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11 results on '"generalized dimensions"'

1. Analysis of normal human retinal vascular network architecture using multifractal geometry

Author

Ştefan Ţălu, Sebastian Stach, Dan Mihai Călugăru, Carmen Alina Lupaşcu, and Simona Delia Nicoară

Subjects
generalized dimensions, multifractal, retinal vessel segmentation, retinal image analysis, retinal microvasculature, standard box-counting method, Ophthalmology, RE1-994
Abstract

AIM: To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina. METHODS: Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyses were performed using the GraphPad InStat software. RESULTS: The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions (Dq) for q=0, 1, 2, the width of the multifractal spectrum (Δα=αmax - αmin) and the spectrum arms’ heights difference (│Δf│) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D0=1.7014±0.0057; D1=1.6507±0.0058; D2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions, D0=1.6303±0.0051; D1=1.6012±0.0059; D2=1.5531±0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions (Dq) for q=0, 1, 2, the width of the multifractal spectrum (Δα) and the spectrum arms’ heights difference (│Δf│) of the segmented versions was slightly greater than the skeletonised versions. CONCLUSION: The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.

Published
2017
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2. Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information

Author

José M. Angulo and Francisco J. Esquivel

Subjects
complex system, generalized dimensions, multifractality, non-extensivity, seismicity, space-time dynamics, Tsallis entropy, Science, Astrophysics, QB460-466, Physics, QC1-999
Abstract

Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced.

Published
2015
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3. Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information.

Author

Angulo, José M. and Esquivel, Francisco J.

Subjects
*MULTIFRACTALS, *DIMENSIONAL analysis, *ENTROPY, *SCALING hypothesis (Statistical physics), *STRUCTURAL dynamics
Abstract

Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced. [ABSTRACT FROM AUTHOR]

Published
2015
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4. Statistical Estimation of Generalized Dimensions.

Author

Maiorov, V. and Timofeev, E.

Abstract

A statistical estimate for generalized dimensions of a set $$A \subset \mathbb{R}^m$$ based on the computation of average distances to the closest points in a sample of elements of A is given. For smooth manifolds with Lebesgue measures and for self-similar fractals with self-similar measures, the estimate is proved to be consistent. [ABSTRACT FROM AUTHOR]

Published
2002
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5. Multifractal characteristics of the self-assembly material texture of β-Si3N4/SUS316L austenitic stainless steel composites.

Author

Munakata, Fumio, Takeda, Mariko, Nemoto, Kazuhiro, Ookubo, Kazuya, Sato, Yoshihiro, Mizukami, Yuka, Koga, Masashi, Abe, Satoko, Bao, Yue, and Kobayashi, Ryota

Subjects
*AUSTENITIC stainless steel, *ALLOY texture, *STAINLESS steel, *TEXTURE analysis (Image processing), *STEREOLOGY
Abstract

The multifractal dimension D q of β-Si 3 N 4 agglomerates in β-Si 3 N 4 /316 L stainless steel (SUS316L) composites was measured. In addition to capacity dimension D 0 related to the morphology of β-Si 3 N 4 agglomerates, information dimension D 1 for theses samples was related to the entropy of configuration affected by the dispersion of β-Si 3 N 4 particles was confirmed, and the correlation dimension D 2 reflected the connectivity between the particles. The obtained results showed that the multifractal dimensions D q (q = 0, 1, and 2) were effective as indices for evaluating the morphology, arrangement, and connectivity (or dispersibility) of dispersed particles in solid state reaction, and suggested a new method of quantitative stereology. Image 1 • Material texture of the Si 3 N 4 /SUS composite was investigated by multifractal analysis. • The capacity dimension D 0 was related to the morphology of aggregates. • The information dimension D 1 was related to the entropy of configuration of particles. • The correlation dimension D 2 reflected the connectivity between the particles. • The D 0 , D 1 and D 2 were effective as indices for evaluating the self-assembly of texture. [ABSTRACT FROM AUTHOR]

