Statistics in Medicine, ISSN 0277-6715, 08/2015, Volume 34, Issue 18, pp. 2636 - 2661

Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer...

Quermass‐interaction process | breast cancer | Hausdorff measure | pathology | box‐counting dimension | Pathology | Quermass-interaction process | Breast cancer | Box-counting dimension | MEDICINE, RESEARCH & EXPERIMENTAL | WAVELET ANALYSIS | MEDICAL INFORMATICS | RANDOM SETS | SPACES | STATISTICS & PROBABILITY | box-counting dimension | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | CARCINOGENESIS | DIMENSION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | TISSUES | UNIONS | DISCS | Risk Assessment - methods | Algorithms | Stochastic Processes | Breast Neoplasms - pathology | Computer Simulation | Humans | Diagnosis, Computer-Assisted - methods | Female | Breast Neoplasms - diagnosis | Fractals | Pathology - methods | Carcinoma, Ductal, Breast | Case studies | Models | Analysis

Quermass‐interaction process | breast cancer | Hausdorff measure | pathology | box‐counting dimension | Pathology | Quermass-interaction process | Breast cancer | Box-counting dimension | MEDICINE, RESEARCH & EXPERIMENTAL | WAVELET ANALYSIS | MEDICAL INFORMATICS | RANDOM SETS | SPACES | STATISTICS & PROBABILITY | box-counting dimension | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | CARCINOGENESIS | DIMENSION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | TISSUES | UNIONS | DISCS | Risk Assessment - methods | Algorithms | Stochastic Processes | Breast Neoplasms - pathology | Computer Simulation | Humans | Diagnosis, Computer-Assisted - methods | Female | Breast Neoplasms - diagnosis | Fractals | Pathology - methods | Carcinoma, Ductal, Breast | Case studies | Models | Analysis

Journal Article

Chaos, Solitons and Fractals, ISSN 0960-0779, 2011, Volume 44, Issue 4, pp. 335 - 341

► The electric field in a composite dielectric with a fractal charge distribution is observed. ► The observation is based on a relation between fractal...

DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RANDOM-WALK

DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RANDOM-WALK

Journal Article

2000, Progress in probability, ISBN 9780817662158, Volume 46., x, 292

Book

2004, Progress in probability, ISBN 376437070X, Volume 57., x, 262

Book

1982, Rev. ed. of Fractals, c1977., 460 p., [1] leaf of plates

Book

Remote Sensing, ISSN 2072-4292, 05/2017, Volume 9, Issue 5, p. 445

Microwave remote sensing can measure surface geometry. Via the processing of the Synthetic Aperture Radar (SAR) data, the earth surface geometric parameters...

Random fractal geometry | Synthetic Aperture Radar (SAR) | Integral Equation Model (IEM) | BACKSCATTERING | SURFACE PARAMETERS | INTEGRAL-EQUATION MODEL | SYNTHETIC-APERTURE RADAR | C-BAND | REMOTE SENSING | random fractal geometry | SEMIEMPIRICAL CALIBRATION | SOIL-MOISTURE RETRIEVAL | DUBOIS | ROUGH SURFACES | Parameter estimation | Fractal geometry | Backscattering | Images | Data processing | Fractals | Surface roughness | Mapping | Spectra | Earth surface | Remote sensing | Dispersion | Geometry | Morphology | Radar | Geological mapping | Radar imaging | Models | Mathematical models | Detection | Surface geometry | Synthetic aperture radar

Random fractal geometry | Synthetic Aperture Radar (SAR) | Integral Equation Model (IEM) | BACKSCATTERING | SURFACE PARAMETERS | INTEGRAL-EQUATION MODEL | SYNTHETIC-APERTURE RADAR | C-BAND | REMOTE SENSING | random fractal geometry | SEMIEMPIRICAL CALIBRATION | SOIL-MOISTURE RETRIEVAL | DUBOIS | ROUGH SURFACES | Parameter estimation | Fractal geometry | Backscattering | Images | Data processing | Fractals | Surface roughness | Mapping | Spectra | Earth surface | Remote sensing | Dispersion | Geometry | Morphology | Radar | Geological mapping | Radar imaging | Models | Mathematical models | Detection | Surface geometry | Synthetic aperture radar

Journal Article

1977, ISBN 9780716704744, xvi, 365

Book

COMPTES RENDUS GEOSCIENCE, ISSN 1631-0713, 05/2017, Volume 349, Issue 3, pp. 114 - 125

Determining surface morphology using synthetic aperture radar (SAR) data requires accurate topographic and microtopographic models. To distinguish different...

