Michele Piana

Sara Sommariva, Alberto Sorrentino, Michele Piana et al.

In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time--series. We assume that the neural sources follow a stable MultiVariate AutoRegressive model, and consider three connectivity metrics: Imaginary part of Coherency (IC), generalized Partial Directed Coherence (gPDC) and frequency--domain Granger Causality (fGC). In order to assess the statistical significance of the estimated values, we use the surrogate data test by generating phase--randomized and autoregressive surrogate data. We first consider the ideal case where we know the source time courses exactly. Here we show how, expectedly, even exact knowledge of the source time courses is not sufficient to provide reliable estimates of the connectivity when the number of samples gets small; however, while gPDC and fGC tend to provide a larger number of false positives, the IC becomes less sensitive to the presence of connectivity. Then we proceed with more realistic simulations, where the source time courses are estimated using eLORETA, and the EEG signal is affected by biological noise of increasing intensity. Using the ideal case as a reference, we show that the impact of biological noise on IC estimates is qualitatively different from the impact on gPDC and fGC.

G. Giorgi, M. Brignone, R. Aramini et al.

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation': the latter is a generalization of the classical Lippmann-Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then, the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper.

Sabrina Guastavino, Francesco Marchetti, Federico Benvenuto et al.

Operational flare forecasting aims at providing predictions that can be used to make decisions, typically at a daily scale, about the space weather impacts of flare occurrence. This study shows that video-based deep learning can be used for operational purposes when the training and validation sets used for the network optimization are generated while accounting for the periodicity of the solar cycle. Specifically, the paper describes an algorithm that can be applied to build up sets of active regions that are balanced according to the flare class rates associated to a specific cycle phase. These sets are used to train and validate a Long-term Recurrent Convolutional Network made of a combination of a convolutional neural network and a Long-Short Memory network. The reliability of this approach is assessed in the case of two prediction windows containing the solar storm of March 2015 and September 2017, respectively.

Alberto Sorrentino, Michele Piana

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.

Sara Garbarino, Giacomo Caviglia, Massimo Brignone et al.

This paper describes a general approach to the compartmental modeling of nuclear data based on spectral analysis and statistical optimization. We utilize the renal physiology as test case and validate the method against both synthetic data and real measurements acquired during two micro-PET experiments with murine models.

Mara Scussolini, Sara Garbarino, Gianmario Sambuceti et al.

The present paper proposes a novel computational method for parametric imaging of nuclear medicine data. The mathematical procedure is general enough to work for compartmental models of diverse complexity and is effective in the determination of the parametric maps of all kinetic parameters governing tracer flow. We consider applications to [18F]-fluorodeoxyglucose Positron Emission Tomography (FDG-PET) data and analyze the two-compartment catenary model describing the standard FDG metabolization by an homogeneous tissue, e.g. the liver, and the three-compartment non-catenary model representing the renal physiology. The proposed imaging method starts from the reconstructed FDG-PET images of tracer concentration and preliminarily applies image processing algorithms for noise reduction and image segmentation processes for selecting the region enclosing the organ of physiologic interest. The optimization scheme solves pixelwise the non-linear inverse problem of determining the kinetic parameters from dynamic concentration data through a Gauss-Newton iterative algorithm with a penalty term accounting for the ill-posedness of the problem. We tested our imaging approach on FDG-PET data of murine models obtained by means of a dedicated microPET system, and we analyzed different PET slices containing axial sections of the liver and axial sections of the kidneys. The reconstructed parametric images proved to be reliable and qualitatively effective in the description of the local FDG metabolism with respect to the different physiologies.

Riccardo Aramini, Fabrice Delbary, Mauro C. Beltrametti et al.

