Discovery of Cosmic Fractals

Baryshev, Yu. V.; Teerikorpi, P.; Mandelbrot, Benoît B.

doi:10.1142/9789812388780

Cited by 67 publications

(87 citation statements)

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“…On the other hand should the principle of scale relativity hold, then one would expect to retrieve Einstein's familiar formula in a scaled form [3][4][5]. In a sense we expect a type of scale similarity close to that found between Newton's kinetic energy and the famous energy-mass formula of relativity which differs by a factor of only 1/2 and changing the variable velocity v to the puzzlingly constant speed of light c. Noting that for a continuous manifold the Betti number 2 which counts the three dimensional holes in a manifold is given by 2 b 1 b  and that the same Betti number for a K3 Kähler is 2 , it is possible to show that E = mc 2 may be elevated to quantum relativity, i.e. an effective quantum gravity equation when scaled by 22 b      2 2 This prior intuitive mathematical expectation was confirmed on two counts, namely first experimentally using the WMAP and supernova cosmic measurements [4,19] and second theoretically using numerous sophisticated established theories, all leading to the same robust result, namely a scaling factor 1 22   (see Table 1) [24][25][26].…”

Section: Introductionsupporting

confidence: 52%

“…The present work is mainly concerned with devising a theoretical explanation for the mystery of the so-called missing dark energy of the cosmos [1][2][3][4]. However this is all linked to quantum gravity and we start here from special relativity and address the greatest puzzle of them all which we invariably took and rather wrongly as a given experiential fact of Nature which cannot be reduced or interrogated any further namely the constancy of the speed of light.…”

Section: Introductionmentioning

confidence: 99%

“…As is well known Einstein's special relativity presupposes a smooth space time with Lorentzian symmetry group invariance [1]. Quantum space time on the other hand is modeled via radically different geometrical visualization [1][2][3][4][5][6][7][8]. In string theory, M-theory and super gravity one uses various types of CalabiYau and complex Kähler manifolds for space time extra dimensions [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

Naschie¹

2013

IJMNTA

143

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Time dilation, space contraction and relativistic mass are combined in a novel fashion using Newtonian dynamics. In this way we can surprisingly retrieve an effective quantum gravity energy-mass equation which gives the accurate experimental value of vacuum density. Furthermore Einstein's equation of special relativity E = mc 2 , where m is the mass and c is the velocity of light developed assuming smooth 4D space time is transferred to a rugged Calabi-Yau and K3 fuzzy Kähler manifolds and revised to become, where the division factor 22 maybe interpreted as the compactified bosonic dimensions of Veneziano-Nambu strings. The result is again an accurate effective quantum gravity energy-mass relation akin to the one found using Newtonian dynamics which correctly predicts that 95.4915028% of the energy in the cosmos is the hypothetical missing dark energy. The agreement with WMAP and supernova measurements is in that respect astounding. In addition different theories are used to check the calculations and all lead to the same quantitative result. Thus the theories of varying speed of light, scale relativity, E-infinity theory, M-theory, Heterotic super strings, quantum field in curved space time, Veneziano's dual resonance model, Nash Euclidean embedding and super gravity all reinforce, without any reservation, the above mentioned theoretical result which in turn is in total agreement with the most sophisticated cosmological measurements which was deservingly awarded the 2011 Nobel Prize in Physics. Finally and more importantly from certain viewpoints, we reason that the speed of light is constant because it is a definite probabilistic expectation value of a variable velocity in a hierarchical fractal clopen, i.e. closed and open micro space time.

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Section: Introductionsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

Naschie¹

2013

IJMNTA

143

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“…There has been an intense debate about the most suitable statistical methods for characterizing galaxy properties, particularly galaxy correlations (see Pietronero 1987;Davis 1997;Pietronero et al 1997;Sylos Labini et al 1998;Joyce et al 1999a;Wu et al 1999;Gabrielli & Sylos Labini 2001;Hogg et al 2004;Joyce et al 2005;Baryshev & Teerikorpi 2006;Vasilyev et al 2006;Sylos Labini et al 2007, 2009a. The most suitable statistical method for characterizing the properties of a given stochastic point process depends on the underlying correlations of the point distribution itself.…”

Section: Introductionmentioning

confidence: 99%

Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey – Data release six

Labini

Vasilyev

Baryshev

2009

A&A

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Statistical analyses of finite sample distributions usually assume that fluctuations are self-averaging, i.e. statistically similar in different regions of the given sample volume. By using the scale-length method, we test whether this assumption is satisfied in several samples of the Sloan Digital Sky Survey Data Release Six. We find that the probability density function (PDF) of conditional fluctuations, if filtered on large enough spatial scales (i.e., r > 30 Mpc/h), shows relevant systematic variations in different subvolumes of the survey. Instead for scales of r < 30 Mpc/h, the PDF is statistically stable, and its first moment presents scaling behavior with a negative exponent around one. Thus while up to 30 Mpc/h galaxy structures have well-defined power-law correlations, on larger scales it is not possible to consider whole sample average quantities as meaningful and useful statistical descriptors. This situation stems from galaxy structures corresponding to density fluctuations that are too large in amplitude and too extended in space to be self-averaging on such large scales inside the sample volumes: galaxy distribution is inhomogeneous up to the largest scales, i.e. r ≈ 100 Mpc/h probed by the SDSS samples. We show that cosmological corrections, such as K-corrections and standard evolutionary corrections, do not qualitatively change the relevant behaviors. We consider in detail the relation between several statistical measurements generally used to quantify galaxy fluctuations and the scale-length analysis by discussing how the breaking of self-averaging properties makes it impossible to have a reliable estimation of average fluctuations amplitude, variance, and correlations for r > 30 Mpc/h. Finally we show that the large-amplitude galaxy fluctuations observed in the SDSS samples are at odds with the predictions of the standard ΛCDM model of structure formation.

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“…In a more general or abstract manner it may be noted that organization of matter and all sorts of known phenomena seem to be hierarchically and recursively organized over many orders of magnitude in a fractal manner, that is, as selfsimilar patterns of patterns, etc. (Baryshev and Teerikorpi, 2002).…”

Section: Validity Of the Modelmentioning

confidence: 99%

T-pattern analysis for the study of temporal structure of animal and human behavior: A comprehensive review

Casarrubea

Jónsson

Faulisi

et al. 2015

Journal of Neuroscience Methods

117

104

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A basic tenet in the realm of modern behavioral sciences is that behavior consists of patterns in time. For this reason, investigations of behavior deal with sequences that are not easily perceivable by the unaided observer. This problem calls for improved means of detection, data handling and analysis. This review focuses on the analysis of the temporal structure of behavior carried out by means of a multivariate approach known as T-pattern analysis. Using this technique, recurring sequences of behavioral events, usually hard to detect, can be unveiled and carefully described. T-pattern analysis has been successfully applied in the study of various aspects of human or animal behavior such as behavioral modifications in neuro-psychiatric diseases, route-tracing stereotypy in mice, interaction between human subjects and animal or artificial agents, hormonal–behavioral interactions, patterns of behavior associated with emesis and, in our laboratories, exploration and anxiety-related behaviors in rodents. After describing the theory and concepts of T-pattern analysis, this review will focus on the application of the analysis to the study of the temporal characteristics of behavior in different species from rodents to human beings. This work could represent a useful background for researchers who intend to employ such a refined multivariate approach to the study of behavior

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Discovery of Cosmic Fractals

Cited by 67 publications

References 0 publications

A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey – Data release six

T-pattern analysis for the study of temporal structure of animal and human behavior: A comprehensive review

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