Search results for "Fractals"
showing 10 items of 40 documents
An Ultrasonic Lens Design Based on Prefractal Structures
2016
The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. Thus, both a Fresnel ultrasonic lens and an arrangement of rigid rings based on Cantor prefractals are analyzed. Results show that the focusing capacity of the modified fractal lens is better than the Fresnel lens. This new lens is believed to have potential applications for ultrasonic imaging and medical ultrasound fields.
Temporal Structure of Human Gaze Dynamics Is Invariant During Free Viewing.
2015
We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher or…
The p-Laplacian with respect to measures
2013
We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
VAMPIRE: Vessel assessment and measurement platform for images of the REtina
2011
We present VAMPIRE, a software application for efficient, semi-automatic quantification of retinal vessel properties with large collections of fundus camera images. VAMPIRE is also an international collaborative project of four image processing groups and five clinical centres. The system provides automatic detection of retinal landmarks (optic disc, vasculature), and quantifies key parameters used frequently in investigative studies: vessel width, vessel branching coefficients, and tortuosity. The ultimate vision is to make VAMPIRE available as a public tool, to support quantification and analysis of large collections of fundus camera images.
The effect of fractal contact lenses on peripheral refraction in myopic model eyes.
2014
Purpose: To test multizone contact lenses in model eyes: Fractal Contact Lenses (FCLs), designed to induce myopic peripheral refractive error (PRE). Methods: Zemax ray-tracing software was employed to simulate myopic and accommodation-dependent model eyes fitted with FCLs. PRE, defined in terms of mean sphere M and 90–180 astigmatism J180, was computed at different peripheral positions, ranging from 0 to 35 in steps of 5, and for different pupil diameters (PDs). Simulated visual performance and changes in the PRE were also analyzed for contact lens decentration and model eye accommodation. For comparison purposes, the same simulations were performed with another commercially available conta…
Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development
2005
The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.
Analysis of 55 cases of adenomatoid odontogenic tumor in an Indian population and review of literature
2021
Background This study reviews the demographic, clinical and radiographic features of adenomatoid odontogenic tumor(AOT) diagnosed in an Indian population over 50 years and also evaluate and compare follicular AOT(F-AOT) and extra-follicular AOT(EF-AOT). Material and Methods 55 diagnosed cases of AOT from 1971-2020 were studied retrospectively. The data regarding the age, sex, location, variant of AOT, duration, clinical features, radiographic appearance, treatment and recurrence were collected and analysed. Results Of the 722 odontogenic tumors diagnosed, 7.6% were AOTs with higher prevalence of extra-follicular (67.3%) than follicular (32.7%) variant. All the tumors were intraosseous with …
Fractal dimension versus density of built-up surfaces in the periphery of Brussels
2007
International audience; This paper aims at showing the usefulness of the fractal dimension for characterizing the spatial structure of the built-up surfaces within the periurban fringe. We first discuss our methodology and expectations in terms of operationality of the fractal dimension theoretically and geometrically. An empirical analysis is then performed on the southern periphery of Brussels (Brabant Wallon). The empirical analysis is divided into two parts: first, the effect of the size and shape of the windows on the fractal measures is empirically evaluated; this leads to a methodological discussion about the importance of the scale of analysis as well as the real sense of fractality…
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
2006
We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
Fingerprinting white marbles of archaeometric interest by means of combined SANS and USANS
2007
We have performed a series of USANS and SANS measurements on a selected group of marble samples characterized by similar chemical composition but wide range of known metamorphic conditions. With these samples we start the building up of a data base in an attempt to correlate metamorphism and mesoscopic structure of white marbles. Experimental data have been analysed in terms of a hierarchical model. The present data highlight the importance of the structure at meso scale in identifying the provenance of the marble samples. A remarkable simple relation between the model parameters and the metamorphic degree has been found. This curve might represent a master curve to allow fingerprinting of …