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Coupled Oscillator Networks for von Neumann and Non-von Neumann Computing

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Advances in Artificial Intelligence-based Technologies

Part of the book series: Learning and Analytics in Intelligent Systems ((LAIS,volume 22))

Abstract

The frenetic growth of the need for computation performance and efficiency, along with the intrinsic limitations of the current main solutions, is pushing the scientific community towards unconventional, and sometimes even exotic, alternatives to the standard computing architectures. In this work we provide a panorama of the most relevant alternatives, both according and not to the von Neumann architecture, highlighting which of the classical challenges, such as energy efficiency and/or computational complexity, they are trying to tackle. We focus on the alternatives based on networks of weakly coupled oscillators. This unconventional approach, already introduced by Goto and von Neumann in the 1950s, is recently regaining interest with potential applications to both von Neumann and non-von Neumann type of computing. In this contribution, we present a general framework based on the phase equation derived from the description of nonlinear weakly coupled oscillators, especially useful for computing applications. We then use this formalism to design and prove the working principle and stability assessment of Boolean gates such as NOT and MAJORITY, that can be potentially employed as building blocks for both von Neumann and non-von Neumann architectures.

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References

  1. J.J.P. Eckert, J.W. Mauchly, Electronic numerical integrator and computer, US patent # US757158A (1947)

    Google Scholar 

  2. H.H. Goldstine, A. Goldstine, The electronic numerical integrator and computer (ENIAC). Math. Tables Other Aids Comput. 2, 97 (1946)

    Google Scholar 

  3. J. von Neumann, First draft of a report on the EDVAC. Ann. History Comput. IEEE 15(4), 27–75 (1993)

    Google Scholar 

  4. J.L. Hennessy, D.A. Patterson, Computer Architecture, Sixth Edition: A Quantitative Approach (Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2017)

    Google Scholar 

  5. S. Arora, B. Barak, Computational Complexity: A Modern Approach (Cambridge University Press, Cambridge, 2009)

    Google Scholar 

  6. J. Backus, Can programming be liberated from the von Neumann style?: A functional style and its algebra of programs. Commun. ACM 21, 613–641 (1978). (Aug.)

    Google Scholar 

  7. J.L. Hennessy, D.A. Patterson, A new golden age for computer architecture. Commun ACM 62, 48–60 (2019)

    Google Scholar 

  8. M. Horowitz, 1.1 computing’s energy problem (and what we can do about it), in 2014 IEEE International Solid-State Circuits Conference Digest of Technical Papers (ISSCC) (IEEE, 2014)

    Google Scholar 

  9. J. Nickolls, W.J. Dally, The GPU computing era. IEEE Micro 30, 56–69 (2010)

    Google Scholar 

  10. D. Singh, C.K. Reddy, A survey on platforms for big data analytics. J. Big Data 2 (2014)

    Google Scholar 

  11. Y. LeCun, Y. Bengio, G. Hinton, Deep learning. Nature 521, 436–444 (2015). (May)

    Google Scholar 

  12. I. Goodfellow, J. Bengio, A. Courville, F. Bach, Deep Learning (MIT Press Ltd, 2016)

    Google Scholar 

  13. V. Sze, Y.-H. Chen, J. Emer, A. Suleiman, Z. Zhang, Hardware for machine learning: Challenges and opportunities, in 2017 IEEE Custom Integrated Circuits Conference (CICC) (IEEE, 2017)

    Google Scholar 

  14. V. Sze, Y.-H. Chen, T.-J. Yang, J.S. Emer, Efficient processing of deep neural networks: A tutorial and survey. Proc. IEEE 105, 2295–2329 (2017)

    Google Scholar 

  15. N.P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P. luc Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D.H. Yoon, “In-datacenter performance analysis of a tensor processing unit, in Proceedings of the 44th Annual International Symposium on Computer Architecture (ACM, 2017)

    Google Scholar 

  16. N. Jouppi, C. Young, N. Patil, D. Patterson, Motivation for and evaluation of the first tensor processing unit. IEEE Micro 38, 10–19 (2018)

    Google Scholar 

  17. C. Li, D. Belkin, Y. Li, P. Yan, M. Hu, N. Ge, H. Jiang, E. Montgomery, P. Lin, Z. Wang, W. Song, J.P. Strachan, M. Barnell, Q. Wu, R. S. Williams, J.J. Yang, Q. Xia, Efficient and self-adaptive in-situ learning in multilayer memristor neural networks. Nat. Commun. 9 (2018)

