Stem cell therapy is a regenerative medicine technique consisting in introducing new cells into a damaged tissue in order to restore it. In this paper we present our multidisciplinary approach about the possible use of the Human Mesenchymal Stem Cells in treating heart failure. A multidisciplinary team composed by biologists, mathematicians, cardiologists and bioengineers was selected in order to investigate the feasibility of repairing the necrotic tissue damaged by myocardial infarction by means of Mesenchymal Stem Cells and to implement a new software simulator able to reproduce cells implantation, migration and proliferation. In the first step, biologists and cardiologists studied the Human Mesenchymal Stem Cells and measured selected parameters. Stem cells were isolated and cultured in order to study their growth and characterization. In the second step, mathematicians and bioengineers developed a new numerical model based on the studies and the data measured during in vitro experiments. The first version of the software simulator named MiStTher is able to give a first qualitative description of the stem cell therapy in some simplified schemes.

We investigate via Monte Carlo numerical simulations and theoretical considerations the outflux of random walkers moving in an interval bounded by an interface exhibiting channels (pores, doors) which undergo an open/close cycle according to a periodic schedule. We examine the onset of a limiting boundary behavior characterized by a constant ratio between the outflux and the local density, in the thermodynamic limit. We compare such a limit with the predictions of a theoretical model already obtained in the literature as the homogenization limit of a suitable diffusion problem.

This paper presents a novel approach for the extraction of the transients content of audio signals, usually represented as superposition of stationary, transient, and stochastic components. The proposed model exploits the predictable and peculiar time-scale behavior of transients by modeling them as superposition of suitable wavelet atoms. These latter allow to predict transients information even at scales where the tonal component is dominant. In this way it is possible to avoid, if required, the pre-analysis of the tonal component. Extensive experimental results show that the proposed model achieves good performances with a moderate computational effort and without any user's dependence.