The promise of analog computation

References

• Adamatzky, A., B. De Lacy Costello, and T. Asai. 2005. Reaction-Diffusion Computers. Amsterdam: Elsevier.
   Google Scholar
• Ambs, P. 2010. “Optical Computing: A 60-year Adventure.” Advances in Optical Technologies. Article ID 372652. doi:10.1155/2010/372652.
   Google Scholar
• Basu, A., S. Brink, C. Schlottmann, S. Ramakrishnan, C. Petre, S. Koziol, F. Baskaya, C. M. Twigg, andP. Hasler. 2010. “A Floating Gate Based Field Programmable Analog Array.” IEEE Journal of Solid State Circuits 45: 1781–1794.
   Web of Science ®Google Scholar
• Benzi, R., G. Parisi, A. Sutera, and A. Vulpiani. 1982. “Stochastic Resonance in Climatic Change.” Tellus 34: 10–16.
   Google Scholar
• Blum, L., F. Cucker, M. Shub, and S. Smale. 1998. Complexity and Real Computation. Berlin: Springer-Verlag.
   Google Scholar
• Bournez, O., M. Campagnolo, D. Graça, and E. Hainry. 2006. The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation. In Theory and Applications of Models of Computation (TAMC 2006). Vol. 3959, Lectures Notes in Computer Science. 631–643. Berlin: Springer-Verlag.
   Google Scholar
• Bournez, O., and M. Cosnard. 1996. “On the Computational Power of Dynamical Systems and Hybrid Systems.” Theoretical Computer Science 168 (2): 417–59.
   Web of Science ®Google Scholar
• Branicky, M. 1994. “Analog Computation with Continuous ODEs.” In Proceedings IEEE Workshop on Physics and Computation, 265–74. Dallas, TX.
   Google Scholar
• Das, A., and B. K. Chakrabarti. 2008. “Colloquium: Quantum Annealing and Analog Quantum Computation.” Reviews of Modern Physics 80: 1061–1081.
   Web of Science ®Google Scholar
• Davis, M. 2006. “Why There is No Such Discipline as Hypercomputation.” Applied Mathematics and Computation 178: 4–7.
   Web of Science ®Google Scholar
• Dittrich, P., and P. S. d. Fenizio. 2007. “Chemical Organization Theory.” Bulletin of Mathematical Biology 69 (4): 1199–1231.
   PubMed Web of Science ®Google Scholar
• Frank, M. P. 2005. “Introduction to Reversible Computing: Motivation, Progress, and Challenges.” In Proceedings of the 2nd Conference on Computing Frontiers, 385–390. New York: ACM Press.
   Google Scholar
• Franklin, S., and M. Garzon. 1990. “Neural Computability.” In Progress in Neural Networks. Vol. 1, edited by O. M. Omidvar, 127–145. Norwood, NJ: Ablex.
   Google Scholar
• Garzon, M., and S. Franklin. 1990. “Computation on Graphs: From Neural Networks to Cellular Automata.” In Progress in Neural Networks, Vol. 2, edited by O. M. Omidvar, 229–251. Norwood, NJ: Ablex.
   Google Scholar
• Haykin, S. 1999. Neural Networks: A Comprehenive Foundation. 2nd ed. Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Howe, R. M. 1961. Design Fundamentals of Analog Computer Components. Princeton, NJ: Van Nostrand.
   Google Scholar
• Kirchhoff, G. 1845. “Ueber den durchgang eines elektrischen stromes durch eine ebene, insbesondere durch eine kreisförmige [On the Passage of an Electrical Current Through a Plane, in Particular, Through a Circular Plane].” Annalen der Physik und Chemie 140/64 (4):497–514.
   Google Scholar
• Kirkpatrick, S., C. D. Gellat, and M. P. Vecchi. 1983. “Optimization by Simulated Annealing.” Science 220: 671–680.
   PubMed Web of Science ®Google Scholar
• Knudsen, E., S. du Lac, and S. Esterly. 1987. “Computational Maps in the Brain.” Annual Review of Neuroscience 10: 41–65.
   PubMed Web of Science ®Google Scholar
• Lipshitz, L., and L. A. Rubel. 1987. “A Differentially Algebraic Replacment Theorem.” Proceedings of the American Mathematical Society 99 (2): 367–72.
