A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
A theoretical quantum neural network model is proposed using a nonlinear Schrödinger wave equation. The model proposes that there exists a nonlinear Schrödinger wave equation that mediates the collective response of a neural lattice. The model is used to explain eye movements when tracking moving targets. Using a recurrent quantum neural network(RQNN) while simulating the eye tracking model, two very interesting phenomena are observed. First, as eye sensor data is processed in a classical neural network, a wave packet is triggered in the quantum neural network.This wave packet moves like a particle. Second, when the eye tracks a fixed target, this wave packet moves not in a continuous but rather in a discrete mode. This result reminds one of the saccadic movements of the eye consisting of ‘jumps’ and ‘rests’. However, such a saccadic movement is intertwined with smooth pursuit movements when the eye has to track a dynamic trajectory. In a sense, this is the first theoretical model explaining the experimental observation reported concerning eye movements in a static scene situation. The resulting prediction is found to be very precise and efficient in comparison to classical objective modeling schemes such as the Kalman filter.
- 1. Amari, S., “Field theory of self-organizing neural nets,” IEEE Trans. SMC 13(5), 741–748 (1983).
- 2. Amit, D., Modeling Brain Function (Springer, Berlin/Heidelberg, 1989).
- 3. Atmanspacher, H., “Quantum theory and consciousness: An overview with selected examples,” Discrete Dynamics 8, 51–73 (2004). CrossRef
- 4. Bahill, A. T., M. J. Iandolo, and B. T. Troost, “Smooth pursuit eye movements in response to unpredictable target waveforms,” Vision Research 20, 923–931 (1980). CrossRef
- 5. Bahill, A. T., and L. Stark, “The Trajectories of Saccadic eye movements,” Sci. Am. 240, 84–93 (1979).
- 6. Behera, L., S. Chaudhury, and M. Gopal, “Applications of self-organizing neural networks in robot tracking control,” IEEE Proc. Control Th. Appl. 145, 134–140 (1998).
- 7. Behera, L., M. Gopal, and S. Chaudhury, “On adaptive control of a robot manipulator using inversion of its neural emulator,” IEEE Tran. Neural Net. 7, 1401–1414 (1996). CrossRef
- 8. Behera, L., and B. Sundaram, “Stochastic filtering and speech enhancement using a recurrent quantum neural network,” Proceedings, ICISIP 165–170 (2004).
- 9. Behrman, E. C., V. Chandrashekar, Z. Wang, C. K. Belur, J. Steck, and S. R. Skinner: “A quantum neural network computes entanglement,” Phys. Rev. Lett., submitted, 2002.
- 10. Behrman, E. C., L. R. Nash, J. E. Steck, V. G. Chandrashekar, and S. R. Skinner, “Simulations of quantum neural networks,” Information Sciences 128, 257–269 (2000). CrossRef
- 11. Bialynicki-Birula, I., and J. Mycielski, “Nonlinear wave mechanics,” Ann. Phys. 100, 62–93 (1976). CrossRef
- 12. Boyd, R., Nonlinear Optics (Academic, New York, 1991).
- 13. Cohen, M. A., and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IEEE Tran. SMC 13, 815–826 (1983).
- 14. Davydov, A. S., Biology and Quantum Mechanics (Pergamon, Oxford, 1982).
- 15. Grewal, M. S., and A. P. Andrews, Kalman Filtering : Theory and Practice Using MATLAB (Wiley-Interscience, 2001).
- 16. Gupta, S., and R. Zia, “Quantum neural networks,” J. Comp. Syst. Sci. 63, 355–383 (2001). CrossRef
- 17. Hagan, S., S. R. Hameroff, and J. A. Tuszynski, “Quantum computation in brain microtubules? Dehoherence and biological feasibility,” Phys. Rev. E 65, 061901 (2002). CrossRef
- 18. Jackson, E. A., Perspectives of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1999).
- 19. Mershin, A., D. V. Nanopoulos, and E. Skoulakis: “Quantum brain?,” Proc. Acad. Athens 74, 148–179 (1999).
- 20. Penrose, R., Shadows of the Mind (Oxford University Press, 1994).
- 21. Scott, A. C., F. Y. F. Chu, and D. W. McLaughlin, “The soliton: A new concept in applied science,” Proc. IEEE 61 (1973).
- 22. Sulem, C., P. L. Sulem, and C. Sulem, Nonlinear Schrödinger Equations: Self-Focusing and Wave Collapse (Springer, 1999) (Applied Mathematical Sciences, Vol. 139).
- 23. Tuszynski, J. A., S. R. Hameroff, M. V. Sataric, B. Trpisova, and M. L. A. Nip, “Ferroelectric behavior in microtubule dipole lattices: Implications for information processing, signaling and assembly/disassembly,” J. Theor. Bio. 174, 371–380 (1995). CrossRef
- 24. Vitiello, G., “Dissipation and memory capacity in the quantum brain model,” Int. J. Mod. Phys. B 9, 973–989 (1995). CrossRef
- A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets
Foundations of Physics Letters
Volume 18, Issue 4 , pp 357-370
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- nonlinear Schrödinger wave equation
- quantum dynamics
- saccadic eye movements
- neural network
- quantum computation