相关论文: A fractal dimension estimate for a graph-directed …

In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci. U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a…

A fractional matching of a graph $G$ is a function $f:E(G) \to [0,1]$ such that for any $v\in V(G)$, $\sum_{e\in E_G(v)}f(e)\leq 1$ where $E_G(v) = \{e \in E(G): e$ is incident with $v$ in $G\}$. The fractional matching number of $G$ is…

This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from noise, we…

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem…

Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…

Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…

The purpose of the paper is a general analysis of path space measures. Our focus is a certain path space analysis on generalized Bratteli diagrams. We use this in a systematic study of systems of self-similar measures (the term ``IFS…

Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures…

In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…

In this paper, we characterize a novel separation property for IFS-attractors on complete metric spaces. Such a separation property is weaker than the strong open set condition (SOSC) and becomes necessary to reach the equality between the…

In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized…

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of…

This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…

We study fractal sets $\Gamma\subset \mathbb{R}^n$ with non-empty interior $\Omega$, that are attractors of iterated function systems (IFSs) of contracting similarities satisfying the open set condition. Examples for $n=2$ are the closures…

In this article, an iterated function system (IFS) is considered on the real projective line $\mathbb{RP}^1$ so that the attractor is a Cantor-like set. Hausdorff dimension of this attractor is estimated. The existence of a probability…

This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by estimating the triangular prism fractal dimension under different scales with a weight…

We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…

Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic…

A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.

Fractals are a basic tool to phenomenologically describe natural objects having a high degree of temporal or spatial variability. From a physical point of view the fractal properties of natural systems can also be interpreted by using the…