Results 41 to 50 of about 3,079 (209)
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
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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 κ<8, the SLE_κ trace has cut-points.
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Errata to ‘Hausdorff dimension for horseshoes’ [PDF]
Ergodic Theory and Dynamical Systems, 1985 In our paper ‘Hausdorff dimension for horseshoes’ (H. McCluskey and A. Manning, Ergod. Th. & Dynam. Sys. (1983) 3, 251–260), § 3 entitled ‘Continuity across a bifurcation’ should be deleted since the proof of theorem 3 there is wrong.The mistake is that does not in fact imply that δs → 1.
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Cell Segmentation Beyond 2D—A Review of the State‐of‐the‐Art
Advanced Intelligent Discovery, EarlyView.Cell segmentation underpins many biological image analysis tasks, yet most deep learning methods remain limited to 2D despite the inherently 3D nature of cellular processes. This review surveys segmentation approaches beyond 2D, comparing 2.5D and fully 3D methods, analyzing 31 models and 32 volumetric datasets, and introducing a unified reference ...
Fabian Schmeisser +6 more
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A. Baker's conjecture and Hausdorff dimension
Publicationes Mathematicae Debrecen, 2000 Let \(M_n(\varepsilon)\) (for \(n\in \mathbb N\) and for \(\varepsilon >0\)) denote the set of \(x\in \mathbb R\) such that the inequality \[ |P(x)|
Beresnevich, V., Bernik, V.
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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 +7 more
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Fractional dimension of some exceptional sets in continued fractions
Comptes Rendus. MathématiqueIn 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 +2 more
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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
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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
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Nearly-doubling spaces of persistence diagrams
Journal of Computational Geometry, 2023 The space of persistence diagrams under bottleneck distance is known to have infinite doubling dimension. Because many metric search algorithms and data structures have bounds that depend on the dimension of the search space, the high dimensionality ...
Donald Sheehy, Siddharth Sheth
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