Popcorn fractals are instances of Integrated Fractal Systems involving trigonometric functions. In this paper, we study the effect of spherical, swirl and pseudo-horseshoe functions on popcorn fractals to produce talismanic and tantric designs. General Terms Fractal, Algorithm, Turbo C++, Program.

In this paper we investigate some of the mathematical properties of meiotic recombination. Working within the framework of a genetic model with n loci, where alpha alleles are possible at each locus, we find that the proportion of all possible diploid parental genotypes that can produce a particular haploid gamete is exp[-n log(alpha(2)/[2alpha-1])]. We show that this proportion connects recomb...

The conformal loop ensembles CLEκ, defined for 8/3 ≤ κ ≤ 8, are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compu...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgrid-scale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly. In one dimension, the ap...

A new method is proposed to establish the statistical fractal model for liver diseases classification. Firstly, the fractal theory is used to construct the high-order tensor, and then Generalized N-dimensional Principal Component Analysis (GND-PCA) is used to establish the statistical fractal model and select the feature from the region of liver; at the same time different features have differe...

The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two 3D-configuration models, namely a standard slicing and a fractal surface generation within the Menger sponge geometry is presented. It is shown, that for iteration ord...

We construct a string field Hamiltonian describing the dynamics of open and closed strings with effective target-space dimension c ≤ 1. In order to do so, we first derive the Dyson-Schwinger equations for the underlying large N vector+matrix model and formulate them as a set of constraints satisfying decoupled Virasoro and U(1) current algebras. The Hamiltonian consists of a bulk and a boundary...

During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In t...