Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an explanation of how it can arise from a more basic underlying mechanism of competition between opposing forces. We introduce a family of one-dimensional geometri...

In this paper, a new two-parameter distribution called generalized power Akshaya extended from is introduced. This proposed to model lifetime data. Statistical properties like density, hazard, survival and moments are derived. Two parameters estimation introduced using maximum likelihood Bayesian techniques. Finally, an application of real data simulation study illustrate the usefulness distrib...

The opacity of typical objects in the world results in occlusion, an important property of natural scenes that makes inference of the full three-dimensional structure of the world challenging. The relationship between occlusion and low-level image statistics has been hotly debated in the literature, and extensive simulations have been used to determine whether occlusion is responsible for the u...

This study investigated bending, buckling, and free vibration responses of hyperbolic shear deformable functionally graded (FG) higher order beams. The material properties of FG beams are varied through thickness according to power law distribution; here, the FG beam was made of aluminium/alumina, and the hyperbolic shear deformation theory was used to evaluate the effect of shear deformation i...

We introduce a new class of random graph models for complex realworld networks, based on the protean graph model by à Luczak and PraÃlat. Our generalized protean graph models have two distinguishing features. First, they are not growth models, but instead are based on the assumption that a “steady state” of large but finite size has been reached. Second, the models assume that the vertices are ...

We introduce a new class of random graph models for complex realworld networks, based on the protean graph model by à Luczak and PraÃlat. Our generalized protean graph models have two distinguishing features. First, they are not growth models, but instead are based on the assumption that a “steady state” of large but finite size has been reached. Second, the models assume that the vertices are ...

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...

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is applied to the measurements. A link function can also be used to define an alternative structure on a set. We will see that generalized entropies are equivalen...