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...

The geomagnetic activity of the Dst index is analyzed using wavelet transforms and it is shown that the Dst index possesses properties associated with self-affine fractals. For example, the power spectral density obeys a powerlaw dependence on frequency, and therefore the Dst index can be viewed as a self-affine fractal dynamic process. In fact, the behaviour of the Dst index, with a Hurst expo...

Zipf’s law of word frequencies for language discourses is established with statistical rigor. Data show a departure from Zipf’s power law term at low frequencies. This is accounted by a modifying exponential term. Both arise naturally in a model for word frequencies based on Information Theory, algorithmic coding of a text preserving the symbol sequence, concepts from quantum statistical physic...

The nature of CD8(+) T cell memory is still incompletely understood. We have previously reported that the response to an HLA-A2-restricted influenza-derived peptide results in a complex T cell repertoire. In this study we extend this analysis and describe the repertoire with more rigor. In one individual we defined 141 distinct T cell clonotypes on the basis of the unique DNA sequence of the th...

The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to ?2: S(k) / k ?2. In addition, river networks are fractal trees that satisfy several power-law relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces ...

Use of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture...

After the shale reservoir is hydraulically fractured, gas transported to horizontal well through various media. Hydraulic fracturing produces hydraulic fractures and generates secondary fractures. The fracture induction areas are filled with water phases. In this work, using power-law distribution porous media fractal theory, as accounting for seepage mechanisms in both phases, a multi-scale mi...

We investigate the sandpile model on the two-dimensional Sierpinski gasket fractal. We find that the model displays interesting critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes, and topplings and calculate the associated critical exponents t51.5160.04, a51.6360.04, and m51.3660.04. The avalanche size distribution shows power-law behavior modulated by lo...

Many physical processes have distributions of times between events that have non-normalizable, power law probability density functions ~PDF’s!. The moments of such distributions are not defined. We found that the PDF’s of the times between events of ventricular tachyarrhythmia ~rapid heart rate! and premature ventricular contractions have a power law form indicative of a non-normalizable distri...