We used Allan factor analysis to classify time series of the discharges of single presympathetic neurons in the cat medullary lateral tegmental field (LTF) and rostral ventrolateral medulla (RVLM) and of the postganglionic vertebral sympathetic nerve. These time series fell into two classes of fractal-based point processes characterized by statistically self-similar behavior reflecting long-ran...

This paper seeks to check the validity of a hypothesis known as the “apparent fractal conjecture” (Ribeiro 1999: gr-qc/9909093), which states that the observed fractal structure of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in fractal characterization, are calculated along the past light cone. Since general relativity states that ...

We report a numerical study of van der Waals adsorption and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distribution of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to cros...

“Our analysis finds Earth’s lakes are power-law distributed for lakes ≥ 8.5 km2 (Fig. 2). Lakes < 8.5 km2 deviate from the power-law distribution such that there are fewer of these small lakes than expected if small lakes conformed to the same power-law distribution as large lakes. Across the range of lake sizes conforming to a power-law distribution, the tail exponent is τ = 1.97 (+ /− 0.01), ...

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transf...

A new algorithm, called herein the random power domain algorithm, is discussed; it generates the image corresponding to an iterated function system with probabilities, a technique used in fractal image decoding. A simple complexity analysis for the algorithm is also derived.

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scalin...

&lt;p style='text-indent:20px;'&gt;We obtain the solutions of fractal fractional differential equations with power law kernel by reproducing Hilbert space method in this paper. We also apply Laplace transform to get exact problems. compare approximate solutions. demonstrate our results some tables and figures. prove efficiency proposed technique for equations.&lt;/p&gt;