Related papers: Multifractal analysis of weighted networks by a mo…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
Adversarial attacks have been proven to be potential threats to Deep Neural Networks (DNNs), and many methods are proposed to defend against adversarial attacks. However, while enhancing the robustness, the clean accuracy will decline to a…
Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross…
The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
Adversarial social network analysis studies how graphs can be rewired or otherwise manipulated to evade social network analysis tools. While there is ample literature on manipulating simple networks, more sophisticated network types are…
In this paper, we propose a Network-Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network-structured settings. To asses predictive uncertainity, we…
The sixth-generation (6G) of wireless communication networks aims to leverage artificial intelligence tools for efficient and robust network optimization. This is especially the case since traditional optimization methods often face high…
Neural networks have been known for a long time as a tool for different types of classification, but only just in the last decade they have showed their entire power. Along with appearing of hardware that is capable to support demanding…
We propose a general model of unweighted and undirected networks having the scale-free property and fractal nature. Unlike the existing models of fractal scale-free networks (FSFNs), the present model can systematically and widely change…
In the federated learning setting, multiple clients jointly train a model under the coordination of the central server, while the training data is kept on the client to ensure privacy. Normally, inconsistent distribution of data across…
Recently, facial attribute classification (FAC) has attracted significant attention in the computer vision community. Great progress has been made along with the availability of challenging FAC datasets. However, conventional FAC methods…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
Networks are characterized by structural features, such as degree distribution, triangular closures, and assortativity. This paper addresses the problem of reconstructing instances of continuously (and non-negatively) weighted networks from…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
A multifractal analysis (MFA) is performed on three-dimensional grayscale images associated with natural porous structures (soil samples). First, computed tomography (CT) scans are carried out on the samples to generate 3D grayscale images.…
With the heterogeneous nature of tissue texture, using a single resolution approach for optimum classification might not suffice. In contrast, a multiresolution wavelet packet analysis can decompose the input signal into a set of frequency…
Objective: The present study introduces a fractional wavelet scattering network (FrScatNet), which is a generalized translation invariant version of the classical wavelet scattering network (ScatNet). Methods: In our approach, the FrScatNet…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…