10.1145/640136.604180.

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17

Ancona, D., G. Lagorio, and E. Zucca. "A core calculus for Java exceptions." ACM SIGPLAN Notices 36, no. 11 (November 2001): 16–30. http://dx.doi.org/10.1145/504311.504284.

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18

Gabay, Yarom, and Assaf J. Kfoury. "A calculus for java's reference objects." ACM SIGPLAN Notices 42, no. 8 (August 2007): 9–17. http://dx.doi.org/10.1145/1294297.1294299.

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19

Lee, Shinn-Der, and Daniel P. Friedman. "Enriching the lambda calculus with contexts." ACM SIGPLAN Notices 31, no. 6 (June 15, 1996): 239–50. http://dx.doi.org/10.1145/232629.232652.

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20

Walkingshaw, Eric, and Martin Erwig. "A calculus for modeling and implementing variation." ACM SIGPLAN Notices 48, no. 3 (April 10, 2013): 132–40. http://dx.doi.org/10.1145/2480361.2371421.

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21

Omar, Cyrus, Ian Voysey, Michael Hilton, Jonathan Aldrich, and Matthew A. Hammer. "Hazelnut: a bidirectionally typed structure editor calculus." ACM SIGPLAN Notices 52, no. 1 (May 11, 2017): 86–99. http://dx.doi.org/10.1145/3093333.3009900.

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22

Downen, Paul, Luke Maurer, Zena M. Ariola, and Simon Peyton Jones. "Sequent calculus as a compiler intermediate language." ACM SIGPLAN Notices 51, no. 9 (December 5, 2016): 74–88. http://dx.doi.org/10.1145/3022670.2951931.

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23

Cousot, Patrick`, and Radhia Cousot. "A galois connection calculus for abstract interpretation." ACM SIGPLAN Notices 49, no. 1 (January 13, 2014): 3–4. http://dx.doi.org/10.1145/2578855.2537850.

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24

Walker, David, Lester Mackey, Jay Ligatti, George A. Reis, and David I. August. "Static typing for a faulty lambda calculus." ACM SIGPLAN Notices 41, no. 9 (September 16, 2006): 38–49. http://dx.doi.org/10.1145/1160074.1159809.

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25

Charguéraud, Arthur, and François Pottier. "Functional translation of a calculus of capabilities." ACM SIGPLAN Notices 43, no. 9 (September 27, 2008): 213–24. http://dx.doi.org/10.1145/1411203.1411235.

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26

Chen, Gang. "Coercive subtyping for the calculus of constructions." ACM SIGPLAN Notices 38, no. 1 (January 15, 2003): 150–59. http://dx.doi.org/10.1145/640128.604145.

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27

Ohori, Atsushi, and Kiyoshi Yamatodani. "An interoperable calculus for external object access." ACM SIGPLAN Notices 37, no. 9 (September 17, 2002): 60–71. http://dx.doi.org/10.1145/583852.581485.

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28

Navarro Pérez, Juan Antonio, and Andrey Rybalchenko. "Separation logic + superposition calculus = heap theorem prover." ACM SIGPLAN Notices 46, no. 6 (June 4, 2011): 556–66. http://dx.doi.org/10.1145/1993316.1993563.

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29

Yerizon, Siti Fatimah, and Fridgo Tasman. "Development of a GeoGebra-Assisted Calculus Worksheet to Enhance Students’ Understanding." International Journal of Information and Education Technology 11, no. 10 (2021): 456–63. http://dx.doi.org/10.18178/ijiet.2021.11.10.1550.

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The goal of this study is to develop a GeoGebra-assisted worksheet to enhance students' understanding of calculus. Many studies report that students have difficulty understanding calculus. GeoGebra provides an alternative method to overcome the difficulties associated with calculus. The Plomp development model consists of three phases: specifically, preliminary analysis, prototype development and an assessment was used in this study. The subjects of this study were 37 students. The results of this study are valid in terms of content, presentation, linguistics and graphics and practical in terms of implementation, time, ease of use and effective in terms of its potential impact on students' mathematical understanding. The GeoGebra-assisted worksheet can help students rediscover the given concept, while the use of visualization of the calculus concept can significantly enhance students’ mathematical understanding. Likewise, GeoGebra-assisted worksheets can be used to enhance students’ understanding of calculus. Teachers are suggested using GeoGebra in order to build students’ understanding on calculus subject.

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30

Igarashi, Atsushi, and Naoki Kobayashi. "A generic type system for the Pi-calculus." ACM SIGPLAN Notices 36, no. 3 (March 2001): 128–41. http://dx.doi.org/10.1145/373243.360215.

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31

Hardin, Thérèse, Luc Maranget, and Bruno Pagano. "Functional back-ends within the lambda-sigma calculus." ACM SIGPLAN Notices 31, no. 6 (June 15, 1996): 25–33. http://dx.doi.org/10.1145/232629.232632.

