arXiv subjects

Nicolas Robert

Publications and source records attributed to Nicolas Robert.

3 recordsLinked to original sources

arXiv2025

OLIVAW: ACIMOV's GitHub robot assisting agile collaborative ontology development

Agile and collaborative approaches to ontologies design are crucial because they contribute to making them userdriven, up-to-date, and able to evolve alongside the systems they support, hence proper continuous validation tooling is required to ensure ontologies match developers' requirements all along their development. We propose OLIVAW (Ontology Long-lived Integration Via ACIMOV Workflow), a tool supporting the ACIMOV methodology on GitHub. It relies on W3C Standards to assist the development of modular ontologies through GitHub Composite Actions, pre-commit hooks, or a command line interface. OLIVAW was tested on several ontology projects to ensure its usefulness, genericity and reusability. A template repository is available for a quick start. OLIVAW is

cs.SE↗

arXiv2025

GUE-corners process in two-periodic Aztec diamonds

Links between uniform Aztec diamonds and random matrices are numerous in the literature. In particular, it has been established that, after appropriate rescaling, the probability density function of a certain subclass of dominos converges to the GUE-corners (GUE minor) process in the large size limit. We are interested to see whether this result holds when we modify the probability measure on the space of configurations. In the first part, we look at the case of biased Aztec diamonds, where different weights are associated to vertical and horizontal dominos. In the second part, we examine the case of two-periodic weightings. In both cases, we give exact expressions for the discrete probability distributions of the particles on the levels close to the contact point (turning point), valid for any finite Aztec diamond. In the scaling limit, we prove the convergence to GUE-corners with a rescaling that depends on the weighting. We include a discussion of our results in the light of recent results by Berggren and Bradinoff, who found, in a very close setting, a marked GUE-corners process rather than the classical GUE-corners process.

math-ph↗

arXiv2023

On $\lambda$-determinants and tiling problems

We review the connections between the octahedral recurrence, $\lambda$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $\lambda$-determinant (and generalizations thereof) of an arbitrary matrix in terms of domino tilings of Aztec diamonds. We also reinterpret the general Robbins-Rumsey formula for the rational function of consecutive minors, given by a summation over pairs of compatible alternating sign matrices, as the partition function for tilings of Aztec diamonds equipped with a general measure.

math-ph↗