Related papers: Hidden variable recurrent fractal interpolation fu…
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in $\br^d$, and the ``IFS'' refers to…
Capitalizing on the rapid development of neural networks, recent video frame interpolation (VFI) methods have achieved notable improvements. However, they still fall short for real-world videos containing large motions. Complex deformation…
It is well known that the reconstruction FID (rFID) of a VAE is poorly correlated with the generation FID (gFID) of a latent diffusion model. We propose interpolated FID (iFID), a simple variant of rFID that exhibits a strong correlation…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
Feature caching approaches accelerate diffusion transformers (DiTs) by storing the output features of computationally expensive modules at certain timesteps, and exploiting them for subsequent steps to reduce redundant computations. Recent…
In this paper we discuss a new method to blend fractal attractors using the code map for the IFS formed by the Hutchinson--Barnsley operators of a finite family of hyperbolic IFSs. We introduce a parameter called blending coefficient to…
In this paper, based on the results from [On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113674], we generate coverings (consisting of finite families of rhombi) of the graph of fractal…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
A finite family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps of a given metric space $X$ is called an iterated function system (shortly IFS). In a case of contractive selfmaps of a complete metric space is well-known that IFS has…
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL…
Development of additive manufacturing in last decade greatly improves tissue engineering. During the manufacturing of porous scaffold, simplified but functionally equivalent models are getting focused for practically reasons. Scaffolds can…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
Video frame interpolation (VFI) serves as a useful tool for many video processing applications. Recently, it has also been applied in the video compression domain for enhancing both conventional video codecs and learning-based compression…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
Implicit Neural Representations (INRs) employ neural networks to represent continuous functions by mapping coordinates to the corresponding values of the target function, with applications e.g., inverse graphics. However, INRs face a…
In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of the functions, but we do not assume any separation condition.…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
We propose a fully multivariate generalization of multifractal detrended fluctuation analysis (MFDFA) and leverage it to develop a fault diagnosis framework for multichannel machine vibration data. We introduce a novel covariance-weighted…
We propose a low-complexity variable forgetting factor (VFF) mechanism for recursive least square (RLS) algorithms in interference suppression applications. The proposed VFF mechanism employs an updated component related to the time average…