    Google Scholar 

  18. Q. Wang, X. Wang, S.H. Lee, F.-H. Meng, W.D. Lu, A deep neural network accelerator based on tiled RRAM architecture, in 2019 IEEE International Electron Devices Meeting (IEDM) (IEEE, 2019)

    Google Scholar 

  19. S.H. Lee, X. Zhu, W.D. Lu, Nanoscale resistive switching devices for memory and computing applications. Nano Res. 13, 1228–1243 (2020)

    Google Scholar 

  20. P. Benioff, The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by turing machines. J. Stat. Phys. 22, 563–591 (1980)

    Google Scholar 

  21. R.P. Feynman, Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)

    Google Scholar 

  22. Y. Manin, Computable and Uncomputable (in Russian) (Sovetskoye Radio, Moscow, 1980)

    Google Scholar 

  23. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge Series on information and the Natural Sciences, Cambridge University Press, 10th Aniversary ed., 2010)

    Google Scholar 

  24. P.W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in 1994 Proceedings of 35th Annual Symposium on Foundations of Computer Science (1994), pp. 124–134

    Google Scholar 

  25. M. Dyakonov, When will useful quantum computers be constructed? Not in the foreseeable future, this physicist argues. here’s why: The case against: Quantum computing. IEEE Spectrum 56, 24–29 (2019). (Mar)

    Google Scholar 

  26. S. Yu, Neuro-inspired computing with emerging nonvolatile memorys. Proc. IEEE 106, 260–285 (2018)

    Google Scholar 

  27. G.W. Burr, R.M. Shelby, A. Sebastian, S. Kim, S. Kim, S. Sidler, K. Virwani, M. Ishii, P. Narayanan, A. Fumarola, L.L. Sanches, I. Boybat, M.L. Gallo, K. Moon, J. Woo, H. Hwang, Y. Leblebici, Neuromorphic computing using non-volatile memory. Adv. Phys. X 2, 89–124 (2016)

    Google Scholar 

  28. S.B. Furber, F. Galluppi, S. Temple, L.A. Plana, The SpiNNaker project. Proc. IEEE 102, 652–665 (2014)

    Google Scholar 

  29. M. Davies, N. Srinivasa, T.-H. Lin, G. Chinya, Y. Cao, S.H. Choday, G. Dimou, P. Joshi, N. Imam, S. Jain, Y. Liao, C.-K. Lin, A. Lines, R. Liu, D. Mathaikutty, S. McCoy, A. Paul, J. Tse, G. Venkataramanan, Y.-H. Weng, A. Wild, Y. Yang, H. Wang, Loihi: A neuromorphic manycore processor with on-chip learning. IEEE Micro 38, 82–99 (2018)

    Google Scholar 

  30. I. Boybat, M.L. Gallo, S.R. Nandakumar, T. Moraitis, T. Parnell, T. Tuma, B. Rajendran, Y. Leblebici, A. Sebastian, E. Eleftheriou, Neuromorphic computing with multi-memristive synapses. Nat. Commun. 9 (2018)

    Google Scholar 

  31. A. Tavanaei, M. Ghodrati, S.R. Kheradpisheh, T. Masquelier, A. Maida, Deep learning in spiking neural networks. Neural Netw. 111, 47–63 (2019)

    Google Scholar 

  32. G. Singh, L. Chelini, S. Corda, A.J. Awan, S. Stuijk, R. Jordans, H. Corporaal, A.-J. Boonstra, Near-memory computing: Past, present, and future. Microprocessors Microsyst. 71, 102868 (2019)

    Google Scholar 

  33. D. Ielmini, H.-S.P. Wong, In-memory computing with resistive switching devices. Nat. Electron. 1, 333–343 (2018)

    Google Scholar 

  34. F.L. Traversa, F. Bonani, Y.V. Pershin, M. Di Ventra, Dynamic computing random access memory. Nanotechnology 25, 285201 (2014)

    Google Scholar 

  35. Y.V. Pershin, F.L. Traversa, M. Di Ventra, Memcomputing with membrane memcapacitive systems. Nanotechnology 26, 225201 (2015)

    Google Scholar 

  36. A. Sebastian, M.L. Gallo, R. Khaddam-Aljameh, E. Eleftheriou, Memory devices and applications for in-memory computing. Nature Nanotechnol. 15, 529–544 (2020)

