Using a decomposition of the characteristic function of the logarithm of the product of independent generalized gamma-ratio random variables (r.v.’s), we obtain explicit expressions for both the probability density and cumulative distribution functions of the product of independent r.v.’s with generalized F or generalized gamma-ratio distributions in the form of particular mixtures of generaliz...

Distortions in the FID and spin echo due to magnetic field inhomogeneity are proved to have a representation as the characteristic function of some probability distribution. In the special case that the distribution is Cauchy, the model reduces to the conventional Lorentzian model. A more general and flexible representation is presented using the Fourier transform of a logspline density. An alg...

How neurons in the cerebral cortex process and transmit information is a long-standing question in systems neuroscience. To analyze neuronal activity from an information-energy efficiency standpoint, Berger and Levy calculated the maximum Shannon mutual information transfer per unit of energy expenditure of an idealized integrateand-fire (IIF) neuron whose excitatory synapses all have the same ...

The probabilities for gaps in the eigenvalue spectrum of finite N ×N random unitary ensembles on the unit circle with a singular weight, and the related Hermitian ensembles on the line with Cauchy weight, are found exactly. The finite cases for exclusion from single and double intervals are given in terms of second-order second-degree ordinary differential equations (ODEs) which are related to ...