Fractal Statistics of Modeled Zoning Patterns in Calcite

2011 ◽  
pp. 65-72
Author(s):  
Natalia Bryksina ◽  
Norman Halden ◽  
Sergio Mejia
Keyword(s):  
Fractal Statistics

Inverse Fractal Statistics in Turbulence and Finance

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4003-4012 ◽  
Author(s):  
Mogens H. Jensen ◽  
Anders Johansen ◽  
Ingve Simonsen
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Exit Time ◽  
Optimal Investment ◽  
Financial Data ◽  
Data Sets ◽  
Investment Horizon ◽  
Scaling Exponents ◽  
Fractal Statistics ◽  
Gain Loss

We consider inverse statistics in turbulence and financial data. By inverse statistics, also sometimes called exit time statistics, we "turn" the variables around such that the fluctuating variable becomes the fixed variable, while the fixed variable becomes fluctuating. In that sense we can probe distinct regimes of the data sets. In the case of turbulence, we obtain a new set of (multi)-scaling exponents which monitor the dissipation regime. In the case of economics, we obtain a distribution of waiting times needed to achieve a predefined level of return. Such a distribution typically goes through a maximum at a time called the optimal investment horizon[Formula: see text], since this defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels of return, we report on a quantitative gain-loss asymmetry most pronounced for short horizons.

The fractal statistics of liquid slug lengths

1990 ◽  
Vol 16 (6) ◽  
pp. 1117-1126 ◽  
Author(s):  
G. Sæther ◽  
K. Bendiksen ◽  
J. Müller ◽  
E. Frøland
Keyword(s):  
Liquid Slug ◽  
Fractal Statistics

Fractional dynamics of allometry

2012 ◽  
Vol 15 (1) ◽  
Author(s):  
Bruce West ◽  
Damien West
Keyword(s):  
Fractal Geometry ◽  
Empirical Distribution ◽  
Linear Regression Analysis ◽  
The Other ◽  
Fractional Dynamics ◽  
Data Sets ◽  
Fractal Statistics ◽  
Metabolic Data ◽  
Detailed Application ◽  
Dynamic Variables

AbstractAllometry relations (ARs) in physiology are nearly two hundred years old. In general if X ij is a measure of the size of the i th member of a complex host network from species j and Y ij is a property of a complex subnetwork embedded within the host network an intraspecies AR exists between the two when Y ij = aX ijb. We emphasize that the reductionist models of AR interpret X ij and Y ij as dynamic variables, albeit the ARs themselves are explicitly time independent. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret 〈X i〉 and 〈Y i〉 as averages over an ensemble of individuals to yields the interspecies AR 〈Y i〉 = a〈X i〉b. Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of intraspecies ARs is a little over a decade old and although well received it has not been universally accepted. An alternate perspective is given by the interspecies AR based on linear regression analysis of fluctuating data sets. We emphasize that the intraspecies and interspecies ARs are not the same and show that the interspecies AR can only be derived from the intraspecies one for a narrow distribution of fluctuations. This condition is not satisfied by metabolic data as is shown separately for aviary and mammal data sets. The empirical distribution of metabolic allometry coefficients is shown herein to be Pareto in form. A number of reductionist arguments conclude that the allometry exponent is universal, however herein we derive a deterministic relation between the allometry exponent and the allometry coefficient using the fractional calculus. The co-variation relation violates the universality assumption. We conclude that the interspecies physiologic AR is entailed by the scaling behavior of the probability density, which is derived using the fractional probability calculus.

Target signal enhancement in near-surface controlled-source electromagnetic data

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. G59-G67 ◽  
Author(s):  
Alfonso Benavides I. ◽  
Mark E. Everett
Keyword(s):  
Power Law ◽  
Wavelet Transforms ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Near Surface ◽  
Controlled Source ◽  
Electromagnetic Data ◽  
Apparent Conductivity ◽  
Fractal Statistics ◽  
Detection And Localization

Controlled-source electromagnetic-conductivity profiles and maps were obtained on the Brazos Valley, Texas, floodplain to study the fractal statistics of geologic noise and the effects of man-made conductive metal targets. Fourier transform, discrete wavelet transforms, and variogram analyses were used. Targets tend to flatten the power-law power spectrum at small wavenumbers and shift power to higher wavenumbers. Detection and localization of targets can be achieved using wavelet spectrogram techniques. Additionally, variograms from pure background conductivity maps show a power-law trend for all lags, whereas, in the presence of targets, a short power-law trend is followed by a sill corresponding to a loss in spatial correlation. A simple preprocessing step that combines responses from two perpendicular transmitter-receiver orientations enhances the localization of targets and rejects background signals in profiles and 2D apparent-conductivity maps. Finally, a field example shows how the use of wavelet filtering is able to separate target responses from the geologic background.

scholarly journals FRACTAL INDEX, CENTRAL CHARGE AND FRACTONS

2000 ◽  
Vol 15 (31) ◽  
pp. 1931-1939 ◽  
Author(s):  
WELLINGTON DA CRUZ ◽  
ROSEVALDO DE OLIVEIRA
Keyword(s):  
Hausdorff Dimension ◽  
Central Charge ◽  
Statistical Parameter ◽  
Conformal Anomaly ◽  
Fermi Velocity ◽  
Conformal Field ◽  
Fractal Index ◽  
Fractal Statistics ◽  
Universal Classes ◽  
Dilogarithm Function

We introduce the notion of fractal index associated with the universal class h of particles or quasiparticles, termed fractons which obey specific fractal statistics. A connection between fractons and conformal field theory (CFT)-quasiparticles is established taking into account the central charge c[ν] and the particle-hole duality ν↔1/ν, for integer-value ν of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as [Formula: see text]. The Hausdorff dimension h which labeled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.

scholarly journals Philippine Poverty as Moving Fractals

2016 ◽  
Vol 6 (2) ◽  
pp. 18
Author(s):  
Roselle Jardin Ranario
Keyword(s):  
Pattern Analysis ◽  
Fractal Model ◽  
The Philippines ◽  
Data Sets ◽  
Policy Makers ◽  
Root Cause ◽  
Recent Innovation ◽  
Analytical Foundation ◽  
Fractal Statistics ◽  
Key Indicators

A recent innovation in the field of statistics is using fractal analysis where data sets are analyzed for anomaly detection, pattern analysis, and root cause analysis. In application of the fractal statistics, this paper examines the incidence of Philippine poverty from 2003 to 2012 based on its fractal dimension in the hope of providing policy makers a different approach in addressing sustained growth among the poor. Poverty is like a moving fractal where patterns simply repeat in various scales and variations.  What are the key implications of fractal poverty for policy and research? How can the fractal poverty provide an analytical foundation to make a pathway out of poverty accessible to Filipinos presently suffering in extreme poverty? The fractal model shows that poverty incidence is dictated by provinces whose poverty incidence are high. This means that if the poverty incidence of the province will be primarily addressed, it will affect the poverty scenario of the Philippines. Policy makers if looking for key indicators why Filipinos have some difficulty escaping poverty may focus on the province with the highest incidence. 

Sign in / Sign up

Export Citation Format

Share Document