4,062 research outputs found
Fluctuation scaling in complex systems: Taylor's law and beyond
Complex systems consist of many interacting elements which participate in
some dynamical process. The activity of various elements is often different and
the fluctuation in the activity of an element grows monotonically with the
average activity. This relationship is often of the form "", where the exponent is predominantly in
the range . This power law has been observed in a very wide range of
disciplines, ranging from population dynamics through the Internet to the stock
market and it is often treated under the names \emph{Taylor's law} or
\emph{fluctuation scaling}. This review attempts to show how general the above
scaling relationship is by surveying the literature, as well as by reporting
some new empirical data and model calculations. We also show some basic
principles that can underlie the generality of the phenomenon. This is followed
by a mean-field framework based on sums of random variables. In this context
the emergence of fluctuation scaling is equivalent to some corresponding limit
theorems. In certain physical systems fluctuation scaling can be related to
finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic
Molecular transport through a bottleneck driven by external force
The transport phenomena of Lennard-Jones molecules through a structural
bottleneck driven by an external force are investigated by molecular dynamics
simulations. We observe two distinct molecular flow regimes distinguished by a
critical external force and find scaling behaviors between external
forces and flow rates. Below the threshold , molecules are essentially
stuck in the bottleneck due to the attractive interaction between the
molecules, while above , molecules can smoothly move in the pipe. A
critical flow rate corresponding to satisfies a simple
relationship with angles and the value of can be estimated by a simple
argument. We further clarify the role of the temperature dependence in the
molecular flows through the bottleneck.Comment: 14 pages, 12 figure
Fluctuation-induced traffic congestion in heterogeneous networks
In studies of complex heterogeneous networks, particularly of the Internet,
significant attention was paid to analyzing network failures caused by hardware
faults or overload, where the network reaction was modeled as rerouting of
traffic away from failed or congested elements. Here we model another type of
the network reaction to congestion -- a sharp reduction of the input traffic
rate through congested routes which occurs on much shorter time scales. We
consider the onset of congestion in the Internet where local mismatch between
demand and capacity results in traffic losses and show that it can be described
as a phase transition characterized by strong non-Gaussian loss fluctuations at
a mesoscopic time scale. The fluctuations, caused by noise in input traffic,
are exacerbated by the heterogeneous nature of the network manifested in a
scale-free load distribution. They result in the network strongly overreacting
to the first signs of congestion by significantly reducing input traffic along
the communication paths where congestion is utterly negligible.Comment: 4 pages, 3 figure
Waiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem
We evaluate the average waiting time between observing the price of financial
markets and the next price change, especially in an on-line foreign exchange
trading service for individual customers via the internet. Basic technical idea
of our present work is dependent on the so-called renewal-reward theorem.
Assuming that stochastic processes of the market price changes could be
regarded as a renewal process, we use the theorem to calculate the average
waiting time of the process. In the conventional derivation of the theorem, it
is apparently hard to evaluate the higher order moments of the waiting time. To
overcome this type of difficulties, we attempt to derive the waiting time
distribution Omega(s) directly for arbitrary time interval distribution (first
passage time distribution) of the stochastic process P_{W}(tau) and observation
time distribution P_{O}(t) of customers. Our analysis enables us to evaluate
not only the first moment (the average waiting time) but also any order of the
higher moments of the waiting time. Moreover, in our formalism, it is possible
to model the observation of the price on the internet by the customers in terms
of the observation time distribution P_{O}(t). We apply our analysis to the
stochastic process of the on-line foreign exchange rate for individual
customers from the Sony bank and compare the moments with the empirical data
analysis.Comment: 8pages, 11figures, using IEEEtran.cl
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