Factor analysis as a dimension reduction technique is widely used with compositional data. Using the method for raw data or for improperly transformed data will, however, lead to biased results and consequently to misleading interpretations. Although some procedures, suitable for factor analysis with compositional data, were already developed, they require pre-knowledge of variable groups, or a...

Aerial gamma-ray spectrometric technique is used herein to evaluate the radioactive heat production (HP) of Ar-Rassafeh Badyieh Area (Area-2), Syria. The nine already established lithological scored units Area-2 have been separately characterized for HP parameter. Concentration-number (C-N) model and log-log plots associated with fractal are proposed applied as a new approach map measured equiv...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

We study the betweenness centrality of fractal and nonfractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution P(C...

The objective of this study is to identify the most suitable portions of the C1 coking coal seam in the North Block of the East-Parvadeh coal deposit (Central Iran), according to ash and sulfur values, using C-N fractal modeling. Based on the C-N log-log plots, different geochemical populations were evaluated based on their sulfur and ash content. They were then divided into five populations ea...

We derive a new lower bound p c > 0:8107 for the critical value of Mandelbrot's dyadic fractal percolation model. This is achieved by taking the random fractal set (to be denoted A 1) and adding to it a countable number of straight line segments, chosen in a certain (non-random) way as to simplify greatly the connectivity structure. We denote the modiied model thus obtained by C 1 , and write C...

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on th...

where N is the number of resistors. We find a generic phase transition at/3 =/3c = -1. Also, we develop a transfer matrix technique which determines all even positive moments. The thermodynamical formalism is applied to the Hilfer-Blumen hierarchy of generalized Sierpinski gasket fractal networks, and the crossover from fractal to lattice behavior is studied. At this crossover we find a sharp p...

Outlier detection based on the Mahalanobis distance (MD) requires an appropriate transformation in case of compositional data. For the family of logratio transformations (additive, centered and isometric logratio transformation) it is shown that the MDs based on classical estimates are invariant to these transformations, and that the MDs based on affine equivariant estimators of location and co...

2014 In a recent article we have shown that, by applying sophisticated summation methods to Wilson-Fisher’s 03B5-expansion, it is possible from the presently known terms of the series to obtain accurate values of critical exponents for the 0 ( n ) symmetric n-vector model : these values are consistent with the best estimates obtained from threedimensional Renormalization Group calculations and,...