Related papers: Neural Network Operator-Based Fractal Approximatio…
In this paper we define an internal binary operation between functions called in the text \emph{fractal convolution}, that applies a pair of mappings into a fractal function. This is done by means of a suitable Iterated Function System. We…
Designing effective neural networks requires tuning architectural elements. This study integrates fractional calculus into neural networks by introducing fractional order derivatives (FDO) as tunable parameters in activation functions,…
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…
This paper proposes fractional order graph neural networks (FGNNs), optimized by the approximation strategy to address the challenges of local optimum of classic and fractional graph neural networks which are specialised at aggregating…
This article constructs a fractal interpolation function, also referred to as $\alpha$-fractal function, using Suzuki-type generalized $\varphi$-contraction mappings (STGPC). The STGPC is a generalization of $\varphi$-contraction mappings.…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sierpi\'nski gaskets. Further, we collect some results regarding smoothness of the constructed FIF. We prove, in particular, that the FIF are…
This paper focuses on the hypothesis of optimizing time series predictions using fractal interpolation techniques. In general, the accuracy of machine learning model predictions is closely related to the quality and quantitative aspects of…
In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $\alpha$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times…
A novel method for constructing a nonlinear fractal histopolation function associated with a given histogram is introduced in this paper. In contrast to classical fractal interpolation methods, which produce continuous and interpolatory…
Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and…
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated function system (IFS) corresponding to the data set is the graph of the FIF. Coalescence…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
Image restoration problems are typically ill-posed requiring the design of suitable priors. These priors are typically hand-designed and are fully instantiated throughout the process. In this paper, we introduce a novel framework for…
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting…
This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier…
We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
We demonstrate that simple feed-forward neural networks (NNs) can accurately compute correlation functions of conformal field theories (CFTs) on a line. Strikingly, by optimising a NN solely on crossing symmetry and providing only the…