The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition technique, which is mainly used to detect straight lines in digital images and which has been recently extended to the automatic recognition of algebraic plane curves. Although defined in very different ways, in numerical applications both transforms ultimately take an image as an input and provide, as an output, a function defined on a parameter space. The parameters in this space describe a family of curves, which represent either the integration domains considered in the (generalized) Radon transform, or the curves to be detected by means of the Hough transform. In both cases, the 2D plot of the intensity values of the output function is the so-called (Radon or Hough) sinogram. While the Hough sinogram is produced by an algorithm whose implementation requires that the parameter space be discretized in cells, the Radon sinogram is mathematically defined on a continuous parameter space, which in turn may need to be discretized just for physical or numerical reasons. In this paper, by considering a more general and n-dimensional setting, we prove that, whether the input image is described as a set of points (possibly with different intensity values) or as a piecewise constant function, its (rescaled) Hough sinogram converges to the corresponding Radon sinogram as the discretization step in the parameter space tends to zero. We also show that this result may have a notable impact on the image reconstruction problem of inverting the Radon sinogram recorded by a medical imaging scanner, and that the description of the Hough transform problem within the framework of regularization theory for inverse problems is worth investigating.

Anna Maria Massone, Federica Sciacchitano, Michele Piana et al.

We describe two inversion methods for the reconstruction of hard X-ray solar images. The methods are tested against experimental visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and synthetic visibilities based on the design of the Spectrometer/Telescope for Imaging X-rays (STIX).

Federico Benvenuto, Michele Piana

In this paper we propose a new statistical stopping rule for constrained maximum likelihood iterative algorithms applied to ill-posed inverse problems. To this aim we extend the definition of Tikhonov regularization in a statistical framework and prove that the application of the proposed stopping rule to the Iterative Space Reconstruction Algorithm (ISRA) in the Gaussian case and Expectation Maximization (EM) in the Poisson case leads to well defined regularization methods according to the given definition. We also prove that, if an inverse problem is genuinely ill-posed in the sense of Tikhonov, the same definition is not satisfied when ISRA and EM are optimized by classical stopping rule like Morozov's discrepancy principle, Pearson's test and Poisson discrepancy principle. The stopping rule is illustrated in the case of image reconstruction from data recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). First, by using a simulated image consisting of structures analogous to those of a real solar flare we validate the fidelity and accuracy with which the proposed stopping rule recovers the input image. Second, the robustness of the method is compared with the other classical stopping rules and its advantages are shown in the case of real data recorded by RHESSI during two different flaring events.

Luca Caldera, Lara Cavinato, Alessio Cirone et al.

Harmonization of T1-weighted MR images across different scanners is crucial for ensuring consistency in neuroimaging studies. This study introduces a novel approach to direct image harmonization, moving beyond feature standardization to ensure that extracted features remain inherently reliable for downstream analysis. Our method enables image transfer in two ways: (1) mapping images to a scanner-free space for uniform appearance across all scanners, and (2) transforming images into the domain of a specific scanner used in model training, embedding its unique characteristics. Our approach presents strong generalization capability, even for unseen scanners not included in the training phase. We validated our method using MR images from diverse cohorts, including healthy controls, traveling subjects, and individuals with Alzheimer's disease (AD). The model's effectiveness is tested in multiple applications, such as brain age prediction (R2 = 0.60 \pm 0.05), biomarker extraction, AD classification (Test Accuracy = 0.86 \pm 0.03), and diagnosis prediction (AUC = 0.95). In all cases, our harmonization technique outperforms state-of-the-art methods, showing improvements in both reliability and predictive accuracy. Moreover, our approach eliminates the need for extensive preprocessing steps, such as skull-stripping, which can introduce errors by misclassifying brain and non-brain structures. This makes our method particularly suitable for applications that require full-head analysis, including research on head trauma and cranial deformities. Additionally, our harmonization model does not require retraining for new datasets, allowing smooth integration into various neuroimaging workflows. By ensuring scanner-invariant image quality, our approach provides a robust and efficient solution for improving neuroimaging studies across diverse settings. The code is available at this link.

Edoardo Legnaro, Sabrina Guastavino, Michele Piana et al.

A solar active region can significantly disrupt the Sun Earth space environment, often leading to severe space weather events such as solar flares and coronal mass ejections. As a consequence, the automatic classification of active region groups is the crucial starting point for accurately and promptly predicting solar activity. This study presents our results concerned with the application of deep learning techniques to the classification of active region cutouts based on the Mount Wilson classification scheme. Specifically, we have explored the latest advancements in image classification architectures, from Convolutional Neural Networks to Vision Transformers, and reported on their performances for the active region classification task, showing that the crucial point for their effectiveness consists in a robust training process based on the latest advances in the field.

