2,390 research outputs found
On signal-noise decomposition of timeseries using the continuous wavelet transform: Application to sunspot index
We show that the continuous wavelet transform can provide a unique
decomposition of a timeseries in to 'signal-like' and 'noise-like' components:
From the overall wavelet spectrum two mutually independent skeleton spectra
can be extracted, allowing the separate detection and monitoring in even
non-stationary timeseries of the evolution of (a) both stable but also
transient, evolving periodicities, such as the output of low dimensional
dynamical systems and (b) scale-invariant structures, such as discontinuities,
self-similar structures or noise. An indicative application to the
monthly-averaged sunspot index reveals, apart from the well-known 11-year
periodicity, 3 of its harmonics, the 2-year periodicity (quasi-biennial
oscillation, QBO) and several more (some of which detected previously in
various solar, earth-solar connection and climate indices), here proposed being
just harmonics of the QBO, in all supporting the double-cycle solar magnetic
dynamo model (Benevolenskaya, 1998, 2000). The scale maximal spectrum reveals
the presence of 1/f fluctuations with timescales up to 1 year in the sunspot
number, indicating that the solar magnetic configurations involved in the
transient solar activity phenomena with those characteristic timescales are in
a self-organized-critical state (SOC), as previously proposed for the solar
flare occurence (Lu and Hamilton, 1991).Comment: 22 pages, 2 figure
Applications of topology in computer algorithms
The aim of this paper is to discuss some applications of general topology in
computer algorithms including modeling and simulation, and also in computer
graphics and image processing. While the progress in these areas heavily
depends on advances in computing hardware, the major intellectual achievements
are the algorithms. The applications of general topology in other branches of
mathematics are not discussed, since they are not applications of mathematics
outside of mathematics.Comment: This paper is based on the invited lecture at International
Conference on Topology and Applications held in August 23--27, 1999, at
Kanagawa University in Yokohama, Japa
The Algorithmic Information Content for randomly perturbed systems
In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai
entropy relative to a partition for randomly perturbed dynamical systems. Our
estimates use the entropy for the unperturbed system and are obtained using the
notion of Algorithmic Information Content. The main result is an extension of
known results to study time series obtained by the observation of real systems.Comment: 17 pages, 1 figur
Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model
We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.fractals, iterated function system, self-similarity, Sierpinski gasket, stochastic growth
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