List of publications

Current Projects:

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Computing using soliton collisions

In most present-day conceptions of a "computer," information travels between logical elements fixed in space. This is true for abstract models like Turing machines, as well as real silicon-chip-based electronic computers. This work views computation in an entirely different way: information is carried through space by particles, computation occurs when these particles collide. The most recent work focuses on the storage of information in states of optical solitons, the transformation of these states when solitons collide, and the computational power of solitonic systems. The long-term goal is the construction of a new kind of computer using soliton collisions, as well as the basic understanding of information processing in nonlinear waves. The most recent work is reflected in the following papers.

"Particle Dreams" #5, Matt Howarth, Fantagraphics Books, 1987.

" Making beam splitters with dark soliton collisions", K. Steiglitz, Phys. Rev. A, 82, 043831, October 2010.

" Soliton-guided phase shifter and beam splitter", K. Steiglitz, Phys. Rev. A, 81, 033835, March 2010.

" Photon trapping and transfer with solitons", K. Steiglitz and D. Rand, Phys. Rev. A, 79, 021802(R), Feb. 2009.

" Observation of temporal vector soliton propagation and collision in birefringent fiber", D. Rand, I. Glesk, C.-S. Brès, D.A. Nolan, X. Chen, J. Koh, J.W. Fleischer, K. Steiglitz, P.R. Prucnal, Phys. Rev. Lett., 98, 053902, Feb. 1, 2007.

" Quantum phase noise reduction in soliton collisions and application to nondemolition measurements", D. Rand, K. Steiglitz, P. R. Prucnal, Phys. Rev. A 72, 041805(R) (Rapid Communications) (pp. 1-4), October 28, 2005.

"Quantum Phase Noise Reduction in Soliton Collisions", D. Rand, K. Steiglitz, P. R. Prucnal, 18th Annual Meeting of the IEEE Lasers & Electro-Optics Society, Sydney, Australia, October 23-27, 2005.

"Quantum theory of Manakov solitons", D. Rand, K. Steiglitz, P. R. Prucnal, Phys. Rev. A 71, 053805 (pp. 1-10), May 11, 2005.

"Multicomponent gap solitons in superposed grating structures", D. Rand, K. Steiglitz, P. R. Prucnal, Optics Letters. vol. 30, issue 13, July 2005, pp. 1695-1697.

"Signal standardization in collision-based soliton computing", D. Rand, K. Steiglitz, P. R. Prucnal, Int. J. of Unconventional Computing, vol. 1, pp. 31-45, 2005.

"Vacuum-Induced Fluctuations of Manakov Solitons based on a Linearization Approximation", D. Rand, K. Steiglitz, P. Prucnal, 17th Annual Lasers and Electro Optics Society Meeting, Rio Mar, Puerto Rico, Nov. 7-11, 2004.

"Noise-immune universal computation using Manakov soliton collision cycles," D. Rand, K. Steiglitz, P. Prucnal, Nonlinear Guided Waves and Their Applications Topical Meeting, Toronto, Canada, April 4-7, 2004.

"Collisions of two solitons in an arbitrary number of coupled nonlinear Schrödinger equations," M. Soljacic, K. Steiglitz, S. Sears, M. Segev, M. Jakubowski, R. Squier, Phys. Rev. Lett., 90, 25, 254102 (June 26, 2003). Click here for (pdf)

"Computing with solitons: A review and prospectus," M. H. Jakubowski, K. Steiglitz, R. K. Squier, Multiple-Valued Logic, vol. 6, nos. 5-6, pp. 439-462, 2001. Also, Chapter 10 in Collision-Based Computing, A. Adamatzky (ed.), Springer, 2002. Click here for (postscript), (pdf)

"Information transfer via cascaded collisions of vector solitons," C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, K. Steiglitz, Optics Lett., vol. 26, no. 19, pp. 1498-1500, Oct. 1, 2001. Click here for (pdf)

"Multistable collision cycles of Manakov spatial solitons" K. Steiglitz, Phys. Rev. E, vol. 63, April 2001, 46607. Click here for (postscript), (pdf), (tex.tar.gz)

"Time-gated Manakov spatial solitons are computationally universal," K. Steiglitz, Phys. Rev. E, 63, 16608 (2001). Click here for (postscript), (pdf), (tex.tar.gz)

"Bouncing of Vector Solitons," C. Anastassiou, K. Steiglitz, D. Lewis, M. Segev, J.A. Giordmaine, Conference on Quantum Electronics and Laser Science, Trends in Optics and Photonics 40, Technical Digest, (OSA, Wash. D.C., 2000), p. 46.

