This Special Issue of Mathematics and Computers in Simulation collects a selection of peer-reviewed original articles on research topics developed in connection with IMACS2023, the IMACS World Congress, held in Rome (Italy) at the Faculty of Engineering, Sapienza University of Rome on September 11 - 15, 2023, that we organized, in the role of Local Scientific Committee, together with Rosa Maria Spitaleri, Congress Chair.

In this editorial the historical premises of the world Congress IMACS2023 are delineated in order to appreciate the development of IMACS as a scientific association keeping up with the ultimate scientific aspirations of society in the fields of Applied Mathematics and Scientific Computing. The World Congress, IMACS2023, the last considered step, celebrates successfully such a prestigious story.

Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can be used to reduce the computational load required to evaluate the numerical solution of the EEG inverse problem. To this end, in this paper we use the random dipole sampling method, in which a Monte Carlo technique is used to reduce the number of neural sources. This is equivalent to reducing the number of the unknowns in the inverse problem and can be seen as a first regularization step. Then, we solve the reduced EEG inverse problem with two popular inversion methods, the weighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolution brain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is the error estimates of the reconstructed activity map obtained with the randomized version of wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstrate the effectiveness of the random dipole sampling method.