In earlier work, we showed using Kulback-Leibler (KL) divergence that tags form a power law distribution very quickly. Yet there is one major observed deviation from the ideal power law distribution for the top 25 tags, a large “bump” in increased frequency for the top 7-10 tags. We originally hypothesized that the “bump” in the data could be caused by a preferential attachment mechanism. Howev...

In the study of the spectra of power-law graphs, there are basically two competing approaches. One is to prove analogues of Wigner's semicircle law, whereas the other predicts that the eigenvalues follow a power-law distribution. Although the semicircle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matric...

In the study of the spectra of power law graphs, there are basically two competing approaches. One is to prove analogues of Wigner’s semi-circle law while the other predicts that the eigenvalues follow a power law distributions. Although the semi-circle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matric...

Objective(s): One applications of nanotechnology is in the area of medicine which is called nanomedicine. Primary instruments in nanomedicine can help us to detect diseases and used for drug delivery to inaccessible areas of human tissues. An important issue in simulating the motion of nanoparticles is modeling blood flow as a Newtonian or non-Newtonian fluid. Sometimes blood flow is simulated ...

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of...

A granular column is subjected to a small amplitude impact on its top. For a generalized power-law contact force between neighboring grains, numerical simulations show that the propagation of the impulse wave is controlled by dispersion. This leads quantitatively to a power-law decrease of the amplitude of the wave with depth. We find numerically the dependence of this power-law exponent on the...

Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and ...

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesi...

Benford’s Law gives the expected frequencies of the digits in tabulated data and asserts that the lower digits (1, 2, and 3) are expected to occur more frequently than the higher digits. This study tested whether the law applied to two large earth science data sets. The first test analyzed streamflow statistics and the finding was a close conformity to Benford’s Law. The second test analyzed th...

A constitutive law for rock behaviors including the brittle, transient and steady-state behaviors is derived to recognize the temporal seismicity patterns on surface displacement or prior and subsequent to mainshocks, and formulated as the relaxation modulus (i.e., the ratio of stress to strain) following a temporal power-law relaxation. This constitutive law is transformable into the empirical...