BACKSCATTERING | GEOSCIENCES, MULTIDISCIPLINARY | INTEGRAL-EQUATION MODEL | Integral Equation Model (IEM) | Random Fractal Geometry | SEMIEMPIRICAL CALIBRATION | TERRASAR-X | BAND | PARAMETERS | Synthetic Aperture Radar (SAR) | SCATTERING

BACKSCATTERING | GEOSCIENCES, MULTIDISCIPLINARY | INTEGRAL-EQUATION MODEL | Integral Equation Model (IEM) | Random Fractal Geometry | SEMIEMPIRICAL CALIBRATION | TERRASAR-X | BAND | PARAMETERS | Synthetic Aperture Radar (SAR) | SCATTERING

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2014, Volume 279, pp. 212 - 226

Natural rock, such as sandstone, has a large number of discontinuous, multi-scale, geometry-irregular pores, forming a complex porous structure. This porous...

Mechanical properties | Fractal system control function | Porous structure | Sandstone | Three-dimensional reconstruction | Simulated annealing | PERMEABILITY | MICROTOMOGRAPHY | RANDOM-MEDIA | MICROSTRUCTURES | MARINE-SEDIMENTS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FLUID | ATTENUATION | SANDSTONE PORES | PROPAGATION | GEOMETRY | Control systems | Analysis | Algorithms | Reconstruction | Rock | Fractal analysis | Fractals | Mathematical models | Three dimensional

Mechanical properties | Fractal system control function | Porous structure | Sandstone | Three-dimensional reconstruction | Simulated annealing | PERMEABILITY | MICROTOMOGRAPHY | RANDOM-MEDIA | MICROSTRUCTURES | MARINE-SEDIMENTS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FLUID | ATTENUATION | SANDSTONE PORES | PROPAGATION | GEOMETRY | Control systems | Analysis | Algorithms | Reconstruction | Rock | Fractal analysis | Fractals | Mathematical models | Three dimensional

Journal Article

1994, Wiley series in probability and mathematical statistics. Applied probability and statistics, ISBN 9780471937579, xiv, 389

Book

Nature Chemistry, ISSN 1755-4330, 06/2010, Volume 2, Issue 6, pp. 472 - 477

It has long been appreciated that the transport properties of molecules can control reaction kinetics. This effect can be characterized by the time it takes a...

ORGANIZATION | ANOMALOUS DIFFUSION | 1ST-PASSAGE TIMES | CHICKEN ERYTHROCYTE NUCLEI | FRACTAL NATURE | CHROMATIN | FLUORESCENCE | RANDOM-WALKS | MOLECULE | DYNAMICS | CHEMISTRY, MULTIDISCIPLINARY | Transcription Factors - metabolism | Animals | Humans | Transcription, Genetic | Catalysis | Kinetics | Cell Nucleus

ORGANIZATION | ANOMALOUS DIFFUSION | 1ST-PASSAGE TIMES | CHICKEN ERYTHROCYTE NUCLEI | FRACTAL NATURE | CHROMATIN | FLUORESCENCE | RANDOM-WALKS | MOLECULE | DYNAMICS | CHEMISTRY, MULTIDISCIPLINARY | Transcription Factors - metabolism | Animals | Humans | Transcription, Genetic | Catalysis | Kinetics | Cell Nucleus

Journal Article

Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 02/2019, Volume 29, Issue 2, p. 023105

In this work, we consider a class of recursively grown fractal networks Gn(t) whose topology is controlled by two integer parameters, t and n. We first analyse...

MATHEMATICS, APPLIED | TIMES | RANDOM-WALKS | DYNAMICS | PHYSICS, MATHEMATICAL | KEMENYS CONSTANT | GEOMETRY | Physics - Statistical Mechanics

MATHEMATICS, APPLIED | TIMES | RANDOM-WALKS | DYNAMICS | PHYSICS, MATHEMATICAL | KEMENYS CONSTANT | GEOMETRY | Physics - Statistical Mechanics

Journal Article

Fractals, ISSN 0218-348X, 03/2015, Volume 23, Issue 1, pp. 1540012 - 1-1540012-9

The fractal dimension of random walker (FDRW) is an important parameter for description of electrical conductivity in porous media. However, it is somewhat...

