Results 51 to 60 of about 65,125 (273)

Hausdorff dimension of three-period orbits in Birkhoff billiards

, 2011
We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.Comment: 10 pages, 1 ...
Falconer K J, Rychlik M, Sergei Merenkov, Stojanov L, Tabachnikov S, Vadim Zharnitsky, Wojtkovski M P   +6 more
core   +1 more source

Polymorphism Crystal Structure Prediction with Adaptive Space Group Diversity Control

Advanced Science, EarlyView.
Polymorphic materials exhibit diverse properties despite identical compositions, but predicting their crystal structures remains challenging. This study introduces ParetoCSP2, a multi‐objective genetic algorithm incorporating genotypic age, energy, and space group diversity.
Sadman Sadeed Omee, Lai Wei, Sourin Dey, Jianjun Hu   +3 more
wiley   +1 more source

Fractional dimension of some exceptional sets in continued fractions

Comptes Rendus. Mathématique
In this paper, we calculate the Hausdorff dimension of some exceptional sets that emerge from specific constraints imposed on the partial quotients of continued fractions.
Hussain, Mumtaz, Smith, Rebecca, Zhang, Zhenliang   +2 more
doaj   +1 more source

On sets containing a unit distance in every direction

Discrete Analysis, 2021
On sets containing a unit distance in every direction, Discrete Analysis 2021:5, 13 pp. A _Kakeya set_ in $\mathbb R^d$ is a subset $A\subset\mathbb R^d$ that contains a line in every direction. Besicovitch famously proved that a Kakeya set in $\mathbb
Pablo Shmerkin, Han Yu
doaj   +1 more source

RefineCatDiff: Toward High‐Quality Medical Image Segmentation via a Categorical Diffusion Refinement Framework

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, Hongjian Yu, Jiaan Huang, Xin Hua, Hengjia Liu, Zhimian Ma, Zhen Wang, Zhijiang Du, Lining Sun   +8 more
wiley   +1 more source

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, Fougère F, Gaspari G, Grossman T, Grossman T, Jean Desbois, Lawler G F, Lawler G F, Mandelbrot B B, Schramm O Sheffield S Wilson D B, Stéphane Ouvry, Werner W, Werner W, Werner W, Werner W   +14 more
core   +1 more source

On the Hausdorff dimension of the Gieseking fractal

Topology and its Applications, 2002
The Cannon-Thurston map \(\phi:\overline{\mathbb{R}}\longrightarrow \overline{\mathbb{C}}\) associated to the Gieseking manifold (a complete, finite-volume, non-orientable, hyperbolic three-manifold) determines a set \(E_{\overline{\mathbb{C}}}\) of those points of \(\overline{\mathbb{C}}\) which are images of at least two points of \(\overline{\mathbb{
Joan Porti, Warren Dicks
openaire   +3 more sources

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, Lei Wang, Shanjun Wu, Jiewei Jiang, Wei Qiang, Yangyang Wang, Shihong Wang, Yi Shao, Wei Chen, Zhongwen Li   +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