scholarly journals Self-Similarity and Scaling Behavior of Scale-free Gravitational Clustering

1996 ◽  
Vol 465 ◽  
pp. 14 ◽  
Author(s):  
S. Colombi ◽  
F. R. Bouchet ◽  
L. Hernquist
Keyword(s):  
Scaling Behavior ◽  
Self Similarity ◽  
Scale Free ◽  
Gravitational Clustering

scholarly journals Antigen receptor repertoires of one of the smallest known vertebrates

2021 ◽  
Vol 7 (1) ◽  
pp. eabd8180
Author(s):  
Orlando B. Giorgetti ◽  
Prashant Shingate ◽  
Connor P. O’Meara ◽  
Vydianathan Ravi ◽  
Nisha E. Pillai ◽  
...  
Keyword(s):  
Immune Responses ◽  
Antigen Receptor ◽  
Fundamental Property ◽  
Cell Receptor ◽  
Immune Reactivity ◽  
Self Similarity ◽  
Frequency Distributions ◽  
Scale Free ◽  
Scale Free Networks ◽  
Incomplete Sampling

The rules underlying the structure of antigen receptor repertoires are not yet fully defined, despite their enormous importance for the understanding of adaptive immunity. With current technology, the large antigen receptor repertoires of mice and humans cannot be comprehensively studied. To circumvent the problems associated with incomplete sampling, we have studied the immunogenetic features of one of the smallest known vertebrates, the cyprinid fish Paedocypris sp. “Singkep” (“minifish”). Despite its small size, minifish has the key genetic facilities characterizing the principal vertebrate lymphocyte lineages. As described for mammals, the frequency distributions of immunoglobulin and T cell receptor clonotypes exhibit the features of fractal systems, demonstrating that self-similarity is a fundamental property of antigen receptor repertoires of vertebrates, irrespective of body size. Hence, minifish achieve immunocompetence via a few thousand lymphocytes organized in robust scale-free networks, thereby ensuring immune reactivity even when cells are lost or clone sizes fluctuate during immune responses.

SMALL-WORLD AND SCALE-FREE PROPERTIES OF THE n-DIMENSIONAL SIERPINSKI CUBE NETWORKS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050001
Author(s):  
CHENG ZENG ◽  
MENG ZHOU ◽  
YUMEI XUE
Keyword(s):  
Small World ◽  
The Self ◽  
Self Similarity ◽  
Scale Free ◽  
Evolving Networks

In this paper, we construct evolving networks from [Formula: see text]-dimensional Sierpinski cube. Using the self-similarity of Sierpinski cube, we show the evolving networks have scale-free and small-world properties.

scholarly journals Onset of power-law scaling behavior in idiotypic random and scale-free networks

2012 ◽  
Vol 376 (45) ◽  
pp. 3158-3163
Author(s):  
Elder S. Claudino ◽  
M.L. Lyra ◽  
Iram Gleria ◽  
Paulo R.A. Campos ◽  
Delvis Bertrand
Keyword(s):  
Power Law ◽  
Scaling Behavior ◽  
Scale Free ◽  
Scale Free Networks

The Geometry of Dla: Different Aspects of the Departure from Self-Similarity

1994 ◽  
Vol 367 ◽  
Author(s):  
B.B. Mandelbrot ◽  
A. Vespignani ◽  
H. Kaufman
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Properties ◽  
Finite Size ◽  
Scaling Behavior ◽  
Self Similarity ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Large Numbers ◽  
The One

AbstractIn order to understand better the morphology and the asymptotic behavior in Diffusion Limited Aggregation (DLA), we studied a large numbers of very large off-lattice circular clusters. We inspected both dynamical and geometric asymptotic properties, namely the moments of the particle's sticking distances and the scaling behavior of the transverse growth crosscuts, i.e., the one dimensional cuts by circles. The emerging picture for radial DLA departs from simple self-similarity for any finite size. It corresponds qualitatively to the scenario of infinite drift starting from the familiar five armed shape for small sizes and proceeding to an increasingly tight multi-armed shape. We show quantitatively how the lacunarity of circular clusters becomes increasingly “compact” with size. Finally, we find agreement among transverse cuts dimensions for clusters grown in different geometries, suggesting that the question of universality is best addressed on the crosscut.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

scholarly journals Detecting different topologies immanent in scale-free networks with the same degree distribution

2019 ◽  
Vol 116 (14) ◽  
pp. 6701-6706 ◽  
Author(s):  
Dimitrios Tsiotas
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Topology ◽  
Degree Distribution ◽  
Growth Process ◽  
Preferential Attachment ◽  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks ◽  
Definition Of

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

scholarly journals Quantifying resolution in cosmological N-body simulations using self-similarity

2020 ◽  
Author(s):  
Michael Joyce ◽  
Lehman Garrison ◽  
Daniel Eisenstein
Keyword(s):  
Spatial Resolution ◽  
Correlation Functions ◽  
Self Similarity ◽  
Scale Free ◽  
Time Stepping ◽  
Resolution Limits ◽  
Small Scales ◽  
Small Force ◽  
Point Correlation ◽  
Excellent Tool

Abstract We demonstrate that testing for self-similarity in scale-free simulations provides an excellent tool to quantify the resolution at small scales of cosmological N-body simulations. Analysing two-point correlation functions measured in simulations using Abacus, we show how observed deviations from self-similarity reveal the range of time and distance scales in which convergence is obtained. While the well-converged scales show accuracy below 1%, our results show that, with a small force softening length, the spatial resolution is essentially determined by the mass resolution. At later times the lower cut-off scale on convergence evolves in comoving units as a−1/2 (a being the scale factor), consistent with a hypothesis that it is set by two-body collisionality. A corollary of our results is that N-body simulations, particularly at high red-shift, contain a significant spatial range in which clustering appears converged with respect to the time-stepping and force softening but has not actually converged to the physical continuum result. The method developed can be applied to determine the resolution of any clustering statistic and extended to infer resolution limits for non-scale-free simulations.

scholarly journals FRACTAL GEOMETRY OF FINANCIAL TIME SERIES

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 609-616 ◽  
Author(s):  
CARL J.G. EVERTSZ
Keyword(s):  
Time Series ◽  
Stock Price ◽  
Financial Time Series ◽  
Quantitative Measure ◽  
Scaling Behavior ◽  
The Self ◽  
Self Similarity ◽  
Absolute Size ◽  
Stable Random Variables ◽  
German Stock

A simple quantitative measure of the self-similarity in time-series in general and in the stock market in particular is the scaling behavior of the absolute size of the jumps across lags of size k. A stronger form of self-similarity entails that not only this mean absolute value, but also the full distributions of lag-k jumps have a scaling behavior characterized by the above Hurst exponent. In 1963, Benoit Mandelbrot showed that cotton prices have such a strong form of (distributional) self-similarity, and for the first time introduced Lévy’s stable random variables in the modeling of price records. This paper discusses the analysis of the self-similarity of high-frequency DEM-USD exchange rate records and the 30 main German stock price records. Distributional self-similarity is found in both cases and some of its consequences are discussed.

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