Results 81 to 90 of about 3,112 (208)
A Hausdorff dimension for finite sets
CoRR, 2015 The classical Hausdorff dimension of finite or countable sets is zero. We define an analog for finite sets, called finite Hausdorff dimension which is non-trivial. It turns out that a finite bound for the finite Hausdorff dimension guarantees that every point of the set has "nearby" neighbors.
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Journal of Oral Rehabilitation, EarlyView.In this study, an integrated deep learning approach was developed for the evaluation of temporomandibular joint disorders using multicentre CBCT images. The mandibular condyle was first automatically segmented using the nnU‐Net v2 architecture. Subsequently, 3D‐CNN algorithms classified the condyles as healthy or unhealthy and further distinguished ...
İbrahim Şevki Bayrakdar +5 more
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Calculation of Hausdorff dimensions of basins of ergodic measures in encoding spaces
Журнал Белорусского государственного университета: Математика, информатика, 2018 In the article we consider spaces XN of sequences of elements of finite alphabet X (encoding spaces) and ergodic measures on them, basins of ergodic measures and Hausdorff dimensions of such basins with respect to ultrametrics defined by a product of ...
Pavel N. Varabei
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Hausdorff dimension of collision times in one-dimensional log-gases
AIP AdvancesWe consider systems of multiple Brownian particles in one dimension that repel mutually via a logarithmic potential on the real line, more specifically the Dyson model.
Nicole Hufnagel, Sergio Andraus
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On the Visibility of Homogeneous Cantor Sets
Fractal and FractionalThe problems associated with the visible set have been explored by various scholars. In this paper, we investigate the Hausdorff dimension and the topological properties of the visible set in relation to the products of homogeneous Cantor sets.
Yi Cai, Yufei Chen
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Artificial Intelligence in Orthodontics: Part 2—Data Preparation and Performance Evaluation
Orthodontics &Craniofacial Research, EarlyView.ABSTRACT Artificial intelligence (AI) is increasingly integrated into orthodontic research and clinical workflows. Yet, the reliability and clinical value of these systems depend fundamentally on the quality of the data used to train them and the rigour with which their performance is evaluated.
Khuram Naveed +5 more
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On the Hausdorff dimension of circular Furstenberg sets
Discrete AnalysisOn the Hausdorff dimension of circular Furstenberg sets, Discrete Analysis 2024:18, 83 pp. In the late 1990s, Wolff proved the following result. Suppose that the set $E\subset \mathbb R^2$ contains circles centered at all points of a Borel set with ...
Katrin Fässler +2 more
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Projections of measures with small supports
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2021 In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.
Bilel Selmi
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Hausdorff dimension of wild fractals [PDF]
Transactions of the American Mathematical Society, 1992 We show that for every s ∈ [ n
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Computational and Systems Oncology, Volume 6, Issue 1, December 2026.ABSTRACT Breast cancer is still a serious problem in the world arena, where its early and prompt detection is the most important factor in improving patient prognosis and survival. The use of traditional diagnostic techniques, such as imaging (e.g., mammography and ultrasound) and subsequent histopathological examination, is the mainstay, which ...
Likhon Chandra Sarkar +6 more
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