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Thanks to the great interest posed by researchers and companies, recommendation systems became a cornerstone of machine learning applications. However, concerns have arisen recently about the need for reproducibility, making it challenging to identify suitable pipelines. Several frameworks have been proposed to improve reproducibility, covering the entire process from data reading to performance evaluation. Despite this effort, these solutions often overlook the role of data management, do not promote interoperability, and neglect data analysis despite its well-known impact on recommender performance. To address these gaps, we propose DataRec, which facilitates using and manipulating recommendation datasets. DataRec supports reading and writing in various formats, offers filtering and splitting techniques, and enables data distribution analysis using well-known metrics. It encourages a unified approach to data manipulation by allowing data export in formats compatible with several recommendation frameworks.

In specific domains like fashion, music, and movie recommendation, the multi-faceted features characterizing products and services may influence each customer on online selling platforms differently, paving the way to novel multimodal recommendation models that can learn from such multimodal content. According to the literature, the common multimodal recommendation pipeline involves (i) extracting multimodal features, (ii) refining their high-level representations to suit the recommendation task, (iii) optionally fusing all multimodal features, and (iv) predicting the user-item score. While great effort has been put into designing optimal solutions for (ii-iv), to the best of our knowledge, very little attention has been devoted to exploring procedures for (i). In this respect, the existing literature outlines the large availability of multimodal datasets and the ever-growing number of large models accounting for multimodal-aware tasks, but (at the same time) an unjustified adoption of limited standardized solutions. This motivates us to explore more extensive techniques for the (i) stage of the pipeline. To this end, this paper settles as the first attempt to offer a large-scale benchmarking for multimodal recommender systems, with a specific focus on multimodal extractors. Specifically, we take advantage of two popular and recent frameworks for multimodal feature extraction and reproducibility in recommendation, Ducho and Elliot, to offer a unified and ready-to-use experimental environment able to run extensive benchmarking analyses leveraging novel multimodal feature extractors. Results, largely validated under different hyper-parameter settings for the chosen extractors, provide important insights on how to train and tune the next generation of multimodal recommendation algorithms.

Modern Machine Learning (ML) has significantly advanced various research fields, but the opaque nature of ML models hinders their adoption in several domains. Explainable AI (XAI) addresses this challenge by providing additional information to help users understand the internal decision-making process of ML models. In the field of neuroscience, enriching a ML model for brain decoding with attribution-based XAI techniques means being able to highlight which brain areas correlate with the task at hand, thus offering valuable insights to domain experts. In this paper, we analyze human and Computer Vision (CV) systems in parallel, training and explaining two ML models based respectively on functional Magnetic Resonance Imaging (fMRI) and movie frames. We do so by leveraging the "StudyForrest" dataset, which includes functional Magnetic Resonance Imaging (fMRI) scans of subjects watching the "Forrest Gump" movie, emotion annotations, and eye-tracking data. For human vision the ML task is to link fMRI data with emotional annotations, and the explanations highlight the brain regions strongly correlated with the label. On the other hand, for computer vision, the input data is movie frames, and the explanations are pixel-level heatmaps. We cross-analyzed our results, linking human attention (obtained through eye-tracking) with XAI saliency on CV models and brain region activations. We show how a parallel analysis of human and computer vision can provide useful information for both the neuroscience community (allocation theory) and the ML community (biological plausibility of convolutional models)., Comment: This work has been accepted to be presented to The 2nd World Conference on eXplainable Artificial Intelligence (xAI 2024), July 17-19, 2024 - Malta

This paper investigates stationary mean-field games (MFGs) on the torus with Lipschitz non-homogeneous diffusion and logarithmic-like couplings. The primary objective is to understand the existence of $C^{1,\alpha}$ solutions to address the research gap between low-regularity results for bounded and measurable diffusions and the smooth results modeled by the Laplacian. We use the Hopf--Cole transformation to convert the MFG system into a scalar elliptic equation. Then, we apply Morrey space methods to establish the existence and regularity of solutions. The introduction of Morrey space methods offers a novel approach to address regularity issues in the context of MFGs., Comment: 26 pages

We prove local boundedness, Harnack's inequality and local regularity for weak solutions of quasilinear degenerate elliptic equations in divergence form with Rough coefficients. Degeneracy is encoded by a non-negative, symmetric, measurable matrix valued function Q(x) and two suitable non-negative weight functions. We setup an axiomatic approach in terms of suitable geometric conditions and local Sobolev-Poincar\'e inequalities. Data integrability is close to L1 and is exploited in terms of a suitable Stummel-Kato class that in some cases is necessary for local regularity.

This paper proposes an optimal management strategy for a Renewable Energy Community defined according to the Italian legislation. The specific case study is composed by a set of houses equipped with smart appliances, that share a PV plant. The objective is to minimize the cost of electrical energy use for each member of the community, taking into account the discount achievable from government incentives with proper shaping of the community daily consumption. Such incentives are indeed proportional to the shared energy, i.e. the portion of the renewable energy consumed at each hour by community members. The management algorithm allows an optimal coordination of houses power demands, according to the degree of flexibility granted by users. Moreover, a policy to fairly distribute the obtained discount is introduced. Simulation results show the potentialities of the approach.

Renewable Energy Communities (RECs) have been officially introduced into the European legislation through the Clean Energy for all Europeans package. A REC is defined as an association of citizens, commercial activities, enterprises, and local authorities that own small-scale power plants based on Renewable Energy Sources (RESs). The community has the objective of maximizing the share of renewable energy, i.e. the self-consumption of the energy generated by the community RES power plants and to generally optimize the use of electrical energy. This paper describes the ComER project, developed by the University of Cassino and the Campus Bio-Medico University of Rome. The project focuses on the main technical problems to face for the realization of a REC. The principal objective is to develop methods and tools necessary for the management and control of RECs. In particular, this paper describes the rules established for RECs in the Italian legislations, the organization of the ComER project, the adopted solutions and the first obtained results.

Variational inequalities with thin obstacles and Signorini-type boundary conditions are classical problems in the calculus of variations, arising in numerous applications. In the linear case many refined results are known, while in the nonlinear setting our understanding is still at a preliminary stage. In this paper we prove $C^1$ regularity for the solutions to a general class of quasi-linear variational inequalities with thin obstacles and $C^{1, \alpha}$ regularity for variational inequalities under Signorini-type conditions on the boundary of a domain.

We study regularity for solutions of quasilinear elliptic equations of the form $\div \A(x,u,\nabla u) = \div \F $ in bounded domains in $\R^n$. The vector field $\A$ is assumed to be continuous in $u$, and its growth in $\nabla u$ is like that of the $p$-Laplace operator. We establish interior gradient estimates in weighted Morrey spaces for weak solutions $u$ to the equation under a small BMO condition in $x$ for $\A$. As a consequence, we obtain that $\nabla u$ is in the classical Morrey space $\calM^{q,\lambda}$ or weighted space $L^q_w$ whenever $|\F|^{\frac{1}{p-1}}$ is respectively in $\calM^{q,\lambda}$ or $L^q_w$, where $q$ is any number greater than $p$ and $w$ is any weight in the Muckenhoupt class $A_{\frac{q}{p}}$. In addition, our two-weight estimate allows the possibility to acquire the regularity for $\nabla u$ in a weighted Morrey space that is different from the functional space that the data $|\F|^{\frac{1}{p-1}}$ belongs to.

In this paper we show that the shear modulus $\mu$ of an isotropic elastic body can be stably recovered by the knowledge of one single displacement field whose boundary data can be assigned independently of the unknown elasticity tensor.

In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form.