Fabiana Camattari, Sabrina Guastavino, Francesco Marchetti et al.

The purpose of this study is to introduce a new approach to feature ranking for classification tasks, called in what follows greedy feature selection. In statistical learning, feature selection is usually realized by means of methods that are independent of the classifier applied to perform the prediction using that reduced number of features. Instead, greedy feature selection identifies the most important feature at each step and according to the selected classifier. In the paper, the benefits of such scheme are investigated theoretically in terms of model capacity indicators, such as the Vapnik-Chervonenkis (VC) dimension or the kernel alignment, and tested numerically by considering its application to the problem of predicting geo-effective manifestations of the active Sun.

Chiara Curletto, Paolo Massa, Valeria Tagliafico et al.

Solar flares are the most explosive phenomena in the solar system and the main trigger of the events' chain that starts from Coronal Mass Ejections and leads to geomagnetic storms with possible impacts on the infrastructures at Earth. Data-driven solar flare forecasting relies on either deep learning approaches, which are operationally promising but with a low explainability degree, or machine learning algorithms, which can provide information on the physical descriptors that mostly impact the prediction. This paper describes a web-based technological platform for the execution of a computational pipeline of feature-based machine learning methods that provide predictions of the flare occurrence, feature ranking information, and assessment of the prediction performances.

Margherita Lampani, Sabrina Guastavino, Michele Piana et al.

Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear regression to standardized features, without considering their physical meaning. This may limit model explainability, particularly in scientific applications. This study proposes a physics-informed approach to feature-based machine learning that constructs non-linear feature maps informed by physical laws and dimensional analysis. These maps enhance model interpretability and, when physical laws are unknown, allow for the identification of relevant mechanisms through feature ranking. The method aims to improve both predictive performance in regression tasks and classification skill scores by integrating domain knowledge into the learning process, while also enabling the potential discovery of new physical equations within the context of explainable machine learning.

Sabrina Guastavino, Katsiaryna Bahamazava, Emma Perracchione et al.

This study addresses the prediction of geomagnetic disturbances by exploiting machine learning techniques. Specifically, the Long-Short Term Memory recurrent neural network, which is particularly suited for application over long time series, is employed in the analysis of in-situ measurements of solar wind plasma and magnetic field acquired over more than one solar cycle, from $2005$ to $2019$, at the Lagrangian point L$1$. The problem is approached as a binary classification aiming to predict one hour in advance a decrease in the SYM-H geomagnetic activity index below the threshold of $-50$ nT, which is generally regarded as indicative of magnetospheric perturbations. The strong class imbalance issue is tackled by using an appropriate loss function tailored to optimize appropriate skill scores in the training phase of the neural network. Beside classical skill scores, value-weighted skill scores are then employed to evaluate predictions, suitable in the study of problems, such as the one faced here, characterized by strong temporal variability. For the first time, the content of magnetic helicity and energy carried by solar transients, associated with their detection and likelihood of geo-effectiveness, were considered as input features of the network architecture. Their predictive capabilities are demonstrated through a correlation-driven feature selection method to rank the most relevant characteristics involved in the neural network prediction model. The optimal performance of the adopted neural network in properly forecasting the onset of geomagnetic storms, which is a crucial point for giving real warnings in an operational setting, is finally showed.

Michele Piana, Federico Benvenuto, Anna Maria Massone et al.

AI-FLARES (Artificial Intelligence for the Analysis of Solar Flares Data) is a research project funded by the Agenzia Spaziale Italiana and by the Istituto Nazionale di Astrofisica within the framework of the ``Attività di Studio per la Comunità Scientifica Nazionale Sole, Sistema Solare ed Esopianeti'' program. The topic addressed by this project was the development and use of computational methods for the analysis of remote sensing space data associated to solar flare emission. This paper overviews the main results obtained by the project, with specific focus on solar flare forecasting, reconstruction of morphologies of the flaring sources, and interpretation of acceleration mechanisms triggered by solar flares.

Giulio Paolucci, Isabella Cama, Cristina Campi et al.

The analysis of the psoas muscle in morphological and functional imaging has proved to be an accurate approach to assess sarcopenia, i.e. a systemic loss of skeletal muscle mass and function that may be correlated to multifactorial etiological aspects. The inclusion of sarcopenia assessment into a radiological workflow would need the implementation of computational pipelines for image processing that guarantee segmentation reliability and a significant degree of automation. The present study utilizes three-dimensional numerical schemes for psoas segmentation in low-dose X-ray computed tomography images. Specifically, here we focused on the level set methodology and compared the performances of two standard approaches, a classical evolution model and a three-dimension geodesic model, with the performances of an original first-order modification of this latter one. The results of this analysis show that these gradient-based schemes guarantee reliability with respect to manual segmentation and that the first-order scheme requires a computational burden that is significantly smaller than the one needed by the second-order approach.

Francesco Marchetti, Sabrina Guastavino, Cristina Campi et al.

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores.

Sabrina Guastavino, Valentina Candiani, Alessandro Bemporad et al.

Coronal Mass Ejections (CMEs) correspond to dramatic expulsions of plasma and magnetic field from the solar corona into the heliosphere. CMEs are scientifically relevant because they are involved in the physical mechanisms characterizing the active Sun. However, more recently CMEs have attracted attention for their impact on space weather, as they are correlated to geomagnetic storms and may induce the generation of Solar Energetic Particles streams. In this space weather framework, the present paper introduces a physics-driven artificial intelligence (AI) approach to the prediction of CMEs travel time, in which the deterministic drag-based model is exploited to improve the training phase of a cascade of two neural networks fed with both remote sensing and in-situ data. This study shows that the use of physical information in the AI architecture significantly improves both the accuracy and the robustness of the travel time prediction.

Sabrina Guastavino, Michele Piana, Marco Tizzi et al.

The problem of nowcasting extreme weather events can be addressed by applying either numerical methods for the solution of dynamic model equations or data-driven artificial intelligence algorithms. Within this latter framework, the present paper illustrates how a deep learning method, exploiting videos of radar reflectivity frames as input, can be used to realize a warning machine able to sound timely alarms of possible severe thunderstorm events. From a technical viewpoint, the computational core of this approach is the use of a value-weighted skill score for both transforming the probabilistic outcomes of the deep neural network into binary classification and assessing the forecasting performances. The warning machine has been validated against weather radar data recorded in the Liguria region, in Italy,

Francesco Marchetti, Sabrina Guastavino, Michele Piana et al.

Loss functions engineering and the assessment of forecasting performances are two crucial and intertwined aspects of supervised machine learning. This paper focuses on binary classification to introduce a class of loss functions that are defined on probabilistic confusion matrices and that allow an automatic and a priori maximization of the skill scores. The performances of these loss functions are validated during the training phase of two experimental forecasting problems, thus showing that the probability distribution function associated with the confusion matrices significantly impacts the outcome of the score maximization process.

Sabrina Guastavino, Michele Piana, Federico Benvenuto

In this paper we propose a novel approach to realize forecast verification. Specifically, we introduce a strategy for assessing the severity of forecast errors based on the evidence that, on the one hand, a false alarm just anticipating an occurring event is better than one in the middle of consecutive non-occurring events, and that, on the other hand, a miss of an isolated event has a worse impact than a miss of a single event, which is part of several consecutive occurrences. Relying on this idea, we introduce a novel definition of confusion matrix and skill scores giving greater importance to the value of the prediction rather than to its quality. Then, we introduce a deep ensemble learning procedure for binary classification, in which the probabilistic outcomes of a neural network are clustered via optimization of these value-weighted skill scores. We finally show the performances of this approach in the case of three applications concerned with pollution, space weather and stock prize forecasting.

Emma Perracchione, Paolo Massa, Anna Maria Massone et al.

