39 research outputs found
Efficient method of finding scaling exponents from finite-size Monte-Carlo simulations
Monte-Carlo simulations are routinely used for estimating the scaling
exponents of complex systems. However, due to finite-size effects, determining
the exponent values is often difficult and not reliable. Here we present a
novel technique of dealing with the problem of finite-size scaling. This new
method allows not only to decrease the uncertainties of the scaling exponents,
but makes it also possible to determine the exponents of the asymptotic
corrections to the scaling laws. The efficiency of the technique is
demonstrated by finding the scaling exponent of uncorrelated percolation
cluster hulls.Comment: The "previous version" of this is arXiv:0804.1911. This version is
published in EPJ
Leptokurtic Portfolio Theory
The question of optimal portfolio is addressed. The conventional Markowitz
portfolio optimisation is discussed and the shortcomings due to non-Gaussian
security returns are outlined. A method is proposed to minimise the likelihood
of extreme non-Gaussian drawdowns of the portfolio value. The theory is called
Leptokurtic, because it minimises the effects from "fat tails" of returns. The
leptokurtic portfolio theory provides an optimal portfolio for investors, who
define their risk-aversion as unwillingness to experience sharp drawdowns in
asset prices. Two types of risks in asset returns are defined: a fluctuation
risk, that has Gaussian distribution, and a drawdown risk, that deals with
distribution tails. These risks are quantitatively measured by defining the
"noise kernel" -- an ellipsoidal cloud of points in the space of asset returns.
The size of the ellipse is controlled with the threshold parameter: the larger
the threshold parameter, the larger return are accepted for investors as normal
fluctuations. The return vectors falling into the kernel are used for
calculation of fluctuation risk. Analogously, the data points falling outside
the kernel are used for the calculation of drawdown risks. As a result the
portfolio optimisation problem becomes three-dimensional: in addition to the
return, there are two types of risks involved. Optimal portfolio for
drawdown-averse investors is the portfolio minimising variance outside the
noise kernel. The theory has been tested with MSCI North America, Europe and
Pacific total return stock indices.Comment: 10 pages, 2 figures, To be presented in NEXT-SigmaPh
Intersections of moving fractal sets
Intersection of a random fractal or self-affine set with a linear manifold or
another fractal set is studied, assuming that one of the sets is in a
translational motion with respect to the other. It is shown that the mass of
such an intersection is a self-affine function of the relative position of the
two sets. The corresponding Hurst exponent h is a function of the scaling
exponents of the intersecting sets. A generic expression for h is provided, and
its proof is offered for two cases --- intersection of a self-affine curve with
a line, and of two fractal sets. The analytical results are tested using
Monte-Carlo simulations
Impact of COVID-19 Pandemic on Energy Demand in Estonia
The COVID-19 pandemic triggered a question of how to measure and evaluate
adequacy of the applied restrictions. Available studies propose various methods
mainly grouped to statistical and machine learning techniques. The current
paper joins this line of research by introducing a simple-yet-accurate linear
regression model which eliminates effects of weekly cycle, available daylight,
temperature, and wind from the electricity consumption data. The model is
validated using real data and enables the qualitative analysis of economical
impact.Comment: 5 pages, 6 figure
On the fractality of the biological tree-like structures
The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:DsD, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have Ds≥D. The notion of the self-overlapping exponent is introduced to characterise the trees with Ds>D. A model of the human blood-vessel system is proposed. The model is consistent with the processes governing the growth of the blood-vessels and yields Ds=3.4. The model is used to analyse the transport of passive component by blood