335 research outputs found
Multiscaling and Structure Functions in Turbulence: An Alternative Approach
We propose an alternative formulation of structure functions for the velocity
field in fully developed turbulence. Instead of averaging moments of the
velocity differences as a function of the distance, we suggest to average
moments of the distances as a function of the velocity difference. This is like
an ``inverted'' structure function, with a different statistics. On the basis
of shell model calculations we obtain a new multiscaling spectrum.Comment: 4 pages, REVTex, 4 figure
Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli
Inflammatory responses in eucaryotic cells are often associated with
oscillations in the nuclear-cytoplasmic translocation of the transcription
factor NF-kB. In most laboratory realizations, the oscillations are triggered
by a cytokine stimulus, like the tumor necrosis factor alpha, applied as a step
change to a steady level. Here we use a mathematical model to show that an
oscillatory external stimulus can synchronize the NF-kB oscillations into
states where the ratios of the internal to external frequency are close to
rational numbers. We predict a specific response diagram of the TNF-driven
NF-kB system which exhibits bands of synchronization known as "Arnold tongues".
Our model also suggests that when the amplitude of the external stimulus
exceeds a certain threshold there is the possibility of coexistence of multiple
different synchronized states and eventually chaotic dynamics of the nuclear
NF-kB concentration. This could be used as a way of externally controlling
immune response, DNA repair and apoptotic pathways.Comment: 12 pages, 3 figure
Entrainment of noise-induced and limit cycle oscillators under weak noise
Theoretical models that describe oscillations in biological systems are often
either a limit cycle oscillator, where the deterministic nonlinear dynamics
gives sustained periodic oscillations, or a noise-induced oscillator, where a
fixed point is linearly stable with complex eigenvalues and addition of noise
gives oscillations around the fixed point with fluctuating amplitude. We
investigate how each class of model behaves under the external periodic
forcing, taking the well-studied van der Pol equation as an example. We find
that, when the forcing is additive, the noise-induced oscillator can show only
one-to-one entrainment to the external frequency, in contrast to the limit
cycle oscillator which is known to entrain to any ratio. When the external
forcing is multiplicative, on the other hand, the noise-induced oscillator can
show entrainment to a few ratios other than one-to-one, while the limit cycle
oscillator shows entrain to any ratio. The noise blurs the entrainment in
general, but clear entrainment regions for limit cycles can be identified as
long as the noise is not too strong.Comment: 27 pages in preprint style, 12 figues, 2 tabl
Symbolic dynamics of biological feedback networks
We formulate general rules for a coarse-graining of the dynamics, which we
term `symbolic dynamics', of feedback networks with monotone interactions, such
as most biological modules. Networks which are more complex than simple cyclic
structures can exhibit multiple different symbolic dynamics. Nevertheless, we
show several examples where the symbolic dynamics is dominated by a single
pattern that is very robust to changes in parameters and is consistent with the
dynamics being dictated by a single feedback loop. Our analysis provides a
method for extracting these dominant loops from short time series, even if they
only show transient trajectories.Comment: 4 pages, 4 figure
Inverse Statistics in Economics : The gain-loss asymmetry
Inverse statistics in economics is considered. We argue that the natural
candidate for such statistics is the investment horizons distribution. This
distribution of waiting times needed to achieve a predefined level of return is
obtained from (often detrended) historic asset prices. Such a distribution
typically goes through a maximum at a time called the {\em optimal investment
horizon}, , since this defines the most likely waiting time for
obtaining a given return . By considering equal positive and negative
levels of return, we report on a quantitative gain-loss asymmetry most
pronounced for short horizons. It is argued that this asymmetry reflects the
market dynamics and we speculate over the origin of this asymmetry.Comment: Latex, 6 pages, 3 figure
Optimal Investment Horizons
In stochastic finance, one traditionally considers the return as a
competitive measure of an asset, {\it i.e.}, the profit generated by that asset
after some fixed time span , say one week or one year. This measures
how well (or how bad) the asset performs over that given period of time. It has
been established that the distribution of returns exhibits ``fat tails''
indicating that large returns occur more frequently than what is expected from
standard Gaussian stochastic processes (Mandelbrot-1967,Stanley1,Doyne).
Instead of estimating this ``fat tail'' distribution of returns, we propose
here an alternative approach, which is outlined by addressing the following
question: What is the smallest time interval needed for an asset to cross a
fixed return level of say 10%? For a particular asset, we refer to this time as
the {\it investment horizon} and the corresponding distribution as the {\it
investment horizon distribution}. This latter distribution complements that of
returns and provides new and possibly crucial information for portfolio design
and risk-management, as well as for pricing of more exotic options. By
considering historical financial data, exemplified by the Dow Jones Industrial
Average, we obtain a novel set of probability distributions for the investment
horizons which can be used to estimate the optimal investment horizon for a
stock or a future contract.Comment: Latex, 5 pages including 4 figur
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