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Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
Graph generative models can be classified into two prominent families: one-shot models, which generate a graph in one go, and sequential models, which generate a graph by successive additions of nodes and edges. Ideally, between these two…
There are many research available on the study of real-valued fractal interpolation function and fractal dimension of its graph. In this paper, our main focus is to study the dimensional results for vector-valued fractal interpolation…
Integrating high-level context information with low-level details is of central importance in semantic segmentation. Towards this end, most existing segmentation models apply bilinear up-sampling and convolutions to feature maps of…
The reduction of integral field spectroscopy (IFS) data requires several stages and many repetitive operations to convert raw data into, typically, a large number of spectra. Instead there are several semiautomatic data reduction tools and…
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 work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is…
For a contractive iterated function system (IFS), it is known that there is a natural hyperbolic graph structure (augmented tree) on the symbolic space of the IFS that reflects the relationship among neighboring cells, and its hyperbolic…
When the order of an integrator is a complex number, the integrator is called a complex fractional order integrator (CFOI). The impulse response invariant discretization (IRID) method is proposed to approximately discretize the CFOI. The…
Classifier-Free Guidance (CFG) is an essential component of text-to-image diffusion models, and understanding and advancing its operational mechanisms remains a central focus of research. Existing approaches stem from divergent theoretical…
We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
There has been a significant effort in recent years to generalize the traditional concept of iterated function systems (IFS).In this article, we proposed Suzuki contraction in hyperspace and finding out the fixed point for Hutchinson…
We show that for the attractor $(K_{1},\dots,K_{q})$ of a graph directed iterated function system, for each $1\leq j\leq q$ and $\varepsilon>0$ there exits a self-similar set $K\subseteq K_{j}$ that satisfies the strong separation condition…
Vertical federated learning (VFL) enables a paradigm for vertically partitioned data across clients to collaboratively train machine learning models. Feature selection (FS) plays a crucial role in Vertical Federated Learning (VFL) due to…
Spectral graph embedding plays a critical role in graph representation learning by generating low-dimensional vector representations from graph spectral information. However, the embedding space of traditional spectral embedding methods…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…
Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane have uniformly perfect attractor sets, while other conditions imply the attractor is pointwise thin, and thus…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…