Computads for generalised signatures

We introduce a notion of signature whose sorts form a direct category, and study computads for such signatures. Algebras for such a signature are presheaves with an interpretation of every function symbol of the signature, and we describe how computads give rise to signatures. Generalising work of Batanin, we show that computads with certain generator-preserving morphisms form a presheaf category, and describe a forgetful functor from algebras to computads. Algebras free on a computad turn out to be the cofibrant objects for certain cofibrantly generated factorisation system, and the adjunction above induces the universal cofibrant replacement, in the sense of Garner, for this factorisation system. Finally, we conclude by explaining how many-sorted structures, weak $\omega$-categories, and algebraic semi-simplicial Kan complexes are algebras of such signatures, and we propose a notion of weak multiple category.Comment: 39 page

Cartesian product of hypergraphs: properties and algorithms

Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs

On the stability of generalized second price auctions with budgets

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.Peer ReviewedPostprint (author's final draft

Regular Matroids with Graphic Cocircuits

We introduce the notion of graphic cocircuits and show that a large class of regular matroids with graphic cocircuits belongs to the class of signed-graphic matroids. Moreover, we provide an algorithm which determines whether a cographic matroid with graphic cocircuits is signed-graphic or not

Explainable AI-based Intrusion Detection in the Internet of Things

The revolution of Artificial Intelligence (AI) has brought about a significant evolution in the landscape of cyberattacks. In particular, with the increasing power and capabilities of AI, cyberattackers can automate tasks, analyze vast amounts of data, and identify vulnerabilities with greater precision. On the other hand, despite the multiple benefits of the Internet of Things (IoT), it raises severe security issues. Therefore, it is evident that the presence of efficient intrusion detection mechanisms is critical. Although Machine Learning (ML) and Deep Learning (DL)-based IDS have already demonstrated their detection efficiency, they still suffer from false alarms and explainability issues that do not allow security administrators to trust them completely compared to conventional signature/specification-based IDS. In light of the aforementioned remarks, in this paper, we introduce an AI-powered IDS with explainability functions for the IoT. The proposed IDS relies on ML and DL methods, while the SHapley Additive exPlanations (SHAP) method is used to explain decision-making. The evaluation results demonstrate the efficiency of the proposed IDS in terms of detection performance and explainable AI (XAI)

Complexity of Strong Implementability

We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated towards a social choice. This is one of the central questions in mechanism design. If the concept of weak implementation is considered, the Revelation Principle states that one can restrict attention to truthful implementations and direct revelation mechanisms, which implies that implementability of a social choice function is easy to check. For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open so far. In this paper, we show by using methods from polyhedral theory that strong implementability of a social choice function can be decided in polynomial space and that each of the payments needed for strong implementation can always be chosen to be of polynomial encoding length. Moreover, we show that strong implementability of a social choice function involving only a single selfish individual can be decided in polynomial time via linear programming