Results 51 to 60 of about 3,791,283 (277)
Numerical studies of planar closed random walks
, 2008 Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$.
Comtet A +14 more
core +1 more source
Advanced Intelligent Systems, EarlyView.This study proposes RefineCatDiff, a refinement framework for high‐quality medical image segmentation. By developing a categorical distribution‐based discrete diffusion process for refinement, the framework aligns well with the characteristics of image segmentation tasks. Experimental results on multiple datasets across different modalities demonstrate
Feng Liu +8 more
wiley +1 more source
Hausdorff dimension, intersections of projections and exceptional plane sections [PDF]
, 2015 This paper contains new results on two classical topics in fractal geometry: projections, and intersections with affine planes. To keep the notation of the abstract simple, we restrict the discussion to the planar cases of our theorems.
P. Mattila, Tuomas Orponen
semanticscholar +1 more source
Mainstream Artificial Intelligence Technologies in Contemporary Ophthalmology
Advanced Intelligent Systems, EarlyView.This review explores the latest artificial intelligence (AI) technologies in ophthalmology, focusing on four key data types: medical imaging, electronic health records, robotic‐assisted surgery, and genomics. It examines the structural features, use cases, clinical goals, and evaluation metrics of various AI algorithms, while also introducing emerging ...
Shiqi Yin +9 more
wiley +1 more source
Some Dimensional Results of a Class of Homogeneous Moran Sets
Journal of Mathematics, 2021 In this paper, we construct a class of special homogeneous Moran sets: mk-quasi-homogeneous perfect sets, and obtain the Hausdorff dimension of the sets under some conditions.
Jingru Zhang, Yanzhe Li, Manli Lou
doaj +1 more source
Sierpiński Fractals and the Dimension of Their Laplacian Spectrum
Mathematical and Computational Applications, 2023 We establish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated with Sierpiński lattices and infinite Sierpiński gaskets and other post-critically finite self-similar sets.
Mark Pollicott, Julia Slipantschuk
doaj +1 more source
Hausdorff dimension of unique beta expansions [PDF]
, 2014 Given an integer N ⩾ 2 and a real number β > 1, let Γβ, N be the set of all with di ∈ {0, 1, ···, N − 1} for all i ⩾ 1. The infinite sequence (di) is called a β-expansion of x. Let Uβ,N be the set of all x's in Γβ,N which have unique β-expansions.
D. Kong, Wenxia Li
semanticscholar +1 more source
Advanced Intelligent Systems, EarlyView.This article introduces EndoARSS, a novel multitask learning framework that combines surgical activity recognition and semantic segmentation for endoscopic surgery. Utilizing the foundation model with novel modules like task efficient shared low‐rank adapters and spatially aware multiscale attention, EndoARSS can effectively tackle challenges in ...
Guankun Wang +5 more
wiley +1 more source
The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
International Journal of Mathematics and Mathematical Sciences, 2002 We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have ...
Hongwen Guo, Dihe Hu
doaj +1 more source
Effective dimension in some general metric spaces [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We introduce the concept of effective dimension for a general metric space. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to Euclidean space.
Elvira Mayordomo
doaj +1 more source