A concentrated Cauchy distribution with finite moments

The Cauchy distribution has no moments (expected value, variance, etc.), because the defining integrals diverge. A way to “concentrate” the Cauchy distribution, in order to get finite moments, is suggested by an elementary problem in mechanics, giving the Cauchy distribution as a special case. The concentrated distribution has finite moments of all orders, while keeping … Read more


A generalized Weiszfeld method is proposed for the multi–facility location problem. The problem is relaxed using probabilistic assignments, and is decomposed into single facility location problems, that are coupled by these assignments, and can be solved in parallel. The probabilistic assignments are updated at each iteration, using the distances to the current centers. The method … Read more

On linear infeasibility arising in intensity-modulated radiation therapy inverse planning

Intensity–modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {a,ß}–relaxation, meaning that no more than a percent of the inequalities are violated by no more than ß … Read more