304 research outputs found
Entropy computing via integration over fractal measures
We discuss the properties of invariant measures corresponding to iterated
function systems (IFSs) with place-dependent probabilities and compute their
Renyi entropies, generalized dimensions, and multifractal spectra. It is shown
that with certain dynamical systems one can associate the corresponding IFSs in
such a way that their generalized entropies are equal. This provides a new
method of computing entropy for some classical and quantum dynamical systems.
Numerical techniques are based on integration over the fractal measures.Comment: 14 pages in Latex, Revtex + 4 figures in .ps attached (revised
version, new title, several changes, to appear in CHAOS
Linguistic complexity: English vs. Polish, text vs. corpus
We analyze the rank-frequency distributions of words in selected English and
Polish texts. We show that for the lemmatized (basic) word forms the
scale-invariant regime breaks after about two decades, while it might be
consistent for the whole range of ranks for the inflected word forms. We also
find that for a corpus consisting of texts written by different authors the
basic scale-invariant regime is broken more strongly than in the case of
comparable corpus consisting of texts written by the same author. Similarly,
for a corpus consisting of texts translated into Polish from other languages
the scale-invariant regime is broken more strongly than for a comparable corpus
of native Polish texts. Moreover, we find that if the words are tagged with
their proper part of speech, only verbs show rank-frequency distribution that
is almost scale-invariant
Sign and amplitude representation of the forex networks
We decompose the exchange rates returns of 41 currencies (incl. gold) into
their sign and amplitude components. Then we group together all exchange rates
with a common base currency, construct Minimal Spanning Trees for each group
independently, and analyze properties of these trees. We show that both the
sign and the amplitude time series have similar correlation properties as far
as the core network structure is concerned. There exist however interesting
peripheral differences that may open a new perspective to view the Forex
dynamics.Comment: Article based on talk by S. Gworek given at FENS'08 Conference,
Rzeszow, Polan
Scale free effects in world currency exchange network
A large collection of daily time series for 60 world currencies' exchange
rates is considered. The correlation matrices are calculated and the
corresponding Minimal Spanning Tree (MST) graphs are constructed for each of
those currencies used as reference for the remaining ones. It is shown that
multiplicity of the MST graphs' nodes to a good approximation develops a power
like, scale free distribution with the scaling exponent similar as for several
other complex systems studied so far. Furthermore, quantitative arguments in
favor of the hierarchical organization of the world currency exchange network
are provided by relating the structure of the above MST graphs and their
scaling exponents to those that are derived from an exactly solvable
hierarchical network model. A special status of the USD during the period
considered can be attributed to some departures of the MST features, when this
currency (or some other tied to it) is used as reference, from characteristics
typical to such a hierarchical clustering of nodes towards those that
correspond to the random graphs. Even though in general the basic structure of
the MST is robust with respect to changing the reference currency some trace of
a systematic transition from somewhat dispersed -- like the USD case -- towards
more compact MST topology can be observed when correlations increase.Comment: Eur. Phys. J. B (2008) in pres
World currency exchange rate cross-correlations
World currency network constitutes one of the most complex structures that is
associated with the contemporary civilization. On a way towards quantifying its
characteristics we study the cross correlations in changes of the daily foreign
exchange rates within the basket of 60 currencies in the period December 1998
-- May 2005. Such a dynamics turns out to predominantly involve one outstanding
eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends
however crucially on which currency is used as a base currency for the
remaining ones. Most prominent it looks from the perspective of a peripheral
currency. This largest eigenvalue is seen to systematically decrease and thus
the structure of correlations becomes more heterogeneous, when more significant
currencies are used as reference. An extreme case in this later respect is the
USD in the period considered. Besides providing further insight into subtle
nature of complexity, these observations point to a formal procedure that in
general can be used for practical purposes of measuring the relative currencies
significance on various time horizons.Comment: 4 pages, 3 figures, LaTe
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