Traditional online file management systems, such as Google Drive and OneDrive, provide convenient platforms for collaborative editing and sharing, but they come with inherent limitations. These systems often offer limited storage space and operate on centralized...

Riemannian methods have established themselves as state-of-the-art approaches in Brain-Computer Interfaces (BCI) in terms of performance. However, their adoption by experimenters is often hindered by a lack of interpretability. In this work, we propose a set of tools designed to enhance practitioners' understanding of the decisions made by Riemannian methods. Specifically, we develop techniques to quantify and visualize the influence of the different sensors on classification outcomes. Our approach includes a visualization tool for high-dimensional covariance matrices, a classifieragnostic tool that focuses on the classification process, as well as methods that leverage the data's topology to better characterize the role of each sensor. We demonstrate these tools on a specific dataset and provide Python code to facilitate their use by practitioners, thereby promoting the adoption of Riemannian methods in BCI.

Let $$G=(V\cup T,E)$$ be a graph where $$V\cup T$$ is the set of vertices, with T a subset of distinguished vertices, called terminals, and E the set of edges. Given a weight function $$w: V\rightarrow \mathbb N{\setminus } \{0\}$$ associated with the nonterminal nodes, the multi-terminal vertex separator problem consists in partitioning $$V\cup T$$ into $$k+1$$ subsets $$\{S, V_1,\dots , V_k\}$$ such that there is no edge between two different subsets $$V_i$$ and $$V_j$$ , each $$V_i$$ contains exactly one terminal and the weight of S is minimum. In this paper, we characterize the polytope of the solutions of this problem for two classes of the graph, and we show that the two linear systems are totally dual integral. Then, we study the polytope for the graphs that are decomposable by 1-node cutsets. We show that if G decomposes into $$G_1, \dots , G_k$$ , then the polytope in G can be obtained from those in $${\bar{G}}_1, \dots , {\bar{G}}_k$$ , where $${\bar{G}}_1, \dots , {\bar{G}}_k$$ are graphs related to $$G_1, \dots , G_k$$ , respectively. We also derive a procedure for composing facets and give some algorithmic consequences for solving the problem in G from $${\bar{G}}_1, \dots , {\bar{G}}_k$$ .

We propose a family a metrics over the set of full-rank $$n\times p$$ real matrices, and apply them to the landing framework for optimization under orthogonality...

The goal of this paper is to show how different machine learning tools on the Riemannian manifold $$\mathcal {P}_d$$ of Symmetric Positive Definite (SPD) matrices...

Object-centric Predictive Monitoring has recently gained attention due to advances in machine learning and rise of Object-Centric Event Logs (OCELs), which comprehensively capture object interactions. This paper presents a modular framework supporting customizable pipelines for predictive analysis across diverse event logs. The framework comprises three core components: Preprocessing (preserving object relationships via graph structures), Graph Embedding Model, and Prediction Model. We experimentally evaluated various combinations of embeddings and predictors on three public OCELs. Results show that no single configuration consistently dominates. However, GAT and Graph Transformer models perform best for predicting remaining time and the number of events. Performance improves with larger embedding and subgraphs, particularly for neuralbased models. Finally, GAT delivered the most stable and highperforming results across all event logs in generalization tests.

When training large models, such as neural networks, the full derivatives of order 2 and beyond are usually inaccessible, due to their computational cost. Therefore, among the second-order optimization methods, it is common to bypass the computation of the Hessian by...

Discriminator Guidance has become a popular method for efficiently refining pre-trained Score-Matching Diffusion models. However, in this paper, we demonstrate that the standard implementation of this technique does not necessarily lead to a distribution closer to...

Finite mixtures of classifiers (a.k.a. randomized ensembles) have been proposed as a way to improve robustness against adversarial attacks. However, existing attacks have been shown to not suit this kind of classifier. In this paper, we discuss the problem of...

This paper addresses decision-aiding problems involving multiple objectives and uncertain states of the world. Inspired by the capability approach, we focus on cases where a policy maker chooses an act that, combined with a state of the world, leads to a set of choices for citizens. While no preferential information is available to construct importance parameters for the criteria, we can obtain probabilities for the different states. To effectively support decision-aiding in this context, we propose two procedures that merge the potential set of choices for each state of the world taking into account their respective probabilities. Our procedures satisfy several fundamental and desirable propositions that characterize the outcomes.

In the very large debates on ethics of algorithms, this paper proposes an analysis on human responsibility. On the one hand, algorithms are designed by some humans, who bear a part of responsibility in the results and unexpected impacts. Nevertheless, we show how the fact they cannot embrace the full situations of use and consequences leads to an unreachable limit. On the other hand, using technology is never free of responsibility, even if there also exist limits to characterise. Massive uses by unprofessional users introduce additional questions that modify the possibilities to be ethically responsible. The article is structured in such a way as to show how the limits have gradually evolved, leaving unthought of issues and a failure to share responsibility.