The construction of fractal generalized zone plates from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us, for instance, to increase the number of foci of a conventional fractal zone plate while keeping the self-similarity property within the axial irradiance. The focusing properties of these fractal diffractive optical elements for points not only along but also in the close vicinity of the optical axis are investigated. In both cases analytical expressions for the irradiance are derived. Numerical simulations of the energetic efficiency of fractal generalized zone plates under plane wave illumination are carried out. In addition, some effects on the axial irradiance caused by variations in the area of their transparent rings are shown.
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http://dx.doi.org/10.1364/josaa.26.001161 | DOI Listing |
Imaging Sci Dent
December 2024
Department of Biostatistics and Medical Informatics, Faculty of Medicine, Suleyman Demirel University, Isparta, Turkey.
Purpose: Periarticular and generalized osteoporosis are well-known comorbidities of rheumatoid arthritis (RA), associated with either the disease itself or glucocorticoid therapy. This study was performed to quantitatively evaluate changes in the jawbones of patients with RA using fractal analysis (FA).
Materials And Methods: The study comprised 186 participants, including 144 women and 42 men.
Med Image Anal
November 2024
Department of Radiology and Nuclear Medicine, St. Olav's University Hospital, Trondheim, Norway; Department of Circulation and Medical Imaging, NTNU - Norwegian University of Science and Technology, Trondheim, Norway.
In medical image analysis, the utilization of biophysical models for signal analysis offers valuable insights into the underlying tissue types and microstructural processes. In diffusion-weighted magnetic resonance imaging (DWI), a major challenge lies in accurately estimating model parameters from the acquired data due to the inherently low signal-to-noise ratio (SNR) of the signal measurements and the complexity of solving the ill-posed inverse problem. Conventional model fitting approaches treat individual voxels as independent.
View Article and Find Full Text PDFJ Stat Theory Pract
September 2024
Statistics Online Computational Resource, University of Michigan, 426 North Ingalls Str, Ann Arbor, Michigan 48109-2003.
In this paper, we propose a novel deep neural network (DNN) architecture with fractal structure and attention blocks. The new method is tested to identify and segment 2D and 3D brain tumor masks in normal and pathological neuroimaging data. To circumvent the problem of limited 3D volumetric datasets with raw and ground truth tumor masks, we utilized data augmentation using affine transformations to significantly expand the training data prior to estimating the network model parameters.
View Article and Find Full Text PDFComput Methods Programs Biomed
December 2024
Department of Industrial Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address:
Background And Objective: Cancer's complex and multifaceted nature makes it challenging to identify unique molecular and pathophysiological signatures, thereby hindering the development of effective therapies. This paper presents a novel fractal-fractional cancer model to study the complex interplay among stem cells, effectors cells, and tumor cells in the presence and absence of chemotherapy. The cancer model with effective treatment through chemotherapy drugs is considered and discussed in detail.
View Article and Find Full Text PDFGels
November 2024
Departamento de Ingeniería Química, Universidad Nacional de Colombia Sede Manizales, Campus La Nubia, km 9 vía al Aeropuerto, Manizales 170003, Colombia.
The tanning industry is among the most environmentally harmful activities globally due to the pollution of lakes and rivers from its effluents. Hexavalent chromium, a metal in tannery effluents, has adverse effects on human health and ecosystems, requiring the development of removal techniques. This study assessed the efficacy of organobentonite/alginate hydrogel beads in removing Cr(VI) from a fixed-bed adsorption column system.
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