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fractal dimension

Heiko Hoffmann
The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomena that in the Bak-Tang-Wiesenfeld (BTW) model, sites inside an avalanche area largely return to their original state after the passing of an avalanche, forming, effectively, critically arranged clusters of sites...
February 2018: Physical Review. E
Wei Huang, Pengcheng Hou, Junfeng Wang, Robert M Ziff, Youjin Deng
We study critical bond percolation on a seven-dimensional hypercubic lattice with periodic boundary conditions (7D) and on the complete graph (CG) of finite volume (number of vertices) V. We numerically confirm that for both cases, the critical number density n(s,V) of clusters of size s obeys a scaling form n(s,V)∼s^{-τ}n[over ̃](s/V^{d_{f}^{*}}) with identical volume fractal dimension d_{f}^{*}=2/3 and exponent τ=1+1/d_{f}^{*}=5/2. We then classify occupied bonds into bridge bonds, which includes branch and junction bonds, and nonbridge bonds; a bridge bond is a branch bond if and only if its deletion produces at least one tree...
February 2018: Physical Review. E
Michelangelo Nigro, Davide Viggiano, Vincenzo Ragone, Tiziana Trabace, Annamaria di Palma, Michele Rossini, Giovambattista Capasso, Loreto Gesualdo, Giuseppe Gigliotti
BACKGROUND: The classical approach to the analysis of kidney biopsies is based on semi-quantitative scores of the amount of sclerosis, inflammatory infiltrate, fibrosis and vascular damage. However, advanced renal lesions may be accompanied by a paucity of clinical features and, conversely, important clinical abnormalities may be accompanied by minimal histopathological changes. The objective of this study is to correlate new, semiautomatic, quantitative features of kidney biopsies (e...
March 14, 2018: BMC Nephrology
J M Alonso, A Arroyuelo, P G Garay, O A Martin, J A Vila
There is a need to develop widely applicable tools to understand glycan organization, diversity and structure. We present a graph-theoretical study of a large sample of glycans in terms of finite dimension, a new metric which is an adaptation to finite sets of the classical Hausdorff "fractal" dimension. Every glycan in the sample is encoded, via finite dimension, as a point of Glycan Space, a new notion introduced in this paper. Two major outcomes were found: (a) the existence of universal bounds that restrict the universe of possible glycans and show, for instance, that the graphs of glycans are a very special type of chemical graph, and (b) how Glycan Space is related to biological domains associated to the analysed glycans...
March 13, 2018: Scientific Reports
Ratna Jyothi, Ajay Kumar Nair, Rahul Venugopal, Arun Sasidharan, Prasanta Kumar Ghosh, John P John, Seema Mehrotra, Ravindra Panth, Bindu M Kutty
Meditation, as taught by most schools of practice, consists of a set of heterogeneous techniques. We wanted to assess if EEG profiles varied across different meditation techniques, proficiency levels and experience of the practitioners. We examined EEG dynamics in Vipassana meditators (Novice, Senior meditators and Teachers) while they engaged in their traditional meditation practice (concentration, mindfulness and loving kindness in a structured manner) as taught by S.N. Goenka. Seniors and Teachers (vs Novices) showed trait increases in delta (1-4 Hz), theta-alpha (6-10 Hz) and low-gamma power (30-40 Hz) at baseline rest; state-trait increases in low-alpha (8-10 Hz) and low-gamma power during concentrative and mindfulness meditation; and theta-alpha and low-gamma power during loving-kindness meditation...
March 8, 2018: Biological Psychology
Fabian Sieland, Jenny Schneider, Detlef W Bahnemann
The effects of the particle size distribution on the charge carrier dynamics and the photocatalytic activity of mixed titanium dioxide (TiO2 ) powder samples were investigated in this work. Instead of the synthesis of the small semiconductor particles, the binary particle size distributions of the powders were obtained by mixing commercially available TiO2 powders with different particle sizes. The pure anatase samples (average diameters: 7, 20, and 125 nm, respectively) were created via ultrasound treatment and discreet drying...
March 8, 2018: Physical Chemistry Chemical Physics: PCCP
Maie Bachmann, Laura Päeske, Kaia Kalev, Katrin Aarma, Andres Lehtmets, Pille Ööpik, Jaanus Lass, Hiie Hinrikus
BACKGROUND AND OBJECTIVE: Depressive disorder is one of the leading causes of burden of disease today and it is presumed to take the first place in the world in 2030. Early detection of depression requires a patient-friendly inexpensive method based on easily measurable objective indicators. This study aims to compare various single-channel electroencephalographic (EEG) measures in application for detection of depression. METHODS: The EEG recordings were performed on a group of 13 medication-free depressive outpatients and 13 gender and age matched controls...
March 2018: Computer Methods and Programs in Biomedicine
Frank Bossler, Johannes Maurath, Katrin Dyhr, Norbert Willenbacher, Erin Koos
The rheological properties of a particle suspension can be substantially altered by adding a small amount of a secondary fluid that is immiscible with the bulk phase. The drastic change in the strength of these capillary suspensions arises due to the capillary forces, induced by the added liquid, leading to a percolating particle network. Using rheological scaling models, fractal dimensions are deduced from the yield stress and from oscillatory strain amplitude sweep data as function of the solid volume fraction...
