940 research outputs found
Stochastics theory of log-periodic patterns
We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge
Are Financial Crashes Predictable?
We critically review recent claims that financial crashes can be predicted
using the idea of log-periodic oscillations or by other methods inspired by the
physics of critical phenomena. In particular, the October 1997 `correction'
does not appear to be the accumulation point of a geometric series of local
minima.Comment: LaTeX, 5 pages + 1 postscript figur
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
Sublinear Estimation of Weighted Matchings in Dynamic Data Streams
This paper presents an algorithm for estimating the weight of a maximum
weighted matching by augmenting any estimation routine for the size of an
unweighted matching. The algorithm is implementable in any streaming model
including dynamic graph streams. We also give the first constant estimation for
the maximum matching size in a dynamic graph stream for planar graphs (or any
graph with bounded arboricity) using space which also
extends to weighted matching. Using previous results by Kapralov, Khanna, and
Sudan (2014) we obtain a approximation for general graphs
using space in random order streams, respectively. In
addition, we give a space lower bound of for any
randomized algorithm estimating the size of a maximum matching up to a
factor for adversarial streams
Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
For a family of logistic-like maps, we investigate the rate of convergence to
the critical attractor when an ensemble of initial conditions is uniformly
spread over the entire phase space. We found that the phase space volume
occupied by the ensemble W(t) depicts a power-law decay with log-periodic
oscillations reflecting the multifractal character of the critical attractor.
We explore the parametric dependence of the power-law exponent and the
amplitude of the log-periodic oscillations with the attractor's fractal
dimension governed by the inflexion of the map near its extremal point.
Further, we investigate the temporal evolution of W(t) for the circle map whose
critical attractor is dense. In this case, we found W(t) to exhibit a rich
pattern with a slow logarithmic decay of the lower bounds. These results are
discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig
Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field
It is demonstrated that decimation of the one dimensional Ising model, with
periodic boundary conditions, results in a non-linear renormalisation
transformation for the couplings which can lead to chaotic behaviour when the
couplings are complex. The recursion relation for the couplings under
decimation is equivalent to the logistic map, or more generally the Mandelbrot
map. In particular an imaginary external magnetic field can give chaotic
trajectories in the space of couplings. The magnitude of the field must be
greater than a minimum value which tends to zero as the critical point T=0 is
approached, leading to a gap equation and associated critical exponent which
are identical to those of the Lee-Yang edge singularity in one dimension.Comment: 8 pages, 2 figures, PlainTeX, corrected some typo
A Phase Front Instability in Periodically Forced Oscillatory Systems
Multiplicity of phase states within frequency locked bands in periodically
forced oscillatory systems may give rise to front structures separating states
with different phases. A new front instability is found within bands where
(). Stationary fronts shifting the
oscillation phase by lose stability below a critical forcing strength and
decompose into traveling fronts each shifting the phase by . The
instability designates a transition from stationary two-phase patterns to
traveling -phase patterns
Extension of Lorenz Unpredictability
It is found that Lorenz systems can be unidirectionally coupled such that the
chaos expands from the drive system. This is true if the response system is not
chaotic, but admits a global attractor, an equilibrium or a cycle. The
extension of sensitivity and period-doubling cascade are theoretically proved,
and the appearance of cyclic chaos as well as intermittency in interconnected
Lorenz systems are demonstrated. A possible connection of our results with the
global weather unpredictability is provided.Comment: 32 pages, 13 figure
Nonextensivity and multifractality in low-dimensional dissipative systems
Power-law sensitivity to initial conditions at the edge of chaos provides a
natural relation between the scaling properties of the dynamics attractor and
its degree of nonextensivity as prescribed in the generalized statistics
recently introduced by one of us (C.T.) and characterized by the entropic index
. We show that general scaling arguments imply that , where and are the
extremes of the multifractal singularity spectrum of the attractor.
This relation is numerically checked to hold in standard one-dimensional
dissipative maps. The above result sheds light on a long-standing puzzle
concerning the relation between the entropic index and the underlying
microscopic dynamics.Comment: 12 pages, TeX, 4 ps figure
Singularites at a Dense Set of Temperature in Husimi Tree
We investigate complex temperature singularities of the three-site
interacting Ising model on the Husimi tree in the presentce of magnetic field.
We show that at certain magnetic field these singularities lie at a dense set
and as a consequence the phase transition condensation take place.Comment: ps file, 10 page
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