Published
2021
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6. Analysis of normal human retinal vascular network architecture using multifractal geometry

Author

Sebastian Stach, Dan Călugăru, Ştefan Ţălu, Simona Delia Nicoară, and Carmen Alina Lupascu

Subjects
0301 basic medicine, Early detection, Geometry, Fundus (eye), 03 medical and health sciences, chemistry.chemical_compound, retinal vessel segmentation, lcsh:Ophthalmology, Clinical Research, Medicine, Segmentation, Retinal microvasculature, business.industry, Retinal, Multifractal system, Generalized dimensions, Multifractal, Retinal vessel, Ophthalmology, 030104 developmental biology, Microvascular Network, Retinal image analysis, Standard box-counting method, chemistry, Vascular network, lcsh:RE1-994, business
Abstract

AIM To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina. METHODS Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyses were performed using the GraphPad InStat software. RESULTS The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions (Dq ) for q=0, 1, 2, the width of the multifractal spectrum (Δα=αmax - αmin ) and the spectrum arms' heights difference (|Δf|) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D0 =1.7014±0.0057; D1 =1.6507±0.0058; D2 =1.5772±0.0059; Δα=0.92441±0.0085; |Δf|= 0.1453±0.0051; for skeletonised versions, D0 =1.6303±0.0051; D1 =1.6012±0.0059; D2 =1.5531±0.0058; Δα=0.65032±0.0162; |Δf|= 0.0238±0.0161. The average of generalized dimensions (Dq ) for q=0, 1, 2, the width of the multifractal spectrum (Δα) and the spectrum arms' heights difference (|Δf|) of the segmented versions was slightly greater than the skeletonised versions. CONCLUSION The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.

Published
2017

7. On Measurement of Internal Variables of Complex Self-Organized Systems and Their Relation to Multifractal Spectra

Author

Petr Jizba, Tomáš Náhlík, Petr Císař, Dalibor Štys, Štěpán Papáček, Faculty of Fisheries and Protection of Waters [University of South Bohemia], University of South Bohemia, Department of Mathematics [Prague] (FNSPE), Czech Technical University in Prague (CTU), Fernando A. Kuipers, Poul E. Heegaard, and TC 6

Subjects
Discrete mathematics, Relation (database), Computer science, principal component analysis, Observable, Multifractal spectra, 02 engineering and technology, Multifractal system, 021001 nanoscience & nanotechnology, 01 natural sciences, multifractal spectra, Rényi entropy, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], generalized dimensions, 0103 physical sciences, Attractor, Principal component analysis, Internal variable, [INFO]Computer Science [cs], Statistical physics, 010306 general physics, 0210 nano-technology
Abstract

Part 2: Full Papers; International audience; We propose a method for characterizing structured, experimentally observable, complex self-organized systems. The method in question is based on the observation that number of self-organized systems can be mathematically perceived as consisting of several interconnected multifractal components. We illustrate our key results with ensuing applications. The relation of the results obtained to known examples of strange attractors is also discussed.

Published
2012
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9. Multifractal analysis of the pore- and solid-phases in binary two-dimensional images of natural porous structures

Author

Edith Perrier, Annette Dathe, and Ana M. Tarquis

Subjects
Characteristic length, Pixel, Matemáticas, Soil Science, Binary number, Geometry, pore space, 04 agricultural and veterinary sciences, Multifractal system, 010502 geochemistry & geophysics, 01 natural sciences, Spectral line, generalized dimensions, multifractal analysis, 040103 agronomy & agriculture, 0401 agriculture, forestry, and fisheries, Probability distribution, Geología, Porosity, soil structure, Image resolution, 0105 earth and related environmental sciences, Mathematics, solid mass
Abstract