Fractal Dimension | Pore Fractal | Random Walker | Tortuosity | PERMEABILITY | ROCKS | MULTIDISCIPLINARY SCIENCES | PERCOLATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MASS | ARCHIES LAW | SOIL | DIFFUSION | TORTUOUS STREAMTUBES | GEOMETRY | Analysis | Models | Electrical conductivity | Fractal analysis | Media | Sponges | Fractals | Mathematical models | Porosity | Two dimensional | Three dimensional models

Fractal Dimension | Pore Fractal | Random Walker | Tortuosity | PERMEABILITY | ROCKS | MULTIDISCIPLINARY SCIENCES | PERCOLATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MASS | ARCHIES LAW | SOIL | DIFFUSION | TORTUOUS STREAMTUBES | GEOMETRY | Analysis | Models | Electrical conductivity | Fractal analysis | Media | Sponges | Fractals | Mathematical models | Porosity | Two dimensional | Three dimensional models

Journal Article

Flow, Turbulence and Combustion, ISSN 1386-6184, 8/2019, Volume 103, Issue 2, pp. 293 - 322

In this work, the reconstruction of sub-grid scales in large eddy simulation (LES) of turbulent flows in stratocumulus clouds is addressed. The approach is...

Engineering | Turbulence | Fluid- and Aerodynamics | Lagrangian particles | Sub-grid scale model | Engineering Thermodynamics, Heat and Mass Transfer | Engineering Fluid Dynamics | Automotive Engineering | Large Eddy simulation | Fractal interpolation technique | PARTICLES | CHANNEL FLOW | ISOTROPIC TURBULENCE | PROBABILITY DENSITY | MODEL | ENERGY-DISSIPATION RATES | ENTRAINMENT | MECHANICS | THERMODYNAMICS | LES | 2-PARTICLE DISPERSION | MARINE STRATOCUMULUS | Stratocumulus clouds | Models | Numerical analysis

Engineering | Turbulence | Fluid- and Aerodynamics | Lagrangian particles | Sub-grid scale model | Engineering Thermodynamics, Heat and Mass Transfer | Engineering Fluid Dynamics | Automotive Engineering | Large Eddy simulation | Fractal interpolation technique | PARTICLES | CHANNEL FLOW | ISOTROPIC TURBULENCE | PROBABILITY DENSITY | MODEL | ENERGY-DISSIPATION RATES | ENTRAINMENT | MECHANICS | THERMODYNAMICS | LES | 2-PARTICLE DISPERSION | MARINE STRATOCUMULUS | Stratocumulus clouds | Models | Numerical analysis

Journal Article

Dynamical Systems, ISSN 1468-9367, 04/2019, Volume 34, Issue 2, pp. 274 - 300

This paper deals with the asymptotic behaviour of solutions for non-autonomous stochastic fractional Ginzburg-Landau equations driven by multiplicative noise...

37L55 | Non-autonomous stochastic fractional Ginzburg-Landau equation | random dynamical system | 35Q56 | random attractor | fractal dimension | multiplicative noise | 60H15 | Non-autonomous stochastic fractional Ginzburg–Landau equation | EXISTENCE | MATHEMATICS, APPLIED | WELL-POSEDNESS | DRIVEN | PHYSICS, MATHEMATICAL | SUFFICIENT | ASYMPTOTIC-BEHAVIOR | WEAK | SETS | WAVE-EQUATION | RANDOM DYNAMICAL-SYSTEMS | Attractors (mathematics) | Fractals | Fractal geometry | Asymptotic properties | Mathematical analysis | Formulas (mathematics)

37L55 | Non-autonomous stochastic fractional Ginzburg-Landau equation | random dynamical system | 35Q56 | random attractor | fractal dimension | multiplicative noise | 60H15 | Non-autonomous stochastic fractional Ginzburg–Landau equation | EXISTENCE | MATHEMATICS, APPLIED | WELL-POSEDNESS | DRIVEN | PHYSICS, MATHEMATICAL | SUFFICIENT | ASYMPTOTIC-BEHAVIOR | WEAK | SETS | WAVE-EQUATION | RANDOM DYNAMICAL-SYSTEMS | Attractors (mathematics) | Fractals | Fractal geometry | Asymptotic properties | Mathematical analysis | Formulas (mathematics)

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 05/2018, Volume 38, Issue 3, pp. 982 - 1011

We consider several different models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation....

