Results 51 to 60 of about 3,079 (209)
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.
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Effective dimension in some general metric spaces [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We introduce the concept of effective dimension for a general metric space. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to Euclidean space.
Elvira Mayordomo
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Hausdorff dimension and oracle constructions
Theoretical Computer Science, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Sierpiński Fractals and the Dimension of Their Laplacian Spectrum
Mathematical and Computational Applications, 2023 We establish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated with Sierpiński lattices and infinite Sierpiński gaskets and other post-critically finite self-similar sets.
Mark Pollicott, Julia Slipantschuk
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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
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The μ-topological Hausdorff dimension
Extracta Mathematicae, 2019 In 2015, R. Balkaa, Z. Buczolich and M. Elekes introduced the topological Hausdorff dimension which is a combination of the definitions of the topological dimension and the Hausdorff dimension.
Hela Lofti
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ChemSusChem, Volume 18, Issue 6, March 15, 2025.The product profile of enzymatically hydrolyzed PET can be modified by medium engineering and thereby adapted to a desired product. TPA, MHET or BHET can be forced as the predominant product using a basic pH (blue), 25 % ethylene glycol (EG) and IsPETasewt (green) or ≥25 % EG and LCCICCG (pink), respectively.
Tobias Heinks +8 more
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Synchrotron‐Based Deep Learning Network of the Inner Ear: Development and Expert Validation
The Laryngoscope, EarlyView.A deep learning network to automatically segment the inner ear from preoperative clinical scans was developed using synchrotron‐radiation phase contrast imaging (SR‐PCI). On an unseen test set, the network significantly outperformed seven expert otologists/radiologists, the mean expert segmentation, and a simultaneous truth and performance level ...
Ashley Micuda +11 more
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On fractal faithfulness and fine fractal properties of random variables with independent -digits
Modern Stochastics: Theory and Applications, 2016 We develop a new technique to prove the faithfulness of the Hausdorff–Besicovitch dimension calculation of the family $\varPhi ({Q}^{\ast })$ of cylinders generated by ${Q}^{\ast }$-expansion of real numbers.
Muslem Ibragim, Grygoriy Torbin
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Laser &Photonics Reviews, EarlyView.Bayesian optimization combined with in situ quantitative phase imaging enables autonomous correction of layer‐height deviations in projection multi‐photon lithography. By jointly tuning model parameters and grayscale exposure settings, the method achieves more uniform and accurate layers within 300 prints, offering a fast, data‐efficient route to ...
Jason E. Johnson, Xianfan Xu
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