    Google Scholar 

  37. F.L. Traversa, M. Di Ventra, Universal memcomputing machines. IEEE Trans. Neural Netw. Learn. Syst. 26(11), 2702 (2015)

    Google Scholar 

  38. M. Di Ventra, F.L. Traversa, Perspective: Memcomputing: Leveraging memory and physics to compute efficiently. J. Appl. Phys. 123, 180901 (2018)

    Google Scholar 

  39. Y.R. Pei, F.L. Traversa, M.D. Ventra, On the universality of memcomputing machines. IEEE Trans. Neural Netw. Learn. Syst. 30, 1610–1620 (2019)

    Google Scholar 

  40. F.L. Traversa, C. Ramella, F. Bonani, M. Di Ventra, Memcomputing NP-complete problems in polynomial time using polynomial resources and collective states. Sci. Adv. 1(6), e1500031 (2015)

    Google Scholar 

  41. F.L. Traversa, M. Di Ventra, Polynomial-time solution of prime factorization and np-complete problems with digital memcomputing machines. Chaos: Interdiscip. J. Nonlinear Sci. 27, 023107 (2017)

    Google Scholar 

  42. F.L. Traversa, M. Di Ventra, Memcomputing integer linear programming (2018). arXiv:1808.09999

  43. H. Manukian, F.L. Traversa, M. Di Ventra, “Memcomputing numerical inversion with self-organizing logic gates. IEEE Trans. Neural Netw. Learn. Syst. 99, 1–6 (2017)

    Google Scholar 

  44. M. Di Ventra, F.L. Traversa, Absence of chaos in digital memcomputing machines with solutions. Phys. Lett. A 381, 3255 (2017)

    Google Scholar 

  45. M. Di Ventra, F.L. Traversa, Absence of periodic orbits in digital memcomputing machines with solutions. Chaos: Interdiscipl. J. Nonlinear Sci. 27, 101101 (2017)

    Google Scholar 

  46. F.L. Traversa, P. Cicotti, F. Sheldon, M. Di Ventra, Evidence of exponential speed-up in the solution of hard optimization problems. Complexity 2018, 1–13 (2018)

    Google Scholar 

  47. F. Sheldon, P. Cicotti, F.L. Traversa, M.D. Ventra, Stress-testing memcomputing on hard combinatorial optimization problems. IEEE Trans. Neural Netw. Learn. Syst. 31(6), 2222–2226 (2020)

    Google Scholar 

  48. F.L. Traversa, Aircraft loading optimization: Memcomputing the 5th airbus problem (2019). arXiv:1903.08189

  49. F. Sheldon, F.L. Traversa, M.D. Ventra, Taming a nonconvex landscape with dynamical long-range order: Memcomputing ising benchmarks. Phys. Rev. E 100 (2019)

    Google Scholar 

  50. H. Manukian, F.L. Traversa, M. Di Ventra, Accelerating deep learning with memcomputing. Neural Netw. 110, 1–7 (2019)

    Google Scholar 

  51. K.Y. Camsari, R. Faria, B.M. Sutton, S. Datta, Stochastic p -bits for invertible logic. Phys. Rev. X 7 (2017)

    Google Scholar 

  52. K.Y. Camsari, S. Salahuddin, S. Datta, Implementing p-bits with embedded MTJ. IEEE Electron Device Lett. 38, 1767–1770 (2017)

    Google Scholar 

  53. F. Caravelli, C. Nisoli, Logical gates embedding in artificial spin ice. New J. Phys. 22, 103052 (2020)

    Google Scholar 

  54. E. Goto, New parametron circuit element using nonlinear reactance, in KDD Kenyku Shiryo (1954)

    Google Scholar 

  55. E. Goto, The parametron, a digital computing element which utilizes parametric oscillation. Proc. IRE 47, 1304–1316 (1959)

    Google Scholar 

  56. J. von Neumann, Non-linear capacitance or inductance switching, amplifying, and memory organs. patent # US2815488A (1954)

    Google Scholar 

  57. R. Wigington, A new concept in computing. Proc. IRE 47, 516–523 (1959)

    Google Scholar 

  58. S. Farzeen, G. Ren, C. Chen, An ultra-low power ring oscillator for passive UHF RFID transponders, in 2010 53rd IEEE International Midwest Symposium on Circuits and Systems (IEEE, 2010)

