6 research outputs found
Hysteretic Optimization
We propose a new optimization method based on a demagnetization procedure
well known in magnetism. We show how this procedure can be applied as a general
tool to search for optimal solutions in any system where the configuration
space is endowed with a suitable `distance'. We test the new algorithm on
frustrated magnetic models and the traveling salesman problem. We find that the
new method successfully competes with similar basic algorithms such as
simulated annealing.Comment: 5 pages, 5 figure
Multifractality in Time Series
We apply the concepts of multifractal physics to financial time series in
order to characterize the onset of crash for the Standard & Poor's 500 stock
index x(t). It is found that within the framework of multifractality, the
"analogous" specific heat of the S&P500 discrete price index displays a
shoulder to the right of the main peak for low values of time lags. On
decreasing T, the presence of the shoulder is a consequence of the peaked,
temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80),
we have found that C_{q} displays typical features of a classical phase
transition at a critical point. An example of such dynamic phase transition in
a simple economic model system, based on a mapping with multifractality
phenomena in random multiplicative processes, is also presented by applying
former results obtained with a continuous probability theory for describing
scaling measures.Comment: 22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000