   Web of Science ®Google Scholar
• Lloyd, S., and S. L. Braunstein. 1999. “Quantum Computation Over Continuous Variables.” Physical Review Letters 82: 1784–1787.
   Web of Science ®Google Scholar
• Maass, W., and E. Sontag. 1999. “Analog Neural Nets with Gaussian or Other Common Noise Distributions Cannot Recognize Arbitrary Regular Languages.” Neural Computation 11: 771–782.
   PubMed Web of Science ®Google Scholar
• MacLennan, B. J. 1987. “Technology-independent Design of Neurocomputers: The Universal Field Computer.” In Proceedings of the IEEE First International Conference on Neural Networks, Vol. 3, edited by M.Caudill and C. Butler, 39–49. New York: IEEE Press.
   Google Scholar
• MacLennan, B. J. 1994. “Continuous Computation and the Emergence of the Discrete.” In Origins: Brain & Self-Organization, edited by K.H. Pribram, 121–151. Hillsdale, NJ: Lawrence Erlbaum. web.eecs.utk.edu/mclennan,cogprints.soton.ac.uk/abs/comp/199906001.
   Google Scholar
• MacLennan, B. J. 1997. “Field Computation in Motor Control.” In Self-Organization, Computational Maps and Motor Control, edited by P.G. Morasso and V. Sanguineti, 37–73. Amsterdam: Elsevier. web.eecs.utk.edu/mclennan.
   Google Scholar
• MacLennan, B. J. 2003. “Transcending Turing Computability.” Minds and Machines 13: 3–22.
   Web of Science ®Google Scholar
• MacLennan, B. J. 2004. “Natural Computation and Non-turing Models of Computation.” Theoretical Computer Science 317: 115–145.
   Web of Science ®Google Scholar
• MacLennan, B. J. 2009a. “Analog Computation.” Chap. 1 In Encyclopedia of Complexity and System Science, Entry 19, edited by R. Meyers et al., 161–194, Springer. Reprinted in 2012. Complexity: Theory, Techniques, and Applications, edited by R. A. Meyers, 161–184. Springer.
   Google Scholar
• MacLennan, B. J. 2009b. “Field Computation in Natural and Artificial Intelligence.” Chap. 6 In Encyclopedia of Complexity and System Science, Entry 199, edited by R. Meyers, 3334–3360. Springer.
   Google Scholar
• MacLennan, B. J. 2009c. “Super-Turing or non-Turing? Extending the concept of computation.” International Journal of Unconventional Computing 5 (3–4): 369–387.
   Web of Science ®Google Scholar
• MacLennan, B. J. 2010. “The U-machine: A Model of Generalized Computation.” International Journal of Unconventional Computing 6 (3–4): 265–283.
   Web of Science ®Google Scholar
• Mead, C. 1989. Analog VLSI and Neural Systems. Reading, MA: Addison-Wesley.
   Google Scholar
• Mills, J. W. 1995. Kirkhoff Machines. Technical Report TR439. Dept. of Computer Science, Indiana University.
   Google Scholar
• Mills, J. W. 1996. “The Continuous Retina: Image Processing with a Single-sensor Artificial Neural Field Network.” In Proceedings IEEE Conference on Neural Networks. New York: IEEE Press.
   Google Scholar
• Mills, J. W. B., B. Himebaugh, B. Kopecky, M. Parker, C. Shue, and C. Weilemann. 2006. “‘Empty space’ Computes: The Evolution of an Unconventional Supercomputer.” In Proceedings of the 3rd Conference on Computing Frontiers, 115–126, New York: ACM Press.
   Google Scholar
• Moore, C. 1996. “Recursion Theory on the Reals and Continuous-time Computation.” Theoretical Computer Science 162: 23–44.
   Web of Science ®Google Scholar
• Moore, G. E. 1965. “Cramming More Components onto Integrated Circuits.” Electronics 38 (8): 114–117.
   Web of Science ®Google Scholar
• Omohundro, S. 1984. “Modeling Cellular Automata with Partial Differential Equations.” Physica D 10: 128–34.
