Results 51 to 60 of about 66,461 (287)

BMPCQA: Bioinspired Metaverse Point Cloud Quality Assessment Based on Large Multimodal Models

Advanced Intelligent Systems, EarlyView.
This study presents a bioinspired metaverse point cloud quality assessment metric, which simulates the human visual evaluation process to perform the point cloud quality assessment task. It first extracts rendering projection video features, normal image features, and point cloud patch features, which are then fed into a large multimodal model to ...
Huiyu Duan, Kang Fu, Sijing Wu, Yunhao Li, Zicheng Zhang, Qiang Hu, Xiongkuo Min, Guangtao Zhai   +7 more
wiley   +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

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

Fractal Anatomy of Human Organs: A Narrative Review of Structure, Function, and Clinical Perspectives

Clinical Anatomy, EarlyView.
ABSTRACT Fractal geometry describes complex, self‐similar patterns that repeat across spatial scales and is increasingly recognized as relevant in anatomical research. Indeed, the fractal organization is consistently observed in respiratory, cardiovascular, gastrointestinal, nervous, renal, hepatic, and dermatological systems.
Immacolata Belviso, Jacopo Junio Valerio Branca, Giulia Guarnieri, Annamaria Morelli, Alessandra Pacini, Daniele Della Posta, Domenico Ribatti, Ferdinando Paternostro   +7 more
wiley   +1 more source

Hausdorff dimensions for SLE6

The Annals of Probability, 2004
We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all <8, the SLE_ trace has cut-points.
openaire   +4 more sources

Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
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

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

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
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