=== Topic 1 === Complexity Digest 2000.1 14-Jan-2000 9. Chaotic Maps And Languages, Nonlinearity

Abstract: It is well established that a formal language generated from a unimodal map is regular if and only if the map's kneading sequence is either periodic or eventually periodic. A previously proposed conjecture said that if a language generated from a unimodal map is context-free, then it must be regular, i.e. there exists no proper context-free language which can be generated from a unimodal map. This paper is a step forward in answering this conjecture showing that under two situations the conjecture is true. The main results of this paper are: (1) if the kneading map of a unimodal map is unbounded, then the map's language is not context-free, (2) all nonregular languages generated from the Fibonacci substitutions are context-sensitive, but not context-free. These results strongly suggest that the conjecture may be indeed true.

=== Topic 2 === Complexity Digest 2000.2 21-Jan-2000 11. Seven Pillars of Wisdom for the Complexity Market.

Abstract: There are complex dynamics in modern markets, and their futures can only be influenced but not predicted through analysis. The conclusion is drawn from the seven fundamental patterns in the dynamics: (1) Inability of Analysis - ecosystems of products are emerging in the market, (2) Ineffectiveness of Planning - ecosystem of products are self-organizing, (3) Sensitivity to Fluctuation - small fluctuations in the market cause great changes in the ecosystems of products, (4) Sensitivity to Information - ecosystems of products are exceedingly sensitive to information in the market, (5) Inability of Division - products in ecosystem are under co-evolution process, (6) Insignificance of Law - the laws and rules the govern ecosystem of products are changing, (7) Inability of Prediction - the future activities of ecosystems of products cannot be predicted.

=== Topic 3 === Complexity Digest 2000.21 June-3-2000 1. A Novel Chaotic Secure Communication System

Abstract: A chaotic impulse radio system is an ultrawide-band communication system that uses a train of very narrow baseband impulses as a carrier. In the transmitter of a chaotic impulse radio system, a message signal is modulated by two kinds of pulse carriers. Firstly, a frequency modulation is used to modulate the message signal into a subcarrier that functions as the clock pulses of a chaotic circuit. Driven by the modulated clock pulses, the chaotic circuit outputs a chaotic impulse positioning sequence which generates the positions of the carrier impulses. The specially designed chaotic circuit in the transmitter guarantees that the time intervals between the carrier impulses are chaotic. Thus the energy of the impulse carrier is distributed evenly over the entire bandwidth. In the receiver of a chaotic impulse radio system the message signal is demodulated in two stages. At the first stage, the time interval between two consecutive impulses is recovered. At the second stage, a simple algorithm based on the knowledge of the chaotic circuit in the transmitter is used to calculate partially the locations of the inner clock pulses which in turn are used to demodulate the message signal. No synchronization at any level is needed in this chaotic impulse radio system. The security of this chaotic impulse radio system depends on the hardware parameters of the chaotic circuit and the inner clock pulse train. Simulation results are presented to illustrate the design procedure of an example of this chaotic impulse radio system.