Related papers: Fractal Dimension and Retinal Pathology: A Meta-an…
This paper surveys work on the relation between fractal dimensions and algorithmic information theory over the past thirty years. It covers the basic development of prefix-free Kolmogorov complexity from an information theoretic point of…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
Retinal vessel segmentation is a fundamental step in screening, diagnosis, and treatment of various cardiovascular and ophthalmic diseases. Robustness is one of the most critical requirements for practical utilization, since the test images…
Identifying lesions in fundus images is an important milestone toward an automated and interpretable diagnosis of retinal diseases. To support research in this direction, multiple datasets have been released, proposing groundtruth maps for…
We explore the fractal nature of particle showers using Monte-Carlo simulation. We define the fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
Cause-effect relationships are typically evaluated by comparing outcome responses to binary treatment values, representing two arms of a hypothetical randomized controlled trial. However, in certain applications, treatments of interest are…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
Retinal imaging is fast, non-invasive, and widely available, offering quantifiable structural and vascular signals for ophthalmic and systemic health assessment. This accessibility creates an opportunity to study how quantitative retinal…
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the…
This work joins aspects of reservoir optimization, information-theoretic optimal encoding, and at its center fractal analysis. We build on the observation that, due to the recursive nature of recurrent neural networks, input sequences…
The morphology of blood vessels in retinal fundus images is an important indicator of diseases like glaucoma, hypertension and diabetic retinopathy. The accuracy of retinal blood vessels segmentation affects the quality of retinal image…
We introduce fractal liquids by generalizing classical liquids of integer dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the…
We investigate the Ferrofluid Drop Targeting (FDT) for the treatment of the Retinal Detachment (RD), considering, for the first time, the real 3D geometry of an eye and magnets configurations as well as the viscoelastic rheology of the…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
Medical Imaging is one of the growing fields in the world of computer vision. In this study, we aim to address the Diabetic Retinopathy (DR) problem as one of the open challenges in medical imaging. In this research, we propose a new lesion…
This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard $\varepsilon$ expansion interpolates between integer spacetime dimensions, a new parameter, $\delta$, is used to…
Retinal diseases spanning a broad spectrum can be effectively identified and diagnosed using complementary signals from multimodal data. However, multimodal diagnosis in ophthalmic practice is typically challenged in terms of data…
Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a…