Concavity and efficient points of discrete distributions in probabilistic programming

We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples. Received: October 1998 / Accepted: June 2000?Published online October 18, 2000     

Stochastic resonance in ferromagnetic domain motion

A model for the motion of a single ferromagnetic domain is studied numerically and analytically. A single strip in two dimensions and pinned at two inhomogeneities is considered. We suppose two stable configurations (positively or negatively curved with pinned ends) due to the action of a bistable potential. Further, it is assumed that the domain is driven externally by periodic and noisy magnetic fields. The noise makes the domain able to flip between the two configurations. The small temporally periodic fields synchronize these flippings and the phenomenon of stochastic resonance is observed. The signal to noise ratio of the output is investigated and shows a maximum for a nonvanishing intensity of the applied noise. Its dependency on the stiffness of the domain is studied. Received 14 May 1999 and Received in final form 14 October 1999     

Noise-assisted traffic of spikes through neuronal junctions

The presence of noise, i.e., random fluctuations, in the nervous system raises at least two different questions. First, is there a constructive role noise can play for signal transmission in a neuron channel? Second, what is the advantage of the power spectra observed for the neuron activity to be shaped like 1/f(k)? To address these questions a simple stochastic model for a junction in neural spike traffic channels is presented. Side channel traffic enters main channel traffic depending on the spike rate of the latter one. The main channel traffic itself is triggered by various noise processes such as Poissonian noise or the zero crossings of Gaussian 1/f(k) noise whereas the variation of the exponent k gives rise to a maximum of the overall traffic efficiency. It is shown that the colored noise is superior to the Poissonian and, in certain cases, to deterministic, periodically ordered traffic. Further, if this periodicity itself is modulated by Gaussian noise with different spectral exponents k, then such modulation can lead to noise-assisted traffic as well. The model presented can also be used to consider car traffic at a junction between a main and a side road and to show how randomness can enhance the traffic efficiency in a network. (c) 2001 American Institute of Physics.