Results 21 to 30 of about 187 (146)
Multifractal Structure of Irregular Sets via Weighted Random Sequences
Fractal and FractionalWe study the multifractal structure of irregular sets arising from Fibonacci-weighted sums of sequences of random variables. Focusing on Cantor-type subsets Kε of the unit interval, we construct sequences of free and forced blocks, where the free blocks ...
Najmeddine Attia, Taoufik Moulahi
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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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On interpreting Patterson–Sullivan measures of geometrically finite groups as Hausdorff and packing measures [PDF]
Ergodic Theory and Dynamical Systems, 2015 We provide a new proof of a theorem whose proof was sketched by Sullivan [Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics.Acta Math.149(3–4) (1982), 215–237], namely that if the Poincaré exponent of a geometrically finite Kleinian group$G$is strictly between its minimal and maximal cusp ranks, then ...
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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
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Multifractal Analysis of Refined Sets in Branching Random Walks on Galton–Watson Trees
Fractal and FractionalIn this paper, we investigate refined level sets associated with branching random walks on the boundary of a supercritical Galton–Watson tree. More precisely, for a prescribed deterministic sequence s:=(rn,r˜n), we introduce refined deviation sets ...
Najmeddine Attia
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Journal of Medical Radiation Sciences, EarlyView.This study compares two techniques for creating lead shielding masks to replace the current process for superficial/orthovoltage facial radiotherapy: Plaster Cast Positive Mould (PCPM), CT Scanned 3D Print (CT3DP), and Optical Scan 3D Print (OS3DP). CT3DP was found to be more accurate and preferred over OS3DP.
Rory Hartley +6 more
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Knee Surgery, Sports Traumatology, Arthroscopy, EarlyView.Abstract Purpose Efficient and reliable magnetic resonance imaging (MRI)‐based diagnosis of early avascular necrosis of the femoral head (AVNFH) is essential for guiding treatment but remains challenging due to variability in clinician experience. Deep learning (DL) models offer a promising solution. This review evaluates and summarizes the performance
Khaled Skaik +4 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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A note on the generalized Hausdorff and packing measures of product sets in metric space
Mathematical Inequalities & Applications, 2022 Let $μ$ and $ν$ be two Borel probability measures on two separable metric spaces $\X$ and $\Y$ respectively. For $h, g$ be two Hausdorff functions and $q\in \R$, we introduce and investigate the generalized pseudo-packing measure ${\RRR}_μ^{q, h}$ and the weighted generalized packing measure ${\QQQ}_μ^{q, h}$ to give some product inequalities ...
Guedri, Rihab, Attia, Najmeddine
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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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