BACKGROUND Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. RESULTS The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carri...

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transf...

Many driven threshold systems display a spectrum of avalanche event sizes, often characterized by power-law scaling. An important problem is to compute probabilities of the largest events ("Black Swans"). We develop a data-driven approach to the problem by transforming to the event index frame, and relating this to Shannon information. For earthquakes, we find the 12-month probability for magni...

Although many adaptations occur by selection of beneficial alleles transformed from neutral or deleterious standing variation, new identical mutant alleles that arise as premeiotic clusters have an increased probability of fixation that can rise to the levels that are similar to the fixation of standing variation. Hence, the evidence is still out on the proportion of adaptations that use preexi...

BACKGROUND For analyzing a repeated ordinal response, it is common to use a multivariate cumulative logit model. This model may fit poorly, especially when a nonsymmetric response is available. In these cases, alternative strategies should be utilized. METHODS In this paper, we present a family of power transformations for the cumulative probabilities to model asymmetric departures from the r...

Let S(N) be a random walk on a countable abelian group G which acts on a probability space E by measure–preserving transformations (Tv)v∈G. For any Λ ⊂ E we consider the random return time τ at which TS(τ) ∈ Λ. We show that the corresponding induced skew product transformation is K–mixing whenever a natural subgroup of G acts ergodically on E.

Extreme all-direction wave conditions and joint probabilities of high waves and high water levels are derived at selected locations in the southern Arabian Gulf. The wave conditions are obtained using the spectral wave model SWAN with wind and offshore wave information procured from ocean weather, supplemented with local water level records. Wave transformations from offshore to nearshore and w...

With the ascent of modern epidemiology in the Twentieth Century came a new standard model of prediction in public health and clinical medicine. In this article, we describe the structure of the model. The standard model uses epidemiological measures-most commonly, risk measures-to predict outcomes (prognosis) and effect sizes (treatment) in a patient population that can then be transformed into...

We investigated the manner in which the outputs of the three postreceptoral mechanisms (red-green, blue-yellow and luminance) combine to determine contrast threshold. We used a subthreshold summation paradigm to test whether the combination of the postreceptoral mechanism outputs could be described by a probability summation model which assumes stochastic independence of the mechanisms, and det...