scholarly journals Temporal Behavior of Local Characteristics in Complex Networks with Preferential Attachment-Based Growth

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1567
Author(s):  
Sergei Sidorov ◽  
Sergei Mironov ◽  
Nina Agafonova ◽  
Dmitry Kadomtsev
Keyword(s):  
Preferential Attachment ◽  
Dynamic Processes ◽  
Total Degree ◽  
Temporal Behavior ◽  
Local Characteristics ◽  
Growing Networks ◽  
Order Of Magnitude ◽  
Expected Values ◽  
Fixed Node ◽  
Skewness And Kurtosis

The study of temporal behavior of local characteristics in complex growing networks makes it possible to more accurately understand the processes caused by the development of interconnections and links between parts of the complex system that occur as a result of its growth. The spatial position of an element of the system, determined on the basis of connections with its other elements, is constantly changing as the result of these dynamic processes. In this paper, we examine two non-stationary Markov stochastic processes related to the evolution of Barabási–Albert networks: the first describes the dynamics of the degree of a fixed node in the network, and the second is related to the dynamics of the total degree of its neighbors. We evaluate the temporal behavior of some characteristics of the distributions of these two random variables, which are associated with higher-order moments, including their variation, skewness, and kurtosis. The analysis shows that both distributions have a variation coefficient close to 1, positive skewness, and a kurtosis greater than 3. This means that both distributions have huge standard deviations that are of the same order of magnitude as the expected values. Moreover, they are asymmetric with fat right-hand tails.

scholarly journals Origin and Application of the Twinned Calcite Strain Gauge

Geosciences ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 296
Author(s):  
Richard H. Groshong
Keyword(s):  
Stress Analysis ◽  
Strain Gauge ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Constant Strain Rate ◽  
Axis Orientation ◽  
Order Of Magnitude ◽  
Rate Experiment ◽  
Strain Axis ◽  
Expected Values

This paper is a personal account of the origin and development of the twinned-calcite strain gauge, its experimental verification, and its relationship to stress analysis. The method allows the calculation of the three-dimensional deviatoric strain tensor based on five or more twin sets. A minimum of about 25 twin sets should provide a reasonably accurate result for the magnitude and orientation of the strain tensor. The opposite-signed strain axis orientation is the most accurately located. Where one strain axis is appreciably different from the other two, that axis is generally within about 10° of the correct value. Experiments confirm a magnitude accuracy of 1% strain over the range of 1–12% axial shortening and that samples with more than 40% negative expected values imply multiple or rotational deformations. If two deformations are at a high angle to one another, the strain calculated from the positive and negative expected values separately provides a good estimate of both deformations. Most stress analysis techniques do not provide useful magnitudes, although most provide a good estimate of the principal strain axis directions. Stress analysis based on the number of twin sets per grain provides a better than order-of-magnitude approximation to the differential stress magnitude in a constant strain rate experiment.

scholarly journals Predecessors and Successors in Random Mappings with Exchangeable In-Degrees

2013 ◽  
Vol 50 (3) ◽  
pp. 721-740 ◽  
Author(s):  
Jennie C. Hansen ◽  
Jerzy Jaworski
Keyword(s):  
Asymptotic Behaviour ◽  
Preferential Attachment ◽  
Degree Sequence ◽  
Discrete Distributions ◽  
Threshold Behaviour ◽  
Mapping Model ◽  
Random Mapping ◽  
Exact Distributions ◽  
Random Mappings ◽  
Expected Values

In this paper we characterise the distributions of the number of predecessors and of the number of successors of a given set of vertices, A, in the random mapping model, TnD̂ (see Hansen and Jaworski (2008)), with exchangeable in-degree sequence (D̂1,D̂2,…,D̂n). We show that the exact formulae for these distributions and their expected values can be given in terms of the distributions of simple functions of the in-degree variables D̂1,D̂2,…,D̂n. As an application of these results, we consider two special examples of TnD̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine the exact distributions for the number of predecessors and the number of successors in these cases. We also characterise, for these two special examples, the asymptotic behaviour of the expected numbers of predecessors and successors and interpret these results in terms of the threshold behaviour of epidemic processes on random mapping graphs. The families of discrete distributions obtained in this paper are also of independent interest.

Scale-free growing networks imply linear preferential attachment

2001 ◽  
Vol 65 (1) ◽  
Author(s):  
Kasper Astrup Eriksen ◽  
Michael Hörnquist
Keyword(s):  
Preferential Attachment ◽  
Scale Free ◽  
Growing Networks

Predecessors and Successors in Random Mappings with Exchangeable In-Degrees

2013 ◽  
Vol 50 (03) ◽  
pp. 721-740 ◽  
Author(s):  
Jennie C. Hansen ◽  
Jerzy Jaworski
Keyword(s):  
Asymptotic Behaviour ◽  
Preferential Attachment ◽  
Degree Sequence ◽  
Discrete Distributions ◽  
Threshold Behaviour ◽  
Mapping Model ◽  
Random Mapping ◽  
Exact Distributions ◽  
Random Mappings ◽  
Expected Values

In this paper we characterise the distributions of the number of predecessors and of the number of successors of a given set of vertices, A, in the random mapping model, T n D̂ (see Hansen and Jaworski (2008)), with exchangeable in-degree sequence (D̂ 1,D̂ 2,…,D̂ n ). We show that the exact formulae for these distributions and their expected values can be given in terms of the distributions of simple functions of the in-degree variables D̂ 1,D̂ 2,…,D̂ n . As an application of these results, we consider two special examples of T n D̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine the exact distributions for the number of predecessors and the number of successors in these cases. We also characterise, for these two special examples, the asymptotic behaviour of the expected numbers of predecessors and successors and interpret these results in terms of the threshold behaviour of epidemic processes on random mapping graphs. The families of discrete distributions obtained in this paper are also of independent interest.

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