"Energy Switching Interactions between Colliding Vector Solitons," C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, J. Martin, Phys. Rev. Lett., vol. 83, no. 12, pp. 2332-2335, Sept. 20, 1999. Click here for (ps) (pdf)

"State Transformations of Colliding Optical Solitons and Possible Application to Computation in Bulk Media," M. H. Jakubowski, K. Steiglitz, R. K. Squier, Phys. Rev. E, vol. 58, pp. 6752-8, Nov. 1998. click here for abstract.

"Information Transfer between Solitary Waves in the Saturable Schrödinger Equation," M. H. Jakubowski, K. Steiglitz, R. K. Squier, Phys. Rev. E, vol. 56, pp. 7267-7273, Dec. 1997. click here for abstract.

Solitons and Particles in Cellular Automata: a Bibliography

Embedded Computation using Solitons and Particles: a Bibliography

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Auction Theory and Evolutionary Biology

"Frugality in path auctions," E. Elkind, A. Sahai, K. Steiglitz, ACM-SIAM Symposium on Discrete Algorithms (SODA) 2004, New Orleans, January 11-13, 2004.

A paper with Prof. John Morgan, Haas School of Business, University of California at Berkeley, on the formulation of the replicator equation, and how spiteful behavior may arise in evolutionary biology. Comments most welcome.

" Pairwise Competition and the Replicator Equation," J. Morgan and K. Steiglitz, Bulletin of Mathematical Biology, 65, 2003, pp. 1163-1172.

A paper on spiteful behavior in auctions, with John Morgan and George Reis, '01. Comments most welcome.

" The Spite Motive and Equilibrium Behavior in Auctions," J. Morgan, K. Steiglitz, and G. Reis, Contributions to Economic Analysis & Policy, Vol. 2, No. 1, Article 5, 2003.

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Agent-based simulation

Market-based models have important applications in distributed resource allocation and are becoming increasingly important as agent technology emerges in the internet. In situations with many complex heterogeneous agents, simulation is the only tool for gaining insight into the properties of systems short of actual implementation. This work focuses on the simulation of computational multiagent markets, sometimes called robot markets.

The following papers show that trend-based traders can de-stabilize robot markets, causing both inflationary and deflationary price bubbles.

" An Agent-Based Model of a Minimal Economy," Chris K. Chan and Ken Steiglitz, (pdf, 465K), Working Paper, Department of Computer Science, Princeton University, Princeton, NJ, May 5, 2008. This and the next paper are Chris's reports of his independent work, 2007-8. This work is continuing with Professor Leigh Tesfatsion (Iowa State University) and Mike Honig (Northwestern University).

" An Agent-Based Model of a Minimal Economy," Chris K. Chan and Ken Steiglitz, (pdf, 911K),Working Paper, Department of Computer Science, Princeton University, Princeton, NJ, January 7, 2008.

" Effects of Price Signal Choices on Market Stability," H. Mizuta, K. Steiglitz, and E. Lirov, Journal of Economic Behavior & Organization, vol. 52, issue 2, October 2003, pp. 235-251.

"Simulating the Madness of Crowds: Price Bubbles in an Auction-Mediated Robot Market," K. Steiglitz and D. Shapiro, Computational Economics, vol. 12, pp. 35-59, 1998. Click here for (abstract), (postscript), (pdf).

"Microsimulation of Markets and Endogenous Price Bubbles," K. Steiglitz and L. I. O'Callaghan, 3rd Int. Conf. on Computing in Economics and Finance, June 30-July 2, 1997, at Stanford. click here for extended abstract (ps) (pdf)

These papers are based on the following paper, which shows that value-based traders can stabilize such markets.

"A Computational Market Model Based on Individual Action," K. Steiglitz, M. L. Honig, and L. M. Cohen, Chapter 1 in Market-Based Control: A Paradigm for Distributed Resource Allocation, Scott Clearwater (ed.), World Scientific, Hong Kong, 1996. Click here for (postscript) (pdf).

For an implementation of this artificial market in Java by Sergei Simdyankin and Payam Madjidi at the Royal Institute of Technology, Stockholm, Sweden, see their Artificial Economy Project.

The properties of online auctions reflect human behavior. The following is a start at modeling such behavior and its effects in auctions with deadlines.

"Agent-Based Simulation of Dynamic Online Auctions," H. Mizuta and K. Steiglitz, Winter Simulation Conference, Orlando, FL, Dec. 10-13, 2000. Click here for (pdf)

Robot Markets: a Bibliography

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