Research
Research
Research
Research
3,698+ open-access research outputs.
We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynamical systems (DSs). …
The exact-sequence structure behind the Arnold--Douglas--Gupta family of higher-order mixed finite elements for plane elasticity on barycentric refinements is made explicit. On each macro triangle, th…
We prove that any continuous function f from [0,1]^n to R representable by a finite computation tree with N internal nodes and compositional sparsity s = O(1) admits a deep Kolmogorov-Arnold Network (…
As healthcare systems become increasingly interconnected, ensuring secure and continuous device authentication in health information exchange (HIE) networks is critical to safeguarding patient data an…
Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This wo…
We analyze the universal approximation property of Kolmogorov-Arnold Networks (KANs) in terms of their edge functions. If these functions are all affine, then universality clearly fails. How many non-…
Gaussian basis functions provide an efficient and flexible alternative to spline activations in KANs. In this work, we introduce the partition-of-unity Gaussian KAN (PU-GKAN), a Shepard-type normalize…
Existing theory suggests that Kolmogorov-Arnold Networks (KANs) can overcome the spectral bias commonly observed in neural networks under the assumption that inputs are statistically independent. Howe…
The Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Ar…
Kolmogorov-Arnold Networks (KANs) are a recent neural network architecture offering an alternative to Multilayer Perceptrons (MLPs) with improved explainability and expressibility. However, KANs are s…
The Gaussian scale parameter \(\epsilon\) is central to the behavior of Gaussian Kolmogorov--Arnold Networks (KANs), yet its role in deep edge-based architectures has not been studied systematically. …
Purpose: Quasi-random Sobol-based sampling schemes exhibit deterministic structural artifacts when aggressively undersampled, particularly at low encoding densities required for accelerated 2D SPI/CSI…
This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation in the Navier-Stokes…
We study the dynamics of a parametric family of rational functions of odd degree, where each function is a generalized Blaschke product that maps the unit circle onto itself. The action of the Blaschk…
Ultra-high-definition (UHD) image restoration poses unique challenges due to the high spatial resolution, diverse content, and fine-grained structures present in UHD images. To address these issues, w…
The Melnikov-Arnold integrals (MA-integrals) is a well-known instrument used to measure the splitting of separatrices in Hamiltonian systems. In this article, we explore how calculation of MA-integral…
We consider steady states of the incompressible Euler equation on two-dimensional domains. For non-radial analytic steady states on bounded simply connected domains, it was shown previously that there…
For any $0\leq \gamma < 1/5$, we construct weak solutions $(v, B, p )$ of the Ideal MHD Equations which do not conserve the total kinetic energy, the cross-helicity and lie in $C^\gamma(\mathbb{T}^3\t…
We disprove a conjecture stated in a recent paper by Arnold and Villasenor concerning the sum and the maximum of independent and identically distributed half-normal random variables. Our method is app…
Gait recognition is a biometric modality that identifies individuals from their characteristic walking patterns. Unlike conventional biometric traits, gait can be acquired at a distance and without ac…
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