Modelling linguistic taxonomic dynamics

This paper presents the results of the application of a bit-string model of languages (Schulze and Stauffer 2005) to problems of taxonomic patterns. The questions addressed include the following: (1) Which parameters are minimally ne eded for the development of a taxonomic dynamics leading to the type of distribution of language family sizes currently attested (as measured in the i number of languages per family), which appears to be a power-law? (2) How may such a model be coupled with one of the dynamics of speaker populations leading to the type of language size seen today, which appears to follow a log-normal distribution?Comment: 18 pages including 9 figure

Dynamical systems theory for music dynamics

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the {\pit global} dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra ($\sim f^{-\nu}$) close to {\pit red noise} ($\nu \sim 2$) in the low frequency range. (iii) We define an information entropy which provides a measure of the {\pit local} dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of {\it complexity} in the music, but there is no evidence of an analytical relation between local and global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century.Comment: To appear in CHAOS. Figures and Tables (not included) can be obtained from [email protected]

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture - the Adaptive Culture Heuristic (ACH) - on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size $F$ by a Boolean Binary Perceptron. In this heuristic, $N$ agents, characterized by binary strings of length $F$ which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable $F/N^{1/4}$ so that the number of agents must increase with the fourth power of the problem size, $N \propto F^ 4$, to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with $F^ 6$ which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean Binary Perceptron, given a fixed probability of success

Growth Kinetics in Systems with Local Symmetry

The phase transition kinetics of Ising gauge models are investigated. Despite the absence of a local order parameter, relevant topological excitations that control the ordering kinetics can be identified. Dynamical scaling holds in the approach to equilibrium, and the growth of typical length scale is characteristic of a new universality class with $L(t)\sim \left(t/\ln t\right)^{1/2}$. We suggest that the asymptotic kinetics of the 2D Ising gauge model is dual to that of the 2D annihilating random walks, a process also known as the diffusion-reaction $A+A\to \hbox{inert}$.Comment: 10 pages in Tex, 2 Postscript figures appended, NSF-ITP-93-4

Minority Game of price promotions in fast moving consumer goods markets

A variation of the Minority Game has been applied to study the timing of promotional actions at retailers in the fast moving consumer goods market. The underlying hypotheses for this work are that price promotions are more effective when fewer than average competitors do a promotion, and that a promotion strategy can be based on past sales data. The first assumption has been checked by analysing 1467 promotional actions for three products on the Dutch market (ketchup, mayonnaise and curry sauce) over a 120-week period, both on an aggregated level and on retailer chain level. The second assumption was tested by analysing past sales data with the Minority Game. This revealed that high or low competitor promotional pressure for actual ketchup, mayonnaise, curry sauce and barbecue sauce markets is to some extent predictable up to a forecast of some 10 weeks. Whereas a random guess would be right 50% of the time, a single-agent game can predict the market with a success rate of 56% for a 6 to 9 week forecast. This number is the same for all four mentioned fast moving consumer markets. For a multi-agent game a larger variability in the success rate is obtained, but predictability can be as high as 65%. Contrary to expectation, the actual market does the opposite of what game theory would predict. This points at a systematic oscillation in the market. Even though this result is not fully understood, merely observing that this trend is present in the data could lead to exploitable trading benefits. As a check, random history strings were generated from which the statistical variation in the game prediction was studied. This shows that the odds are 1:1,000,000 that the observed pattern in the market is based on coincidence.Comment: 19 pages, 10 figures, accepted for publication in Physica

Von Neumann Normalisation of a Quantum Random Number Generator

In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies critically on the independence of the source, a notion we rigorously define for our model. In real cases, affected by imperfections in measurement and hardware, one cannot achieve a true un-biasing, but, if the bias "drifts sufficiently slowly", the result can be arbitrarily close to un-biasing. For infinite sequences, normalisation can both increase or decrease the (algorithmic) randomness of the generated sequences. A successful application of von Neumann normalisation---in fact, any un-biasing transformation---does exactly what it promises, un-biasing, one (among infinitely many) symptoms of randomness; it will not produce "true" randomness.Comment: 27 pages, 2 figures. Updated to published versio