相关论文: Box dimension of fractal interpolation surfaces wi…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in…
We introduce two frameworks in order to deal with fractal and multi-fractal analysis for subset sum problems where some embedding into the $1$-dimensional Euclidean space plays an important role. As one of these frameworks, the notion of…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…
An algorithm for calculating generalized fractal dimension of a time series using the general information function is presented. The algorithm is based on a strings sort technique and requires $O(N \log_2 N)$ computations. A rough estimate…
We introduce a fully convolutional fractional scaling component, FCFS. Fully convolutional networks can be applied to any size input and previously did not support non-integer scaling. Our architecture is simple with an efficient single…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant…
$\Phi$-intermediate dimensions interpolate between Hausdorff and box-counting dimensions by restricting admissible coverings to scale windows of the form $[\Phi(r),r]$. Using a family of $\Phi$-dependent kernels, we develop a…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
A novel approach to zipper fractal interpolation theory for functions of several variables is proposed. We develop multivariate zipper fractal functions in a constructive manner. We then perturb a multivariate function to construct its…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation…
Using a recently introduced mapping between a scalar elastic network tethered at its boundaries and a diffusion problem with permanent traps, we study various vibrational properties of progressively tethered disordered fractals. Different…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
It was shown that the conventional Fock matrix calculation, which using stored non-zero two-electron integrals, density prescreening, and data compression methods possesses the linear scaling property with respect to the problem size. This…