Results 31 to 40 of about 3,294 (223)
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
wiley +1 more source
Crystal Structure Prediction of Inorganic Materials: A Benchmark and Modern Evaluation
Advanced Intelligent Discovery, EarlyView.Predicting a crystal’s structure from composition alone is a long‐standing challenge in materials discovery. The CSP180 benchmark of 180 inorganic crystals evaluates thirteen crystal structure prediction algorithms requiring no density functional theory (DFT) against DFT‐based baselines across twelve metrics.
Lai Wei +9 more
wiley +1 more source
Anyons and fractional quantum Hall effect in fractal dimensions
Physical Review Research, 2020 The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal ...
Sourav Manna +3 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 $\mathbb
Pablo Shmerkin, Han Yu
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Kolmogorov complexity and Hausdorff dimension
Information and Computation, 1989 This interesting note develops several formal relationships between program-size complexity of infinite strings and various measures of information content. The idea is to bound the complexity of a maximally complex string in a prescribed set of strings by the Hausdorff dimension as well as the entropy of that set.
openaire +3 more sources
Hausdorff Dimension and Quasiconformal Mappings [PDF]
Journal of the London Mathematical Society, 1973 Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135677/1/jlms0504 ...
Gehring, F. W., Väisälä, J.
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 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
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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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A Geometric Characterization of Steady Laminar Flow
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
wiley +1 more source