    Google Scholar 

  59. D. Houssameddine, U. Ebels, B. Delaët, B. Rodmacq, I. Firastrau, F. Ponthenier, M. Brunet, C. Thirion, J.-P. Michel, L. Prejbeanu-Buda, M.-C. Cyrille, O. Redon, B. Dieny, Spin-torque oscillator using a perpendicular polarizer and a planar free layer. Nat. Mater. 6, 447–453 (2007)

    Google Scholar 

  60. S. Kobayashi, T. Kimura, Injection locking characteristics of an AlGaAs semiconductor laser. IEEE J. Quantum Electron. 16, 915–917 (1980)

    Google Scholar 

  61. X.L. Feng, C.J. White, A. Hajimiri, M.L. Roukes, A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator. Nat. Nanotechnol. 3, 342–346 (2008)

    Google Scholar 

  62. M.B. Elowitz, S. Leibler, A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000)

    Google Scholar 

  63. K.M. Hannay, D.B. Forger, V. Booth, Macroscopic models for networks of coupled biological oscillators. Sci. Adv. 4, e1701047 (2018)

    Google Scholar 

  64. K. Matsuoka, Analysis of a neural oscillator. Biol. Cybern. 104, 297–304 (2011)

    Google Scholar 

  65. F.L. Traversa, Y.V. Pershin, M. Di Ventra, Memory models of adaptive behavior. IEEE Trans. Neural Netw. Learn. Syst. 24, 1437–1448 (2013)

    Google Scholar 

  66. A.T. Winfree, Biological rhythms and the behavior of populations of coupled oscillators. J. Theor. Biol. 16, 15–42 (1967)

    Google Scholar 

  67. J. Roychowdhury, Boolean computation using self-sustaining nonlinear oscillators. Proc. IEEE 103, 1958–1969 (2015)

    Google Scholar 

  68. A. Raychowdhury, A. Parihar, G.H. Smith, V. Narayanan, G. Csaba, M. Jerry, W. Porod, S. Datta, Computing with networks of oscillatory dynamical systems. Proc. IEEE 107, 73–89 (2019)

    Google Scholar 

  69. M. Bonnin, F. Bonani, F.L. Traversa, Logic gates implementation with coupled oscillators, in 2018 IEEE Workshop on Complexity in Engineering (COMPENG) (IEEE, 2018)

    Google Scholar 

  70. G. Csaba, A. Raychowdhury, S. Datta, W. Porod, Computing with coupled oscillators: Theory, devices, and applications, in 2018 IEEE International Symposium on Circuits and Systems (ISCAS) (IEEE, 2018)

    Google Scholar 

  71. T. Wang, J. Roychowdhury, Oscillator-based ising machine (2017). arXiv:1709.08102

  72. J. Chou, S. Bramhavar, S. Ghosh, W. Herzog, Analog coupled oscillator based weighted ising machine. Sci. Rep. 9 (2019)

    Google Scholar 

  73. A. Mallick, M.K. Bashar, D.S. Truesdell, B.H. Calhoun, S. Joshi, N. Shukla, Using synchronized oscillators to compute the maximum independent set. Nat. Commun. 11 (2020)

    Google Scholar 

  74. G. Csaba, W. Porod, Coupled oscillators for computing: A review and perspective. Appl. Phys. Rev. 7, 011302 (2020)

    Google Scholar 

  75. K. Chen, D. Wang, A dynamically coupled neural oscillator network for image segmentation. Neural Netw. 15, 423–439 (2002)

    Google Scholar 

  76. N. Shukla, A. Parihar, M. Cotter, M. Barth, X. Li, N. Chandramoorthy, H. Paik, D.G. Schlom, V. Narayanan, A. Raychowdhury, S. Datta, Pairwise coupled hybrid vanadium dioxide-MOSFET (HVFET) oscillators for non-boolean associative computing, in 2014 IEEE International Electron Devices Meeting (IEEE, 2014)

    Google Scholar 

  77. L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987)

    Google Scholar 

  78. L. Perko, Differential Equations and Dynamical Systems (Springer, New York, 2013)

    Google Scholar 

  79. R. Albert, A.-L. Barabási, Statistical mechanics of complex networks. Rev. Modern Phys. 74, 47–97 (2002)

    Google Scholar 

  80. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D. Hwang, Complex networks: Structure and dynamics. Phys. Rep. 424, 175–308 (2006)

