Related papers: The R-IFSs and their attractors
Intelligent reflecting surface (IRS) has recently received much attention from the research community due to its potential to achieve high spectral and power efficiency cost-effectively. In addition to traditional cellular networks, the use…
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of…
We consider a class of planar self-affine sets which we call "box-like". A box-like self-affine set is the attractor of an iterated function system (IFS) of affine maps where the image of the unit square, [0,1]^2, under arbitrary…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting…
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…
Some recent papers have extended the concept of finite-time stability (FTS) to the context of 2D linear systems, where it has been referred to as finite-region stability (FRS). FRS methodologies make even more sense than the classical FTS…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
We investigate Tree Iterated Function Systems (TIFSs), which we introduce in this paper. TIFSs are the generalizations of Iterated Function Systems in which we take the maps independently at each step and each block. In this paper, we give…
Intelligent Reflecting Surface (IRS) is envisioned to be a technical enabler for the sixth-generation (6G) wireless system. Its potential lies in delivering high performance while maintaining both power efficiency and cost-effectiveness.…
New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our…
In this paper, we present a new feature selection method that is suitable for both unsupervised and supervised problems. We build upon the recently proposed Infinite Feature Selection (IFS) method where feature subsets of all sizes…
This paper investigates the impact of self-supervised learning, specifically image rotations, on various class-incremental learning paradigms. Here, each image with a predefined rotation is considered as a new class for training. At…
We investigate certain spectral properties of the Bernoulli convolution measures on attractor sets arising from iterated function systems on the real line. In particular, we examine collections of orthogonal exponential functions in the…
We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended…
We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding…
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…