HAUSDORFF DIMENSION | MATHEMATICS | SEPARATION PROPERTIES | MATHEMATICS, APPLIED | AFFINE SETS | SELF-SIMILAR SETS | LIPSCHITZ EMBEDDINGS | V-VARIABLE FRACTALS | SIMILARITY | SIERPINSKI CARPETS | Fractal models | Carpets | Self-similarity

HAUSDORFF DIMENSION | MATHEMATICS | SEPARATION PROPERTIES | MATHEMATICS, APPLIED | AFFINE SETS | SELF-SIMILAR SETS | LIPSCHITZ EMBEDDINGS | V-VARIABLE FRACTALS | SIMILARITY | SIERPINSKI CARPETS | Fractal models | Carpets | Self-similarity

Journal Article

Journal of Mathematical Imaging and Vision, ISSN 0924-9907, 1/2019, Volume 61, Issue 1, pp. 140 - 159

This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by...

Mathematical Methods in Physics | Texture analysis | Triangular prism | Signal,Image and Speech Processing | Computer Science | Image Processing and Computer Vision | Applications of Mathematics | Pattern recognition | Fractal descriptors | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | RECOGNITION | CLASSIFICATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Mathematical Methods in Physics | Texture analysis | Triangular prism | Signal,Image and Speech Processing | Computer Science | Image Processing and Computer Vision | Applications of Mathematics | Pattern recognition | Fractal descriptors | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | RECOGNITION | CLASSIFICATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

1994, 2nd ed., ISBN 9783527290789, xxv 427 p., [5] p. of plates

Book

19.
Full Text
Laminar flow through fractal porous materials: the fractional-order transport equation

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2015, Volume 22, Issue 1-3, pp. 889 - 902

•An anomalous time decay of the state variables of a simple mechanical system is obtained.•The exponent of the decay is related to the Hausdorff dimension of...

Transport equations | Fractals | Fractional calculus | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | MODEL | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RANDOM-WALKS | DIFFUSION | CALCULUS APPROACH | GEOMETRY | Laminar flow | Mathematical analysis | Porous materials | Fractal analysis | Media | Derivatives | Porosity | Transport

Transport equations | Fractals | Fractional calculus | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | MODEL | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RANDOM-WALKS | DIFFUSION | CALCULUS APPROACH | GEOMETRY | Laminar flow | Mathematical analysis | Porous materials | Fractal analysis | Media | Derivatives | Porosity | Transport

Journal Article

APPLIED SCIENCES-BASEL, ISSN 2076-3417, 08/2018, Volume 8, Issue 8, p. 1327

As a typical pattern recognition method, communication signal modulation involves many complicated factors. Fractal theory can be used for signal modulation...

feature evaluation | PHYSICS, APPLIED | random forest classifier | MATERIALS SCIENCE, MULTIDISCIPLINARY | fractal dimension | CHEMISTRY, MULTIDISCIPLINARY | pattern recognition | Fractal geometry | Noise | Feature recognition | Time series | Fractals | Entropy | Pattern recognition | Signal classification | Complexity | Learning algorithms | Accuracy | Algorithms | Neural networks | Modulation | Machine learning | Classification | Radio networks | Artificial intelligence | Methods | Communication

feature evaluation | PHYSICS, APPLIED | random forest classifier | MATERIALS SCIENCE, MULTIDISCIPLINARY | fractal dimension | CHEMISTRY, MULTIDISCIPLINARY | pattern recognition | Fractal geometry | Noise | Feature recognition | Time series | Fractals | Entropy | Pattern recognition | Signal classification | Complexity | Learning algorithms | Accuracy | Algorithms | Neural networks | Modulation | Machine learning | Classification | Radio networks | Artificial intelligence | Methods | Communication

Journal Article

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