We use multifractal analysis (MFA) to investigate how the Renyi dimensions of the solid mass and the pore space in porous structures are related to each other. To our knowledge, there is no investigation about the relationship of Renyi or generalized dimensions of two phases of the same structure. Images of three different natural porous structures covering three orders of magnitude were investigated: a microscopic soil structure, a soil void system visible without magnification and a mineral dendrite. Image size was always 1024 x 1024 pixels and box sizes were chosen as powers of 2. MFA was carried out according to the method of moments, i.e., the probability distribution was estimated for moments ranging from - 10 < q < 10 and the Renyi dimensions were calculated from the log/log slope of the probability distribution for the respective moments over box sizes. A meaningful interval of box sizes was determined by estimating the characteristic length of the pore space and taking the next higher power of 2 value as the smallest box size, whereas the greatest box size was determined by optimizing the coefficients of determination of the log/log fits for all q. The optimized box size range spans from 32 to 1024 pixels for all images. Good generalized dimension (Dq) spectra were obtained for this box size range, which are capable of characterizing heterogeneous spatial porous structure. They are alike for all images and phases which the exception of the solid mass of the soil void system, which shows a rather flat Dq behavior. A closer examination reveals that similar patterns of structure gain similar spectra of generalized dimensions. The capacity dimension for q=0 is close to the Euclidian dimension 2 for all investigated images and phases. (c) 2006 Elsevier B.V. All rights reserved.