January 2018: Journal of Rheology
Yoshihiro Kurata, Koichi Hayano, Gaku Ohira, Kazuo Narushima, Tomoyoshi Aoyagi, Hisahiro Matsubara
PURPOSE: The purpose of this study is to assess the heterogeneity of tumor enhancement using fractal analysis on contrast-enhanced computed tomography (CE-CT) for predicting malignant potential of gastrointestinal stromal tumor (GIST). METHODS: We retrospectively identified 64 patients (36 M/28 W; median age: 65) with GISTs who received CE-CT and 18F-fluorodeoxyglucose positron emission tomography (FDG-PET) followed by curative surgery. Fractal analysis was applied to CE-CT image, and fractal dimension (FD) was measured...
March 3, 2018: Abdominal Radiology
Gareth J McKay, Euan N Paterson, Alexander P Maxwell, Christopher C Cardwell, Ruixuan Wang, Stephen Hogg, Thomas J MacGillivray, Emanuele Trucco, Alexander S Doney
The eye provides an opportunistic "window" to view the microcirculation. There is published evidence of an association between retinal microvascular calibre and renal function measured by estimated glomerular filtration rate (eGFR) in individuals with diabetes mellitus. Beyond vascular calibre, few studies have considered other microvascular geometrical features. Here we report novel null findings for measures of vascular spread (vessel fractal dimension), tortuosity, and branching patterns and their relationship with renal function in type 2 diabetes over a mean of 3 years...
March 2, 2018: Scientific Reports
Xin Chen, Jim Graham, Ioannis N Petropoulos, Georgios Ponirakis, Omar Asghar, Uazman Alam, Andrew Marshall, Maryam Ferdousi, Shazli Azmi, Nathan Efron, Rayaz A Malik
Objective: Corneal confocal microscopy (CCM), an in vivo ophthalmic imaging modality, is a noninvasive and objective imaging biomarker for identifying small nerve fiber damage. We have evaluated the diagnostic performance of previously established CCM parameters to a novel automated measure of corneal nerve complexity called the corneal nerve fiber fractal dimension (ACNFrD). Methods: A total of 176 subjects (84 controls and 92 patients with type 1 diabetes) with and without diabetic sensorimotor polyneuropathy (DSPN) underwent CCM...
February 1, 2018: Investigative Ophthalmology & Visual Science
Zhongfan Zhu, Dingzhi Peng, Jie Dou
In this study, Couette flow experiments were performed to estimate the temporal evolution of the 2D and perimeter-based fractal dimension values of kaolinite flocs during flocculation. The fractal dimensions were calculated based on the projected surface area, perimeter length and length of the longest axis of the flocs as determined by sampling observation and an image-processing system. The 2D fractal dimension, which relates the longest axis length and projected surface area of flocs, was found to decrease with the flocculation time, corresponding to the production of some porous flocs from the flow shear...
February 2018: Water Science and Technology: a Journal of the International Association on Water Pollution Research
Constantinos Makrides, Ming Li, Eite Tiesinga, Svetlana Kotochigova
Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions...
February 2018: Science Advances
Natasa Popovic, Miroslav Radunovic, Jelena Badnjar, Tomo Popovic
Hypertension and diabetes mellitus represent modifiable risk factors for vascular disease. They cause microvascular remodeling, and ultimately result in end-organ damage. Therefore, development of methods for noninvasive quantification of the effects of hypertension and diabetes mellitus on microvasculature is of paramount importance. The two goals of the study were: 1) to characterize the geometric complexity and inhomogeneity of retinal vasculature in hypertensive retinopathy (HR) and in proliferative diabetic retinopathy (PDR) by using box counting fractal dimension and lacunarity analysis, and 2) to determine if the combination of these two parameters can be used to describe differences in the vascular tree geometry between HR and PDR...
February 21, 2018: Microvascular Research
Karthik Subramaniam, Alys R Clark, Eric A Hoffman, Merryn H Tawhai
Altered parenchymal microstructure and complexity have been observed in older age. How to distinguish between healthy, expected changes and early signs of pathology remains poorly understood. An objective quantitative analysis of computed tomography (CT) imaging was conducted to compare mean lung density (MLD), tissue density distributions, and tissue heterogeneity in 16 subjects - 8 aged >60 years who were gender- and BMI-matched with 8 subjects aged <30 years. Subjects were never-smoking, with no prior respiratory disease, and no radiologically-identified abnormalities on CT...
February 22, 2018: Journal of Applied Physiology
Anastasia Spyrogianni, Katerina S Karadima, Eirini Goudeli, Vlasis G Mavrantzas, Sotiris E Pratsinis
Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO 2 agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys...
February 14, 2018: Journal of Chemical Physics
Fredrik K Eriksen, Renaud Toussaint, Antoine Léo Turquet, Knut J Måløy, Eirik G Flekkøy
By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements...
January 2018: Physical Review. E
Jie Lin, Matthieu Wyart
The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n=1/β. A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β=2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β=1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β, which is instead significantly affected by finite-dimensional effects...
January 2018: Physical Review. E
Franziska Taubert, Rico Fischer, Jürgen Groeneveld, Sebastian Lehmann, Michael S Müller, Edna Rödig, Thorsten Wiegand, Andreas Huth
Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes...
February 14, 2018: Nature
Francesco Moroni, Marco Magnoni, Vittoria Vergani, Enrico Ammirati, Paolo G Camici
BACKGROUND AND AIMS: Plaque border irregularity is a known imaging characteristic of vulnerable plaques, but its evaluation heavily relies on subjective evaluation and operator expertise. Aim of the present work is to propose a novel fractal-analysis based method for the quantification of atherosclerotic plaque border irregularity and assess its relation with cardiovascular risk factors. METHODS AND RESULTS: Forty-two asymptomatic subjects with carotid stenosis underwent ultrasound evaluation and assessment of cardiovascular risk factors...
2018: PloS One
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