In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show tha...

We study in this paper the correlation between the semantic (data) complexity of first order, proportional, aggregate and Ramsey generalized quantification and their distribution in corpora. We show that, as expected by the theory, such distribution is significantly skewed towards tractable as opposed to intractable quantifiers. We also study whether such relationship can be described by a powe...

A dynamical analogy supported by five scale-free statistics (the Gutenberg-Richter distribution of event sizes, the distribution of interevent intervals, the Omori and inverse Omori laws, and the conditional waiting time until the next event) is shown to exist between two classes of seizures ("focal" in humans and generalized in animals) and earthquakes. Increments in excitatory interneuronal c...

The combined effect of non-Newtonian rheology and irreversible boundary reaction on dispersion in a Herschel-Bulkley fluid through a conduit (pipe/channel) is studied by using generalized dispersion model. The study explains the development of dispersive transport following the injection of a tracer in terms of three effective transport coefficients namely exchange, convective and dispersion co...

It is demonstrated clearly that for the same classical generalized system the Tsallis power-laws with both the 1 > q and the 1 < q can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithme...

We introduce a protocol with a reconfigurable filter system to create non-overlapping single loops in the smart power grid for the realization of the Kirchhoff-Law-Johnson-(like)-Noise secure key distribution system. The protocol is valid for one-dimensional radial networks (chain-like power line) which are typical of the electricity distribution network between the utility and the customer. Th...

It is demonstrated clearly that for the same classic generalized system the Tsallis power-laws with both the 1 > q and the 1 < q can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithmeti...

We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter α and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched...

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional...