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.
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. 12 the outbreak containment. 13 We consider here deterministic compartmental models, based on a system of initial 14 value problems of Ordinary Differential Equations. This theory has been studied since 15 the beginning of the century by W.O. Kermack and A. G. MacKendrick [3] who 16proposed the basic Susceptible-Infected-Removed (SIR) model. The SIR model and its 17 later modifications, such as Susceptible-Exposed-Infected-Removed (SEIR) [4] were later 18 introduced in the study of outbreaks diffusion. These models split the population into 19 : medRxiv preprint groups, compartments, and reproduce their behaviour by formalising their reciprocal 20 interactions. For example, the SIR model groups are Susceptible who can catch the 21 disease, Infected who have the disease and can spread it, and Removed those who have 22 either had the disease or are recovered, immune or isolated until recovery. The SEIR 23 model proposed by Chowell et al. [5] also considers the Exposed group: containing 24 individuals who are in the incubation period. 25The evolution of the Infected group depends on a critical parameter, usually denoted 26 as R0, representing the basic reproductive rate and it measures of how transferable a 27 disease is. This quantity determines whether the infection will spread exponentially, die 28 out, or remain constant. When R 0 > 1 the epidemic is spreading.
The aim of this paper is to present a computational study on scaling techniques in gradient projection-type (GP-type)methods for deblurring of astronomical images corrupted by Poisson noise. In this case, the imaging problem is formulated as a non-negatively constrained minimization problem in which the objective function is the sum of a fit-to-data term, the Kullback–Leibler divergence, and a Tikhonov regularization term. The considered GP-type methods are formulated by a common iteration formula, where the scaling matrix and the step-length parameter characterize the different algorithms. Within this formulation, both first-order and Newton-like methods are analysed, with particular attention to those implementation features and behaviours relevant for the image restoration problem. The numerical experiments show that suited scaling strategies can enable the GP methods to quickly approximate accurate reconstructions and then are useful for designing effective image deblurring algorithms
We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiable Total Variation function. The problem is challenging for its very large size and because a good reconstruction is required in a very short time. For these reasons, we propose to use a gradient projection method, accelerated by exploiting a scaling strategy for defining gradient-based descent directions and generalized Barzilaiâ\u80\u93Borwein rules for the choice of the step-lengths. The numerical results on a 3D phantom are very promising since they show the ability of the scaling strategy to accelerate the convergence in the first iterations
Variational Autoencoders (VAEs) are powerful generative models that merge elements from statistics and information theory with the flexibility offered by deep neural networks to efficiently solve the generation problem for high-dimensional data. The key insight of VAEs is to learn the latent distribution of data in such a way that new meaningful samples can be generated from it. This approach led to tremendous research and variations in the architectural design of VAEs, nourishing the recent field of research known as unsupervised representation learning. In this article, we provide a comparative evaluation of some of the most successful, recent variations of VAEs. We particularly focus the analysis on the energetic efficiency of the different models, in the spirit of the so-called Green AI, aiming both to reduce the carbon footprint and the financial cost of generative techniques. For each architecture, we provide its mathematical formulation, the ideas underlying its design, a detailed model description, a running implementation and quantitative results.
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