Related papers: Some new classes of directed graph IFSs
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be…
Feng and Wang showed that two homogeneous iterated function systems in $\mathbb{R}$ with multiplicatively independent contraction ratios necessarily have different attractors. In this paper, we extend this result to graph directed iterated…
Suppose $\{f_1,...,f_m\}$ is a set of Lipschitz maps of $\mathbb{R}^d$. We form the iterated function system (IFS) by independently choosing the maps so that the map $f_i$ is chosen with probability $p_i$ ($\sum_{i=1}^m p_i=1$). We assume…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C^3 regularity of the maps in the IFS. The key idea,…
In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective…
Unique expansions in non-integer bases $q$ have been investigated in many papers during the last thirty years. They are often conveniently generated by labeled directed graphs. In the first part of this paper we give a precise description…
We consider the configuration model and the uniform simple graph with given degree sequence $\boldsymbol{d}=\left(d_i\right)_{i=1}^n$. We derive quantitative bounds for the errors in (i) joint normal-Poisson approximation to the numbers of…
We study new relations between countable iterated function systems (IFS) with overlaps, Smale endomorphisms and random systems with complete connections. We prove that stationary measures for countable conformal IFS with overlaps and…
In this paper we consider the class of 2-dimensional Artin groups with connected, large type, triangle-free defining graphs (type CLTTF). We classify these groups up to isomorphism, and describe a generating set for the automorphism group…
The aim of the present paper is twofold. We study directed porosity in connection with conformal iterated function systems (CIFS) and with singular integrals. We prove that limit sets of finite CIFS are porous in a stronger sense than…
This paper sets a theoretical foundation for the applications of the fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements of the…
In this paper, motivated by a question posed in \cite{AH}, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorithm to find an induced matching for such graphs and we prove…
This paper is devoted to advancing the theoretical understanding of the iterated immediate snapshot (IIS) complexity of the Weak Symmetry Breaking task (WSB). Our rather unexpected main theorem states that there exist infinitely many values…
The graph fused lasso -- which includes as a special case the one-dimensional fused lasso -- is widely used to reconstruct signals that are piecewise constant on a graph, meaning that nodes connected by an edge tend to have identical…
IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design…
We introduce a new directed graph model for social networks, based on the transitivity of triads. In the Iterated Local Directed Transitivity (ILDT) model, new nodes are born over discrete time-steps, and inherit the link structure of their…
We investigate oriented graphs based on the curve complex $C(S)$ of a closed surface $S$ and induced by functions on the vertex set of $C(S)$. In particular, we introduce the Dehn quasi-homothetic functions, which behave similarly to…
We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we…