Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for some combinatorial optimization problems. Specifically, the combination of Quantum Minimum Finding (obtained from Grover Search) with dynamic programming has proved particularly efficient in improv...
Cet article vise à partager les réflexions qu’ont suscitées certaines composantes numériques du projet Poésie biblique latine antique et médiévale (PoBLAM) financé par l’Agence nationale de la recherche (ANR) et la Deutsche Forschungsgemeinschaft (DFG). Il s’agit de présenter, à partir de questions plus générales que pose l’utilisation dans ce cont...
Active area of research in AI is the theory of manifold learning and finding lower- dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues with these methods related to finding low-dimensional representation of the data, the so-called curse of dimens...
Foucaud et al. [ICALP 2024] demonstrated that some problems in NP can admit (tight) double-exponential lower bounds when parameterized by treewidth or vertex cover number. They showed these first-of-their-kind results by proving conditional lower bounds for certain graph problems, in particular, the metric-based identification problems (Strong) Met...
Il s'agit d'une simple introduction aux structures de données pour étudiants de Licence. On aborde les concepts de liste, d'arbre, d'ensemble et de table de correspondance. Quelques exemples pratiques sont aussi discutées.
We present a Mathematica package to help investigate the existence of Darboux polynomials for (polynomial) ordinary differential equations (ODE). If we denote the derivation encoded by a given ODE by D, the package infers and propagates necessary conditions for a generic ansatz p to be a Darboux polynomial for D. By generic, we mean that not only t...
A ($\lambda,\mu$)-bow metric was defined in (Dragan & Ducoffe, 2023) as a far reaching generalization of an $\alpha_i$-metric (which is equivalent to a ($0,i$)-bow metric). A graph $G=(V,E)$ is said to satisfy ($\lambda,\mu$)-bow metric if for every four vertices $u,v,w,x$ of $G$ the following holds: if two shortest paths $P(u,w)$ and $P(v,x)$ shar...
Dimensionality reduction is an essential step in the processing of analytical chemistry data. When this reduction is carried out by variable selection, it can enable the identification of biochemical pathways. CovSel has been developed to meet this requirement, through a parsimonious selection of non-redundant variables. This article presents the g...
P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem wa...