Space telescopes for solar hard X-ray imaging provide observations made of sampled Fourier components of the incoming photon flux. The aim of this study is to design an image reconstruction method relying on enhanced visibility interpolation in the Fourier domain. % methods heading (mandatory) The interpolation-based method is applied on synthetic visibilities generated by means of the simulation software implemented within the framework of the Spectrometer/Telescope for Imaging X-rays (STIX) mission on board Solar Orbiter. An application to experimental visibilities observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is also considered. In order to interpolate these visibility data we have utilized an approach based on Variably Scaled Kernels (VSKs), which are able to realize feature augmentation by exploiting prior information on the flaring source and which are used here, for the first time, for image reconstruction purposes.} % results heading (mandatory) When compared to an interpolation-based reconstruction algorithm previously introduced for RHESSI, VSKs offer significantly better performances, particularly in the case of STIX imaging, which is characterized by a notably sparse sampling of the Fourier domain. In the case of RHESSI data, this novel approach is particularly reliable when either the flaring sources are characterized by narrow, ribbon-like shapes or high-resolution detectors are utilized for observations. % conclusions heading (optional), leave it empty if necessary The use of VSKs for interpolating hard X-ray visibilities allows a notable image reconstruction accuracy when the information on the flaring source is encoded by a small set of scattered Fourier data and when the visibility surface is affected by significant oscillations in the frequency domain.

Federico Benvenuto, Cristina Campi, Anna Maria Massone et al.

Machine learning is nowadays the methodology of choice for flare forecasting and supervised techniques, in both their traditional and deep versions, are becoming the most frequently used ones for prediction in this area of space weather. Yet, machine learning has not been able so far to realize an operating warning system for flaring storms and the scientific literature of the last decade suggests that its performances in the prediction of intense solar flares are not optimal. The main difficulties related to forecasting solar flaring storms are probably two. First, most methods are conceived to provide probabilistic predictions and not to send binary yes/no indications on the consecutive occurrence of flares along an extended time range. Second, flaring storms are typically characterized by the explosion of high energy events, which are seldom recorded in the databases of space missions; as a consequence, supervised methods are trained on very imbalanced historical sets, which makes them particularly ineffective for the forecasting of intense flares. Yet, in this study we show that supervised machine learning could be utilized in a way to send timely warnings about the most violent and most unexpected flaring event of the last decade, and even to predict with some accuracy the energy budget daily released by magnetic reconnection during the whole time course of the storm. Further, we show that the combination of sparsity-enhancing machine learning and feature ranking could allow the identification of the prominent role that energy played as an Active Region property in the forecasting process.

Francesco Fiz, Helmut Dittmann, Cristina Campi et al.

To meet the current need for skeletal tumor-load estimation in prostate cancer (mCRPC), we developed a novel approach, based on adaptive bone segmentation. In this study, we compared the program output with existing estimates and with the radiological outcome. Seventy-six whole-body 99mTc-DPD-SPECT/CT from mCRPC patients were analyzed. The software identified the whole skeletal volume (SVol) and classified it voxels metastases (MVol) or normal bone (BVol). SVol was compared with the estimation of a commercial software. MVol was compared with manual assessment and with PSA-level. Counts/voxel were extracted from MVol and BVol. After six cycles of 223RaCl2-therapy every patient was re-evaluated as progressing (PD), stabilized (SD) or responsive (PR). SVol correlated with the one of the commercial software (R=0,99, p<0,001). MVol correlated with manually-counted lesions (R=0,61, p<0,001) and PSA (R=0,46, p<0.01). PD had a lower counts/voxel in MVol than PR/SD (715 \pm 190 Vs. 975 \pm 215 and 1058 \pm 255, p<0,05 and p<0,01) and in BVol (PD 275 \pm 60, PR 515 \pm 188 and SD 528 \pm 162 counts/voxel, p<0,001). Segmentation-based tumor load correlated with radiological/laboratory indices. Uptake was linked with the clinical outcome, suggesting that metastases in PD patients have a lower affinity for bone-seeking radionuclides and might benefit less from bone-targeted radioisotope therapies.

Federico Benvenuto, Michele Piana, Cristina Campi et al.

We introduce a hybrid approach to solar flare prediction, whereby a supervised regularization method is used to realize feature importance and an unsupervised clustering method is used to realize the binary flare/no-flare decision. The approach is validated against NOAA SWPC data.

Richard A Schwartz, Gabriele Torre, Anna Maria Massone et al.

Saturation affects a significant rate of images recorded by the Atmospheric Imaging Assembly on the Solar Dynamics Observatory. This paper describes a computational method and a technological pipeline for the de-saturation of such images, based on several mathematical ingredients like Expectation Maximization, image correlation and interpolation. An analysis of the computational properties and demands of the pipeline, together with an assessment of its reliability are performed against a set of data recorded from the Feburary 25 2014 flaring event.