    Google Scholar 

  81. F.C. Hoppensteadt, E.M. Izhikevich, Oscillatory neurocomputers with dynamic connectivity. Phys. Rev. Lett. 82, 2983–2986 (1999)

    Google Scholar 

  82. M. Itoh, L.O. Chua, Star cellular neural networks for associative and dynamic memories. Int. J. Bifurcation Chaos 14, 1725–1772 (2004)

    Google Scholar 

  83. J. Guckenheimer, Isochrons and phaseless sets. J. Math. Biol. 1, 259–273 (1975)

    Google Scholar 

  84. M. Bonnin, F. Corinto, M. Gilli, Phase space decomposition for phase noise and synchronization analysis of planar nonlinear oscillators. IEEE Trans. Circuits Syst. II: Express Briefs 59, 638–642 (2012)

    Google Scholar 

  85. M. Bonnin, F. Corinto, Phase noise and noise induced frequency shift in stochastic nonlinear oscillators. IEEE Trans. Circuits Syst. I: Regular Papers 60, 2104–2115 (2013)

    Google Scholar 

  86. E. Brown, J. Moehlis, P. Holmes, On the phase reduction and response dynamics of neural oscillator populations. Neural Comput. 16, 673–715 (2004)

    Google Scholar 

  87. B. Ermentrout, Type I membranes, phase resetting curves, and synchrony. Neural Comput. 8, 979–1001 (1996)

    Google Scholar 

  88. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin Heidelberg, 2011)

    Google Scholar 

  89. H. Nakao, Phase reduction approach to synchronisation of nonlinear oscillators. Contemporary Phys. 57, 188–214 (2015)

    Google Scholar 

  90. J.-N. Teramae, H. Nakao, G.B. Ermentrout, Stochastic phase reduction for a general class of noisy limit cycle oscillators. Phys. Rev. Lett. 102 (2009)

    Google Scholar 

  91. K.C. Wedgwood, K.K. Lin, R. Thul, S. Coombes, Phase-amplitude descriptions of neural oscillator models. J. Math. Neurosci. 3(1), 2 (2013)

    Google Scholar 

  92. D. Wilson, J. Moehlis, Isostable reduction of periodic orbits. Phys. Rev. E 94(5), 052213 (2016)

    Google Scholar 

  93. K. Yoshimura, K. Arai, Phase reduction of stochastic limit cycle oscillators. Phys. Rev. Lett. 101 (2008)

    Google Scholar 

  94. A. Guillamon, G. Huguet, A computational and geometric approach to phase resetting curves and surfaces. SIAM J. Appl. Dyn. Syst. 8, 1005–1042 (2009)

    Google Scholar 

  95. G. Huguet, R. de la Llave, Computation of limit cycles and their isochrons: Fast algorithms and their convergence. SIAM J. Appl. Dyn. Syst. 12, 1763–1802 (2013)

    Article  MathSciNet  Google Scholar 

  96. E. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (MIT Press, Cambridge, Mass, 2007)

    Google Scholar 

  97. A. Mauroy and I. Mezić, On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics. Chaos: Interdiscip. J. Nonlinear Sci. 22, 033112 (2012)

    Google Scholar 

  98. A. Mauroy, I. Mezić, J. Moehlis, Isostables, isochrons, and Koopman spectrum for the action–angle representation of stable fixed point dynamics. Physica D: Nonlinear Phenomena 261, 19–30 (2013)

    Article  MathSciNet  Google Scholar 

  99. D. Wilson, B. Ermentrout, Phase models beyond weak coupling. Phys. Rev. Lett. 123(16), 164101 (2019)

    Google Scholar 

  100. D. Wilson, B. Ermentrout, Augmented phase reduction of (not so) weakly perturbed coupled oscillators. SIAM Rev. 61(2), 277–315 (2019)

    Article  MathSciNet  Google Scholar 

  101. D. Aronson, G. Ermentrout, N. Kopell, Amplitude response of coupled oscillators. Physica D: Nonlinear Phenomena 41, 403–449 (1990)

    Article  MathSciNet  Google Scholar 

  102. M. Bonnin, F. Corinto, Influence of noise on the phase and amplitude of second-order oscillators. IEEE Trans. Circuits Syst. II: Express Briefs 61(3), 158–162 (2014)

    Article  Google Scholar 

  103. M. Bonnin, F. Corinto, V. Lanza, A mathematical framework for amplitude and phase noise analysis of coupled oscillators. Euro. Phys. J. Special Top. 225, 171–186 (2016)

