Related papers: The R-IFSs and their attractors
Under suitable conditions, with respect to some property on a random iterated function system(RIFS), it is shown how the system satisfies in this property almost surely.
Machine learning classifiers are often trained to recognize a set of pre-defined classes. However, in many applications, it is often desirable to have the flexibility of learning additional concepts, with limited data and without…
For points in $d$ real dimensions, we introduce a geometry for general digit sets. We introduce a positional number system where the basis for our representation is a fixed $d$ by $d$ matrix over $\bz$. Our starting point is a given pair…
We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\mathrm{bv}}$-topology. We characterize the obstruction to minimality and describe the limit set. In…
Semantic segmentation models have two fundamental weaknesses: i) they require large training sets with costly pixel-level annotations, and ii) they have a static output space, constrained to the classes of the training set. Toward…
In a previous paper, dealing with "Applications in $\mathbb{R}^1$," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications…
In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…
The goal of incremental Few-shot Semantic Segmentation (iFSS) is to extend pre-trained segmentation models to new classes via few annotated images without access to old training data. During incrementally learning novel classes, the data…
We define two non-metrizable compact spaces and show that they are attractors of iterated function systems. Both of them, the split square and the split carpet, are constructed using the product of split intervals.
We introduce the integrative task of few-shot classification and segmentation (FS-CS) that aims to both classify and segment target objects in a query image when the target classes are given with a few examples. This task combines two…
In this paper we study some classes of $\alpha$-attractors models in the Jordan frame and we find the corresponding $F(R)$ gravity theory. We study analytically the problem at leading order and we investigate whether the attractor picture…
This article aims to study fractal interpolation functions corresponding to a sequence of iterated function systems (IFSs). For a suitable choice of a sequence of IFS parameters, the corresponding non-stationary fractal function is a better…
Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of…
Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in…
Inspired by a twist maps theorem of Mather we study recurrent invariant sets that are ordered like rigid rotation under the action of the lift of a bimodal circle map $g$ to the $k$-fold cover. For each irrational in the interior of the…
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…
For a unital ring R, a Sylvester rank function is a numerical invariant which can be described in 3 equivalent ways: on finitely presented left R-modules, or on rectangular matrices over R, or on maps between finitely generated projective…
Recursive Best-First Search (RBFS) is a heuristic search algorithm known for its efficient memory usage compared to traditional best-first search methods like A*. Despite its theoretical advantages, RBFS is complex and difficult to teach…
Traditional feature matching methods such as scale-invariant feature transform (SIFT) usually use image intensity or gradient information to detect and describe feature points; however, both intensity and gradient are sensitive to nonlinear…
Navigation is crucial for animal behavior and is assumed to require an internal representation of the external environment, termed a cognitive map. The precise form of this representation is often considered to be a metric representation of…