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32

Ramsey, Norman, and Avi Pfeffer. "Stochastic lambda calculus and monads of probability distributions." ACM SIGPLAN Notices 37, no. 1 (January 2002): 154–65. http://dx.doi.org/10.1145/565816.503288.

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33

Borgström, Johannes, Ugo Dal Lago, Andrew D. Gordon, and Marcin Szymczak. "A lambda-calculus foundation for universal probabilistic programming." ACM SIGPLAN Notices 51, no. 9 (December 5, 2016): 33–46. http://dx.doi.org/10.1145/3022670.2951942.

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34

Kutzner, Arne, and Manfred Schmidt-Schauß. "A non-deterministic call-by-need lambda calculus." ACM SIGPLAN Notices 34, no. 1 (January 1999): 324–35. http://dx.doi.org/10.1145/291251.289462.

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35

Faggian, Claudia. "A term calculus for unitary approach to normalization." ACM SIGPLAN Notices 34, no. 1 (January 1999): 347. http://dx.doi.org/10.1145/291251.289477.

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36

Gengler, Marc, and Matthieu Martel. "Self-applicable partial evaluation for the pi-calculus." ACM SIGPLAN Notices 32, no. 12 (December 1997): 36–46. http://dx.doi.org/10.1145/258994.259000.

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37

Tobisawa, Kazunori. "A Meta Lambda Calculus with Cross-Level Computation." ACM SIGPLAN Notices 50, no. 1 (May 11, 2015): 383–93. http://dx.doi.org/10.1145/2775051.2676976.

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38

Polakow, Jeff. "Embedding a full linear Lambda calculus in Haskell." ACM SIGPLAN Notices 50, no. 12 (January 28, 2016): 177–88. http://dx.doi.org/10.1145/2887747.2804309.

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39

La Torre, Salvatore, Madhusudan Parthasarathy, and Gennaro Parlato. "Analyzing recursive programs using a fixed-point calculus." ACM SIGPLAN Notices 44, no. 6 (May 28, 2009): 211–22. http://dx.doi.org/10.1145/1543135.1542500.

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40

Abadi, Martín. "Access control in a core calculus of dependency." ACM SIGPLAN Notices 41, no. 9 (September 16, 2006): 263–73. http://dx.doi.org/10.1145/1160074.1159839.

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41

Singh, Awadhesh Kumar, and Anup Kumar Bandyopadhyay. "Adding the leads-to operator to Dijkstra's calculus." ACM SIGPLAN Notices 39, no. 2 (February 2004): 12–17. http://dx.doi.org/10.1145/967278.967282.

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42

Bowman, William J., and Amal Ahmed. "Typed closure conversion for the calculus of constructions." ACM SIGPLAN Notices 53, no. 4 (December 2, 2018): 797–811. http://dx.doi.org/10.1145/3296979.3192372.

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43

Grabmayer, Clemens, and Jan Rochel. "Maximal sharing in the Lambda calculus with letrec." ACM SIGPLAN Notices 49, no. 9 (November 26, 2014): 67–80. http://dx.doi.org/10.1145/2692915.2628148.

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44

Rao, V. V. Bapeswara. "Simulation of problems in propositional calculus." SIMULATION 51, no. 4 (October 1988): 163–64. http://dx.doi.org/10.1177/003754978805100403.

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45

JIN, Long-Fei, and Lei LIU. "Bigraphical Semantics of Seal Calculus." Chinese Journal of Computers 31, no. 3 (September 28, 2009): 522–28. http://dx.doi.org/10.3724/sp.j.1016.2008.00522.

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46

Karr, Michael. "A translator from C to a λ-calculus representation." ACM SIGPLAN Notices 31, no. 4 (April 1996): 28–31. http://dx.doi.org/10.1145/249118.249123.

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47

Chen, Sheng, Martin Erwig, and Eric Walkingshaw. "An error-tolerant type system for variational lambda calculus." ACM SIGPLAN Notices 47, no. 9 (October 15, 2012): 29–40. http://dx.doi.org/10.1145/2398856.2364535.

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48

Gaboardi, Marco, and Romain Péchoux. "Algebras and coalgebras in the light affine Lambda calculus." ACM SIGPLAN Notices 50, no. 9 (December 18, 2015): 114–26. http://dx.doi.org/10.1145/2858949.2784759.

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49

Di Gianantonio, Pietro, Furio Honsell, and Luigi Liquori. "A lambda calculus of objects with self-inflicted extension." ACM SIGPLAN Notices 33, no. 10 (October 1998): 166–78. http://dx.doi.org/10.1145/286942.286955.

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50

Alur, Rajeev, Swarat Chaudhuri, and P. Madhusudan. "A fixpoint calculus for local and global program flows." ACM SIGPLAN Notices 41, no. 1 (January 12, 2006): 153–65. http://dx.doi.org/10.1145/1111320.1111051.

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