   Web of Science ®Google Scholar
• Orponen, P. 1997. “A Survey of Continous-time Computation Theory.” In Advances in Algorithms, Languages, and Complexity, edited by D.-Z. Du, and K.-I. Ko,, 209–224. Dordrecht: Kluwer.
   Google Scholar
• Orponen, P., and M. Matamala. 1996. “Universal Computation by Finite Two-dimensional Coupled Map Lattices.” In Proceedings, Physics and Computation, 243–247. Cambridge, MA: New England Complex Systems Institute.
   Google Scholar
• Pour-El, M. 1974. “Abstract Computability and its Relation to the General Purpose Analog Computer (Some Connections Between Logic, Differential Equations and Analog Computers).” Transactions of the American Mathematical Society 199: 1–29.
   Web of Science ®Google Scholar
• Pour-El, M. B., and I. Richards. 1979. “A Computable Ordinary Differential Equation which Possesses No Computable Solution.” Annals of Mathematical Logic 17: 61–90.
   Google Scholar
• Pour-El, M. B., and I. Richards. 1982. “Noncomputability in Models of Physical Phenomena.” International Journal of Theoretical Physics 21: 553–555.
   Web of Science ®Google Scholar
• Rubel, L. A. 1985. “The Brain as an Analog Computer.” Journal of Theoretical Neurobiology 4: 73–81.
   Google Scholar
• Rubel, L. A. 1988. “Some Mathematical Limitations of the General-purpose Analog Computer.” Advances in Applied Mathematics 9: 22–34.
   Web of Science ®Google Scholar
• Rubel, L. A. 1993. “The Extended Analog Computer.” Advances in Applied Mathematics 14: 39–50.
   Web of Science ®Google Scholar
• Rumelhart, D. E., McClelland, J. L., and the PDP Research Group. 1986. Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Cambridge, MA: MIT Press.
   Google Scholar
• Sanger, T. 1996. “Probability Density Estimation for the Interpretation of Neural Population Codes.” Journal of Neurophysiology 76: 2790–3.
   PubMed Web of Science ®Google Scholar
• Santoro, G. E., and E. Tosatti. 2006. “Optimization Using Quantum Mechanics: Quantum Annealing Through Adiabatic Evolution.” Journal of Physics A: Mathematical and General 39 (36): R393.
   Google Scholar
• Shannon, C. E. 1941. “Mathematical Theory of the Differential Analyzer.” Journal of Mathematics and Physics of the Massachusetts Institute Technology 20: 337–354.
   Google Scholar
• Shannon, C. E. 1993. “Mathematical Theory of the Differential Analyzer.” In Claude Elwood Shannon: Collected Papers, edited by N. J. A. Sloane and A. D. Wyner, 496–513. New York: IEEE Press.
   Google Scholar
• Siegelmann, H. T. 1999. Neural Networks and Analog Computation: Beyond the Turing Limit. Boston: Birkhäuser.
   Google Scholar
• Siegelmann, H. T., and E. D. Sontag. 1994. “Analog Computation Via Neural Networks.” Theoretical Computer Science 131: 331–360.
   Web of Science ®Google Scholar
• Small, J. S. 2001. The Analogue Alternative. London: Routledge.
   Google Scholar
• Stannett, M. 1990. “X-machines and the Halting Problem: Building a Super-turing Machine.” Formal Aspects of Computing 2: 331–341.
   Google Scholar
• Truitt, T. D., and A. E. Rogers. 1960. Basics of Analog Computers. New York: John F. Rider.
   Google Scholar
• Turing, A. 1952. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society B 237: 37–72.
   Web of Science ®Google Scholar
• van Gelder, T. 1997. “Dynamics and Cognition.” Chap. 16 In Mind Design II: Philosophy, Psychology and Artificial Intelligence (revised & enlarged ed.), edited by J. Haugeland, 421–450. Cambridge MA: MIT Press.
   Google Scholar
• Wolpert, D. H., and B. J. MacLennan. 1993. A Computationally Universal Field Computer That is Purely Linear. Technical Report CS-93-206:Knoxville: Dept. of Computer Science, University of Tennessee. web.eecs.utk.edu/mclennan.
   Google Scholar