Showing papers by "Kenneth Steiglitz published in 1998"

State transformations of colliding optical solitons and possible application to computation in bulk media

Abstract: Using explicit, bright-soliton solutions for the coupled Manakov system recently described by Radhakrishnan, Lakshmanan, and Hietarinta, we show that collisions of these solitons can be completely described by explicit linear fractional transformations of a complex-valued polarization state. We design sequences of solitons operating on other sequences of solitons that effect logic operations, including controlled NOT gates. Both data and logic operators have the self-restoring and reusability features of digital logic circuits. This suggests a method for implementing computation in a bulk nonlinear medium without interconnecting discrete components.

Simulating the Madness of Crowds: Price Bubbles in an Auction-Mediated Robot Market

Abstract: We simulate a multiagent market with production, consumption, and exchange mediated by a sealed-bid double auction. Marked price bubbles and subsequent crashes occur when value-based (fundamentals-driven) and trend-based traders are both present, and the market equilibrium price is ramped up exogenously. Similarly, negative price bubbles and recoveries occur when the equilibrium price is ramped down. Because the simulated market is auction-mediated, we can observe the operations of traders during these events, and study the interactions that produce and resolve bubbles. Some preliminary circuit-breaker experiments are described, in which bubbles are interrupted during their formation.