Children are proficient integrators of stimulus information. They have followed the three mathematical laws of information integration in several areas of psychology, especially in moral cognition (e.g., Anderson, 1980, 1983, 1991c, 1996a, Chapters 6 and 8). These integration laws provide effective theory for studying cognitive processes through their development. These laws not only mirror th...

From the available literature, the allometric scaling laws generally exist in biology, ecology, etc. These scaling laws obey power law distributions. A possibly better approach to characterize the power law is to utilize fractional derivatives. In this paper, we establish a fractional differential equation model for this allometry by using the Caputo fractional derivatives.

In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a ...

Links between power law probability distributions and marginal distributions of uniform laws on p-spheres in R show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters p and n to the value of the nonextensivity parameter q that characterizes these power laws in the context of non-extensive stat...