Published
2006

10. Multiplicity moments in deep inelastic scattering at HERA

Author

Chekanov, S, Derrick, M, Krakauer, D, Magill, S, Musgrave, B, Pellegrino, A, Repond, J, Stanek, R, Yoshida, R, Mattingly, M C K, Antonioli, P, Bari, G, Basile, M, Bellagamba, L, Boscherini, D, Bruni, A, Bruni, G, Romeo, G C, Cifarelli, L, Cindolo, F, Contin, A, Corradi, M, De Pasquale, S, Giusti, P, Iacobucci, G, Levi, G, Margotti, A, Massam, T, Nania, R, Palmonari, F, Pesci, A, Sartorelli, G, Zichichi, A, Aghuzumtsyan, G, Brock, I, Goers, S, Hartmann, H, Hilger, E, Irrgang, P, Jakob, H P, Kappes, A, Katz, U F, Kerger, R, Kind, O, Paul, E, Rautenberg, J, Schnurbusch, H, Stifutkin, A, Tandler, J, Voss, K C, Weber, A, Wieber, H, Bailey, D S, Brook, N H, Cole, J E, Foster, B, Heath, G P, Heath, H F, Robins, S, Rodrigues, E, Scott, J, Tapper, R J, Wing, M, Capua, M, Mastroberardino, A, Schioppa, M, Susinno, G, Jeoung, H Y, Kim, J Y, Lee, J H, Lim, I T, Ma, K J, Pac, M Y, Caldwell, A, Helbich, M, Liu, W, Liu, X, Mellado, B, Paganis, S, Sampson, S, Schmidke, W B, Sciulli, F, Chwastowski, J, Eskreys, A, Figiel, J, Klimek, K, Olkiewicz, K, Przybycien, M B, Stopa, P, Zawiejski, L, Bednarek, B, Jelen, K, Kisielewska, D, Kowal, A M, Kowal, M, Kowalski, T, Mindur, B, Przybycien, M, Rulikowska-Zarebska, E, Suszycki, L, Szuba, D, Kotanski, A, Bauerdick, L A T, Behrens, U, Borras, K, Chiochia, V, Crittenden, J, Dannheim, D, Desler, K, Drews, G, Fox-Murphy, A, Fricke, U, Geiser, A, Goebel, F, Gottlicher, P, Graciani, R, Haas, T, Hain, W, Hartner, G F, Hebbel, K, Hillert, S, Koch, W, Kotz, U, Kowalski, H, Labes, H, Lohr, B, Mankel, R, Martens, J, Martinez, M, Milite, M, Moritz, M, Notz, D, Petrucci, M C, Polini, A, Savin, A A, Schneekloth, U, Selonke, F, Stonjek, S, Wolf, G, Wollmer, U, Whitmore, J J, Wichmann, R, Youngman, C, Zeuner, W, Coldewey, C, Viani, A L D, Meyer, A, Schlenstedt, S, Barbagli, G, Gallo, E, Pelfer, P G, Bamberger, A, Benen, A, Coppola, N, Markun, P, Raach, H, Wolfle, S, Bell, M, Bussey, P J, Doyle, A T, Glasman, C, Lee, S W, Lupi, A, McCance, G J, Saxon, D H, Skillicorn, I O, Bodmann, B, Gendner, N, Holm, U, Salehi, H, Wick, K, Yildirim, A, Ziegler, A, Carli, T, Garfagnini, A, Gialas, I, Lohrmann, E, Foudas, C, Goncalo, R, Long, K R, Metlica, F, Miller, D B, Tapper, A D, Walker, R, Cloth, P, Filges, D, Ishii, T, Kuze, M, Nagano, K, Tokushuku, K, Yamada, S, Yamazaki, Y, Barakbaev, A N, Boos, E G, Pokrovskiy, N S, Zhautykov, B O, Ahn, S H, Lee, S B, Park, S K, Lim, H, Son, D, Barreiro, F, Garcia, G, Gonzalez, O, Labarga, L, del Peso, J, Redondo, I, Terron, J, Vazquez, M, Barbi, M, Corriveau, F, Padhi, S, Stairs, D G, Tsurugai, T, Antonov, A, Bashkirov, V, Danilov, P, Dolgoshein, B A, Gladkov, D, Sosnovtsev, V, Suchkov, S, Dementiev, R K, Ermolov, P F, Golubkov, Y A, Katkov, I I, Khein, L A, Korotkova, N A, Korzhavina, I A, Kuzmin, V A, Levchenko, B B, Lukina, O Y, Proskuryakov, A S, Shcheglova, L M, Solomin, A N, Vlasov, N N, Zotkin, S A, Bokel, C, Botje, M, Engelen, J, Grijpink, S, Koffeman, E, Kooijman, P, Schagen, S, van Sighem, A, Tassi, E, Tiecke, H, Tuning, N, Velthuis, J J, Vossebeld, J, Wiggers, L, de Wolf, E, Brummer, N, Bylsma, B, Durkin, L S, Gilmore, J, Ginsburg, C M, Kim, C L, Ling, T Y, Boogert, S, Cooper-Sarkar, A M, Devenish, R C E, Ferrando, J, Grosse-Knetter, J, Matsushita, T, Rigby, M, Ruske, O, Sutton, M R, Walczak, R, Bertolin, A, Brugnera, R, Carlin, R, Dal Corso, F, Dusini, S, Limentani, S, Longhin, A, Parenti, A, Posocco, M, Stanco, L, Turcato, M, Adamczyk, L, Iannotti, L, Oh, B Y, Saull, P R B, Toothacker, W S, Iga, Y, D'Agostini, G, Marini, G, Nigro, A, Cormack, C, Hart, J C, McCubbin, N A, Epperson, D, Heusch, C, Sadrozinski, H F W, Seiden, A, Williams, D C, Park, I H, Pavel, N, Abramowicz, H, Dagan, S, Gaareen, A, Kananov, S, Kreisel, A, Levy, A, Abe, T, Fusayasu, T, Kehno, T, Umemori, K, Yamashita, T, Hamatsu, R, Hirose, T, Inuzuka, M, Kitamura, S, Matsuzawa, K, Nishimura, T, Arneodo, M, Cartiglia, N, Cirio, R, Costa, M, Ferrero, M I, Maselli, S, Monaco, V, Peroni, C, Ruspa, M, Sacchi, R, Solano, A, Staiano, A, Bailey, D C, Fagerstroem, C P, Galea, R, Koop, T, Levman, G M, Martin, J F, Mirea, A, Sabetfakhri, A, Butterworth, J M, Gwenlan, C, Hayes, M E, Heaphy, E A, Jones, T W, Lane, J B, West, B J, Ciborowski, J, Ciesielski, R, Grzelak, G, Nowak, R J, Pawlak, J M, Plucinski, P, Smalska, B, Tymieniecka, T, Ukleja, J, Zakrzewski, J A, Zarnecki, A F, Adamus, M, Sztuk, J, Deppe, O, Eisenberg, Y, Gladilin, L K, Hochman, D, Karshon, U, Breitweg, J, Chapin, D, Cross, R, Kcira, D, Lammers, S, Reeder, D D, Smith, W H, Deshpande, A, Dhawan, S, Hughes, V W, Straub, P B, Bhadra, S, Catterall, C D, Frisken, W R, Hall-Wilton, R, Khakzad, M, Menary, S, ZEUS Collaboration, and Zeus (IHEF, IoP, FNWI)

