This chapter reviews the role of theory in body-size scaling and biodiversity scaling. It considers the prospects for theoretical development in spatial scaling. The scaling of biodiversity to area has a history of empirical findings that extend back to the 19th century. Biodiversity scales with ...
Power-law scaling, a central concept in critical phenomena, is found to be useful in deep learning, where optimized test errors on handwritten digit examples converge as a power-law to zero with database size. For rapid decision making with one training epoch, each example is presented only ...
Here I present both model‐based and empirical evidence that this aggregation parameter is likely to scale very generally as the power law kA?∝?A0.5, particularly at large spatial scales. This finding contrasts with the spatial predictions of the Maximum Entropy Theory of Ecology and has ...
The use of allometric equations, typified by power-law scaling, is the predominant paradigm used to explicate the interaction of body measurements in relation to body size (Huxley, 1932). This is often stated as Y=Y0Mb,where Y is a body measurement (for example, longevity, organ weight, ...
A phenomenological theory, taking into account the different character of thermal boundary layers at the bottom and at the free surface, is developed. It predicts a power-law scaling for the nondimensional velocity (Peclet number) and heat flux (Nusselt number) of the form Pe approximately Ma(...
Since in theory the scaling exponents, 尉(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well ...
Fig. 1: NV level scheme and power-law model. Full size image Results Theory Fig. 2: Experimental data from correlation spectroscopy measurement with a single NV centre. Full size image Experiments Correlation spectroscopy with a single NV centre ...
Moreover, the horizontal area increases as a power law of the maximum local retreat, identifying a third exponent. This observation indicates that the geometry of cliff failures are similar for different magnitudes. It is shown that, under a 'scaling hypothesis', the exponents satisfy a precise ...
Probability theoryAn important method for search engine result ranking works by finding the principal eigenvector of the ``Google matrix.'' Recently, a quantum algorithm for generating this eigenvector as a quantum state was presented, with evidence of an exponential speedup of this process for ...
The power-law scaling between body mass and organ weight was produced by the synchronous exponential increments and the allometric exponent is rate of logarithmic cell proliferation rate. Substituting organ weight for erythrocyte weight aided in the development of a power-law scaling relationship between...