Results 51 to 60 of about 2,769 (160)

Dimension inequalities of multifractal Hausdorff measures and multifractal packing measures

MATHEMATICA SCANDINAVICA, 2000
Given a Borel probability measure \(\mu\) on \({\mathbb R}^n\), the core of multifractal analysis consists of computing the (Hausdorff) dimensional multifractal spectrum of \(\mu\), that is, \[ f_{\mu}(\alpha)=\text{ dim}\left\{x: \alpha_{\mu}(x):= \lim_{r\rightarrow 0}{\log\mu B(x,r)\over \log r}=\alpha\right\}, \] and then establishing whether the ...
openaire   +3 more sources

Machine Learning for Local Detection of Separators in Three‐Dimensional Magnetic Fields

Journal of Geophysical Research: Machine Learning and Computation, Volume 3, Issue 3, June 2026.
Abstract Magnetic reconnection is a major plasma phenomenon occurring in various key environments ranging from the Sun and near‐Earth space to astrophysical plasmas. While magnetic reconnection is relatively well‐understood under two‐dimensional (2D) settings, it remains challenging to characterize in three‐dimensional (3D) magnetic fields.
Fanni Franssila, Markku Alho, Ioanna Bouri, Daniel Holmberg, Minna Palmroth, Teemu Roos   +5 more
wiley   +1 more source

Local dimensions in Moran constructions

, 2015
We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^q$-dimensions.
Käenmäki, Antti, Li, Bing, Suomala, Ville   +2 more
core   +1 more source

An extended definition of Anosov representation for relatively hyperbolic groups

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich–Leeb and Zhu, and Zhu–Zimmer, as well as holonomy representations of various ...
Theodore Weisman
wiley   +1 more source

SpineMAE: A bone‐window self‐supervised and structure‐aware framework for 3D cervical vertebra segmentation and fracture classification

Journal of Applied Clinical Medical Physics, Volume 27, Issue 5, May 2026.
Abstract Introduction Accurate segmentation and classification of cervical spine fractures are essential for timely diagnosis and clinical decision‐making in trauma care. Existing deep learning approaches often require extensive manual annotations and struggle to maintain anatomical consistency across vertebral levels, limiting their reliability and ...
Qing Liang, Jingding Zhao, Fang Yang, Lin Shi, Yang Song, Xianjun Chen, Zewen Shi, Qingjiang Pang   +7 more
wiley   +1 more source

Measures and the Law of the Iterated Logarithm

, 2009
Let m be a unidimensional measure with dimension d. A natural question is to ask if the measure m is comparable with the Hausdorff measure (or the packing measure) in dimension d.
Bhouri, Imen, Heurteaux, Yanick
core   +1 more source

Notions of denseness

, 1999
The notion of a completely saturated packing [Fejes Toth, Kuperberg and Kuperberg, Highly saturated packings and reduced coverings, Monats. Math. 125 (1998) 127-145] is a sharper version of maximum density, and the analogous notion of a completely ...
Fejes Tóth, Fejes Tóth, Greg Kuperberg, Morse, Thurston   +4 more
core   +3 more sources

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1151-1298, May 2026.
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

Comparing Two Novel LiDAR‐Based Indices for Quantifying Forest Structural Complexity

Ecology and Evolution, Volume 16, Issue 5, May 2026.
This study compares two LiDAR‐derived forest structural complexity indices: the fractal‐based box dimension (Db$$ {D}_b $$) and the entropy‐based canopy entropy (CE$$ CE $$). Analysis of 170 plots revealed a strong linear correlation (r = 0.823) between Db$$ {D}_b $$ and CE$$ CE $$, but computation was much slower.
Tillman Reuter, Sebastian Seidel, Dominik Seidel   +2 more
wiley   +1 more source

From Low Field to High Value: Robust Cortical Mapping From Low‐Field MRI

Human Brain Mapping, Volume 47, Issue 7, May 2026.
Recon‐any processes a brain MRI acquired with arbitrary contrast, resolution, and field strength to generate morphometric measurements comparable to FreeSurfer's recon‐all, including cortical (parcellation, thickness, etc.) and volumetric (segmentation, regional volumes) outputs.
Karthik Gopinath, Annabel Sorby‐Adams, Jonathan Williams‐Ramirez, Dina Zemlyanker, Jennifer Guo, David Hunt, Christine L. Mac Donald, C. Dirk Keene, Timothy Coalson, Matthew F. Glasser, David Van Essen, Matthew S. Rosen, Oula Puonti, W. Taylor Kimberly, Juan Eugenio Iglesias, Alzheimer's Disease Neuroimaging Initiative   +15 more
wiley   +1 more source