Due to the recent evolution of the COVID-19 outbreak, the scientific community is making efforts to analyse models for understanding the present situation and for predicting future scenarios. In this paper, we propose a forced Susceptible-Exposed-Infected-Recovered-Dead (fSEIRD) differential model for the analysis and forecast of the COVID-19 spread in Italian regions, using the data from the Italian Protezione Civile (Italian Civil Protection Department) from 24/02/2020. In this study, we investigate an adaptation of fSEIRD by proposing two different piecewise time-dependent infection rate functions to fit the current epidemic data affected by progressive movement restriction policies put in place by the Italian government. The proposed models are flexible and can be quickly adapted to monitor various epidemic scenarios. Results on the regions of Lombardia and Emilia-Romagna confirm that the proposed models fit the data very accurately and make reliable predictions.

The inversion of two-dimensional NMR data is an ill-posed problem related to the numerical computation of the inverse Laplace transform. The Uniform Penalty (UPEN) algorithm (Borgia et al 1998 J. Magn. Reson. 132 65–77 ), defined for the inversion of one-dimensional NMR relaxation data, uses Tikhonov-like regularization and optional lower bound constraints in order to implement locally adapted regularization. In this paper, we analyze the regularization properties of this approach. Moreover, we extend the one-dimensional UPEN algorithm to the two-dimensional case and present an efficient implementation based on the Newton Projection method (2DUPEN). Without any a-priori information on the noise norm, 2DUPEN automatically computes the locally adapted regularization parameters and the distribution of the unknown NMR parameters by using variable smoothing. Results of numerical experiments on simulated and real data are presented in order to illustrate the potential of the proposed method in reconstructing peaks and flat regions with the same accuracy.

Due to the recent diffusion of COVID-19 outbreak, the scientific community is making efforts in analysing models for understanding the present situation and predicting future scenarios. In this paper, we propose a Susceptible-Infected-Exposed-Recovered-Dead (SEIRD) differential model [Weitz J. S. and Dushoff J., Scientific reports, 2015] for the analysis and forecast of the COVID-19 spread in Italian regions, using the data from the Italian Protezione Civile from February 24th 2020. In this study, we investigate an adaptation of SEIRD that takes into account the actual policies of the Italian government, consisting of modelling the infection rate as a time-dependent function (SEIRD(rm)). Preliminary results on Lombardia and Emilia-Romagna regions confirm that SEIRD(rm) fits the data more accurately than the original SEIRD model with constant rate infection parameter. Moreover, the increased flexibility in the choice of the infection rate function makes it possible to better control the predictions due to the lockdown policy.

The main limitation of digital image correlation is the remarkable noise affecting the digital image correlation–computed strain distributions. Neither manufacturers of digital image correlation systems nor the literature provide guidelines for optimal filtering of digital image correlation strain distributions. However, filtering is also associated with loss of information (smoothing of the strain gradients). We systematically explored different filtering strategies to reduce noise while minimizing the loss of information in the digital image correlation–computed strain distributions. The first filtering strategy was directly applied to the acquired images that were then fed to the digital image correlation software. Median adaptive low-pass filters and notch filters were used to eliminate noise: both strategies increased (rather than reducing) the noise in the digital image correlation–computed strain distributions. The second strategy explored was a Gaussian low-pass filtering of the strain distributions. When the optimal cutoff frequency was selected, the noise was remarkably reduced (by 70%) without excessive loss of information. At the same time, when non-optimal cutoff frequencies were used, the residual noise and/or loss of information seriously compromised the results. Finally, image combination techniques were applied both to the input images and to the strain distributions. This strategy was extremely time-consuming but not very effective (noise reduction <10%). In conclusion, the only truly effective noise reduction strategy, if measurements are carried out using commercial closed software, consists in filtering the strain distribution.