An efficient implementation of the gliding box lacunarity algorithm

Tolle, Charles R.; McJunkin, Timothy R.; Gorsich, David

doi:10.1016/j.physd.2007.09.017

Cited by 67 publications

(46 citation statements)

References 7 publications

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“…The final dimension in the 2D space is between 1 and 2 (1 ≤ D ≤ 2) [23]. Lacunarity was estimated using the gliding-box algorithm, for different grid orientations [28]. A unit box of size r is chosen randomly and the number of set points p are counted i.e.…”

Section: Lacunaritymentioning

confidence: 99%

Exploiting the Retinal Vascular Geometry in Identifying the Progression to Diabetic Retinopathy Using Penalized Logistic Regression and Random Forests

Leontidis

Al-Diri

Hunter

2016

Emerging Trends and Advanced Technologies for Computational Intelligence

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Many studies have been conducted,investigating the effects that diabetes has to the retinal vasculature. Identifying and quantifying the retinal vascular changes remains a very challenging task, due to the heterogeneity of the retina. Monitoring the progression requires follow-up studies of progressed patients, since human retina naturally adapts to many different stimuli, making it hard to associate any changes with a disease. In this novel study, data from twenty five diabetic patients, who progressed to diabetic retinopathy, were used. The progression was evaluated using multiple geometric features, like vessels widths and angles, tortuosity, central retinal artery and vein equivalent, fractal dimension, lacunarity, in addition to the corresponding descriptive statistics of them. A statistical mixed model design was used to evaluate the significance of the changes between two periods: three years before the onset of diabetic retinopathy and the first year of diabetic retinopathy. Moreover, the discriminative power of these features was evaluated using a random forests classifier and also a penalized logistic regression.The area under the ROC curve after running a ten-fold cross validation was 0.7925 and 0.785 respectively.

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Section: Lacunaritymentioning

confidence: 99%

Exploiting the Retinal Vascular Geometry in Identifying the Progression to Diabetic Retinopathy Using Penalized Logistic Regression and Random Forests

Leontidis

Al-Diri

Hunter

2016

Emerging Trends and Advanced Technologies for Computational Intelligence

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“…First, the record was shifted such that there were no negative values in the time record, the gliding box was centered on each point in the data set, and the (velocity) values within the box were summed. The gliding box lacunarity is defined as (Tolle et al 2008): (6) where: (7) (8) and N was the sample size of the velocity time record.Lacunarity was calculated and plotted as a function of the size of the box, r, in units of seconds (see Fig. 3c,d).…”

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confidence: 99%

Unsteadiness of bivalve clam jet flow according to environmental conditions

Delavan¹,

Webster²

2011

Aquat. Biol.

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To determine whether hard clams Mercenaria mercenaria alter excurrent jet velocity as a function of environmental factors, this laboratory study quantified the excurrent jet velocity as a function of bulk mean crossflow velocity, density of clam patch, and clam size. The excurrent velocity was measured via the non-intrusive particle image velocimetry technique. The flow and unsteady patterns in the time records of vertical velocity near the tip of the excurrent siphon were analyzed by calculating the mean, variance, power spectral density, fractal dimension, lacunarity, and mean jet-to-crossflow ratio. The results revealed that clams vary their excurrent flow characteristics according to bulk mean crossflow velocity; in particular, the texture of the time record of velocity varied. Further, the jet-to-crossflow velocity ratio was larger for smaller clams, and the response of clams to the density of the clam patch was dependent on the size of the animal. These observed behaviors may impact the predation success of blue crabs Callinectes sapidus and knobbed whelks Busycon carica under various environmental conditions. In this context, the results indicated that blue crabs dominate the predator-prey system because of the dependence on clam size and bulk mean crossflow velocity. Alternatively, the varying clam excurrent siphon velocity behavior may provide hydrodynamic signaling of the clam patch recruitment status to settling larvae.KEY WORDS: Predator-prey · Olfactory predation · Jets-in-crossflow · Bivalve · Non-consumptive predator effects · Lacunarity Resale or republication not permitted without written consent of the publisherAquat Biol 13: [175][176][177][178][179][180][181][182][183][184][185][186][187][188][189][190][191] 2011 acteristics of the excurrent flow as a function of bulk mean crossflow velocity and clam size are of interest because the predators of this system, blue crabs and knobbed whelks, both consume clams and use olfactory navigation as a means of locating prey, but the turbulence regimes in which they are successful are highly disparate. Blue crabs are less successful predators during highly turbulent hydrodynamic conditions (Jackson et al. 2007). In contrast, knobbed whelks are successful in highly turbulent regimes (Ferner & Weissburg 2005). Also, blue crabs prefer clams of a small size range despite the fact that they can consume prey over a wide size range (Micheli 1995). Therefore, as clams increase in size, they become less susceptible to predation by blue crabs while maintaining their susceptibility to whelk predation. Thus, there may be alternate strategies for predator avoidance depending on the size of the clams and the turbulence regime of the environment in which they live.The influence of the density of the clam patch was also of interest because there may be predator avoidance strategies depending on the proximity of conspecifics. High-density patches may appear as one large, hard to eat prey to blue crabs, and small clams may have higher survival rates in these ...

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“…The former can give us a measure of complexity of a structure, as long as it can be considered a fractal, just like the retinal network [44]. The latter is a measure of heterogeneity of a fractal structure [45].…”

Section: Fractal Dimension and Lacunaritymentioning

confidence: 99%