    Article  Google Scholar 

  104. M. Bonnin, Amplitude and phase dynamics of noisy oscillators. Int. J. Circuit Theory Appl. 45, 636–659 (2016)

    Google Scholar 

  105. M. Bonnin, Phase oscillator model for noisy oscillators. Euro. Phys. J. Special Top. 226, 3227–3237 (2017)

    Article  Google Scholar 

  106. M. Bonnin, F.L. Traversa, F. Bonani, Colored noise in oscillators. phase-amplitude analysis and a method to avoid the Itô-Stratonovich dilemma. IEEE Trans. Circuits Syst. I: Regular Papers 66, 3917–3927 (2019)

    Article  MathSciNet  Google Scholar 

  107. A. Demir, A. Mehrotra, J. Roychowdhury, Noise in oscillators: A review of state space decomposition approaches. IEEE Trans. Circuits Syst. I: Fund. Theory Appl. 47, 655–674 (2000)

    Article  Google Scholar 

  108. F.X. Kaertner, Analysis of white and f\(^{-\alpha }\) noise in oscillators. Int. J. Circuit Theory Appl. 18, 485–519 (1990)

    Google Scholar 

  109. F.L. Traversa, M. Bonnin, F. Corinto, F. Bonani, Noise in oscillators: A review of state space decomposition approaches. J. Comput. Electroni. 14, 51–61 (2014)

    Article  Google Scholar 

  110. D. Wilson, Phase-amplitude reduction far beyond the weakly perturbed paradigm. Phys. Rev. E 101(2), 022220 (2020)

    Google Scholar 

  111. D. Wilson, A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems. Chaos: Interdiscip. J. Nonlinear Sci. 30(1), 013121 (2020)

    Google Scholar 

  112. T. Djurhuus, V. Krozer, J. Vidkjær, T.K. Johansen, Oscillator phase noise: A geometrical approach. IEEE Trans. Circuits Syst. I: Regular Papers 56(7), 1373–1382 (2008)

    Article  MathSciNet  Google Scholar 

  113. T. Djurhuus, V. Krozer, A study of amplitude-to-phase noise conversion in planar oscillators. Int. J. Circuit Theory Appl. (2020)

    Google Scholar 

  114. F.L. Traversa, F. Bonani, Frequency-domain evaluation of the adjoint Floquet eigenvectors for oscillator noise characterisation. IET Circuits, Dev. Syst. 5(1), 46 (2011)

    Article  Google Scholar 

  115. F.L. Traversa, F. Bonani, Improved harmonic balance implementation of Floquet analysis for nonlinear circuit simulation. AEU - Int. J. Electron. Commun. 66, 357–363 (2012)

    Article  Google Scholar 

  116. F.L. Traversa, F. Bonani, Selective determination of Floquet quantities for the efficient assessment of limit cycle stability and oscillator noise. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 32, 313–317 (2013)

    Article  Google Scholar 

  117. W. Wernick, Complete sets of logical functions. Trans. Am. Math. Soc. 51(1), 117–132 (1942)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electronics and Telecommunication, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    Michele Bonnin & Fabrizio Bonani

  2. MemComputing Inc, 9909 Huennekens Street, Suite 110, 92121, San Diego, CA, USA

    Fabio Lorenzo Traversa

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  1. Michele Bonnin
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  2. Fabio Lorenzo Traversa
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  3. Fabrizio Bonani
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Correspondence to Michele Bonnin .

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Editors and Affiliations

  1. Department of Informatics, University of Piraeus, Piraeus, Greece

    Maria Virvou

  2. Department of Informatics, University of Piraeus, Piraeus, Greece

    George A. Tsihrintzis

  3. Director of Applied Intelligent Systems Laboratory, Department of Nuclear Engineering, Purdue University, West Lafayette, IN, USA

    Lefteri H. Tsoukalas

  4. KES International, Shoreham-by-Sea, UK

    Lakhmi C. Jain

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Bonnin, M., Traversa, F.L., Bonani, F. (2022). Coupled Oscillator Networks for von Neumann and Non-von Neumann Computing. In: Virvou, M., Tsihrintzis, G.A., Tsoukalas, L.H., Jain, L.C. (eds) Advances in Artificial Intelligence-based Technologies. Learning and Analytics in Intelligent Systems, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-80571-5_11

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