The Gaussian kernel, its partial derivatives and the Laplacian kernel, applied at different image scales, play a very important role in image processing and in feature extraction from images. Although they have been extensively studied in the case of...
Emotion plays a nuclear part in human attention, decision-making, and communication. Electroencephalogram (EEG)-based emotion recognition has developed a lot due to the application of Brain-Computer Interface (BCI) and its effectiveness compared to b...
Recent years have witnessed significant advances in single image deblurring due to the increasing popularity of electronic imaging equipment. Most existing blind image deblurring algorithms focus on designing distinctive image priors for blur kernel...
This paper introduces a novel framework for modeling nonlocal fractional system with a p-Laplacian operator under power nonlocal fractional derivatives (PFDs), a generalization encompassing established derivatives like Caputo–Fabrizio, Atangana...
The problem of 3D human pose estimation (HPE) has been the focus of research in recent years, yet precise estimation remains an under-explored challenge. In this paper, the merits of both multiview images and wearable IMUs are combined to enhance the...
In the present paper, we prove several vanishing theorems for the kernel of the Lichnerowicz-type Laplacian and provide estimates for its lowest eigenvalue on closed Riemannian manifolds. As an example of the Lichnerowicz-type Laplacian, we consider...
Associative knowledge networks are often explored by using the so-called spreading activation model to find their key items and their rankings. The spreading activation model is based on the idea of diffusion- or random walk -like spreading of activa...
We consider a family of semiclassically scaled second-order elliptic differential operators on high tensor powers of a Hermitian line bundle (possibly, twisted by an auxiliary Hermitian vector bundle of arbitrary rank) on a Riemannian manifold of bou...
In this paper, we study the kernel and spectral properties of the Bourguignon Laplacian on a closed Riemannian manifold, which acts on the space of symmetric bilinear forms (considered as one-forms with values in the cotangent bundle of this manifold...
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians combine mu...
Parkinson’s disease (PD) is a complex degenerative brain disease that affects nerve cells in the brain responsible for body movement. Machine learning is widely used to track the progression of PD in its early stages by predicting unified Parki...
In this paper, we investigate the heat kernel embedding as a route to graph representation. The heat kernel of the graph encapsulates information concerning the distribution of path lengths and, hence, node affinities on the graph; and is found by ex...
To address the problem that traditional spectral clustering algorithms cannot obtain the complete structural information of networks, this paper proposes a spectral clustering community detection algorithm, PMIK-SC, based on the point-wise mutual inf...
We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the...
We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with b...
In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of...
In the paper, we present a comparison analysis of the methods of the topological alignment and extract the main mathematical principles forming the base of the concept. The main narrative is devoted to the so-called coupled methods dealing with the d...
In graph theory, the weighted Laplacian matrix is the most utilized technique to interpret the local and global properties of a complex graph structure within computer vision applications. However, with increasing graph nodes, the Laplacian matrix&rs...
In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of Atangana–Baleanu operator. The L&eac...
Classification of motor imagery (MI) tasks provides a robust solution for specially-abled people to connect with the milieu for brain-computer interface. Precise selection of uniform tuning parameters of tunable Q wavelet transform (TQWT) for electro...
We construct a family of self-adjoint operators on the prime numbers whose entries depend on pairwise arithmetic divergences, replacing geometric distance with number-theoretic dissimilarity. The resulting spectra encode how coherence propagates thro...
Accurate prediction of an off-normal event in a nuclear reactor is dependent upon the availability of sensory data, reactor core physical condition, and understanding of the underlying phenomenon. This work presents a method to project the data from...
In the modern world, chronic kidney disease is one of the most severe diseases that negatively affects human life. It is becoming a growing problem in both developed and underdeveloped countries. An accurate and timely diagnosis of chronic kidney dis...
Image blurs are a major source of degradation in an imaging system. There are various blur types, such as motion blur and defocus blur, which reduce image quality significantly. Therefore, it is essential to develop methods for recovering approximate...
Extracting high-quality surface wave dispersion curves from crosscorrelation functions (CCFs) of ambient noise data is critical for seismic velocity inversion and subsurface structure interpretation. However, the non-uniform spatial distribution of n...
Recently, graph neural networks (GNNs) have achieved great success in dealing with graph-based data. The basic idea of GNNs is iteratively aggregating the information from neighbors, which is a special form of Laplacian smoothing. However, most of GN...
We present a geometric framework for surface denoising using graph signal processing, which is an emerging field that aims to develop new tools for processing and analyzing graph-structured data. The proposed approach is formulated as a constrained o...
Nonnegative matrix factorization (NMF) is an efficient method for feature learning in the field of machine learning and data mining. To investigate the nonlinear characteristics of datasets, kernel-method-based NMF (KNMF) and its graph-regularized ex...
Remote sensing continues to be an invaluable tool in earthquake damage assessments and emergency response. This study evaluates the effectiveness of multilayer feedforward neural networks, radial basis neural networks, and Random Forests in detecting...
Alzheimer’s disease, an irreversible neurodegenerative disorder, manifests through the progressive deterioration of memory and cognitive functions. While magnetic resonance imaging has become an indispensable neuroimaging modality for Alzheimer...
In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for ins...
The lack of large balanced datasets in the agricultural field is a glaring problem for researchers and developers to design and train optimal deep learning models. This paper shows that using synthetic data augmentation outperforms the standard metho...
In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used in dimension reduction such as isometric feature mapping, Laplacian Eigenmaps, fast indepe...
Unmanned aerial vehicles (UAVs) are widely used in surveillance and combat for their efficiency and autonomy, whilst complex, dynamic environments challenge the modeling of inter-agent relations and information transmission. This research proposes a...
Enhancing the generalization capability of time-series models for streamflow prediction using dimensionality reduction (DR) techniques remains a major challenge in water resources management (WRM). In this study, we investigated eight DR techniques a...
Surgical scene understanding is a key barrier for situation-aware robotic surgeries and the associated surgical training. With the presence of domain shifts and the inclusion of new instruments and tissues, learning domain generalization (DG) plays a...
Satellite multi-view stereo (MVS) is a fundamental task in large-scale Earth surface reconstruction. Recently, learning-based multi-view stereo methods have shown promising results in this field. However, these methods are mainly developed by transfe...
Aiming at the problems of the blurred image defect contour and the surface texture of the aluminum strip suppressing defect feature extraction when collecting photos online in the air cushion furnace production line, we propose an algorithm for the s...
In this paper, we present the supervised multi-view canonical correlation analysis ensemble (SMVCCAE) and its semi-supervised version (SSMVCCAE), which are novel techniques designed to address heterogeneous domain adaptation problems, i.e., situation...
With the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth’s surface objects. However, the...