Subjects
Nuclear and High Energy Physics, Particle physics, HIGH-ENERGY, MONTE-CARLO GENERATOR, PHASE-SPACE BINS, FOS: Physical sciences, 01 natural sciences, High Energy Physics - Experiment, STRANGE ATTRACTORS, Nuclear physics, QCD JETS, High Energy Physics - Experiment (hep-ex), HADRON SPECTRA, 0103 physical sciences, EVENT GENERATOR, GENERALIZED DIMENSIONS, Multiplicity (chemistry), 010306 general physics, QC, Event generator, Physics, Research Groups and Centres\Physics\Low Temperature Physics, 010308 nuclear & particles physics, Scattering, Faculty of Science\Physics, Perturbative QCD, ZEUS, HERA, MULTIPARTON CORRELATIONS, PARTON DISTRIBUTIONS, Deep inelastic scattering, Charged particle, Transverse plane, High Energy Physics::Experiment
Abstract

Multiplicity moments of charged particles in deep inelastic E+P scattering have been measured with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb^{-1}$. The moments for Q^2 > 1000 GeV^2 were studied in the current region of the Breit frame. The evolution of the moments was investigated as a function of restricted regions in polar angle and, for the first time, both in the transverse momentum and in absolute momentum of final-state particles. Analytic perturbative QCD predictions in conjunction with the hypothesis of Local Parton-Hadron Duality (LPHD) reproduce the trends of the moments in polar-angle regions, although some discrepancies are observed. For the moments restricted either in transverse or absolute momentum, the analytic results combined with the LPHD hypothesis show considerable deviations from the measurements. The study indicates a large influence of the hadronisation stage on the multiplicity distributions in the restricted phase-space regions studied here, which is inconsistent with the expectations of the LPHD hypothesis., 19 pages, 6 eps figures, submitted to Phys. Lett. B

Published
2002

11. Analysis of normal human retinal vascular network architecture using multifractal geometry.

Author

Ţălu Ş, Stach S, Călugăru DM, Lupaşcu CA, and Nicoară SD

Abstract

Aim: To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina., Methods: Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyses were performed using the GraphPad InStat software., Results: The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions ( D q ) for q =0, 1, 2, the width of the multifractal spectrum ( Δα=α max - α min ) and the spectrum arms' heights difference ( |Δf| ) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D 0 =1.7014±0.0057; D 1 =1.6507±0.0058; D 2 =1.5772±0.0059; Δα =0.92441±0.0085; |Δf| = 0.1453±0.0051; for skeletonised versions, D 0 =1.6303±0.0051; D 1 =1.6012±0.0059; D 2 =1.5531±0.0058; Δα =0.65032±0.0162; |Δf| = 0.0238±0.0161. The average of generalized dimensions ( D q ) for q =0, 1, 2, the width of the multifractal spectrum ( Δα ) and the spectrum arms' heights difference ( |Δf| ) of the segmented versions was slightly greater than the skeletonised versions., Conclusion: The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.

Published
2017
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