Bipartite partial duals and circuits in medial graphs

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric

On the Effective Action of Noncommutative Yang-Mills Theory

We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the Schwinger parametric representation. Finally, we discuss the results obtained: a noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). To appear in J. Phys. Conf. Se

One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.Comment: 16 pages, 9 figure

Overview of the parametric representation of renormalizable non-commutative field theory

We review here the parametric representation of Feynman amplitudes of renormalizable non-commutative quantum field models.Comment: 10 pages, 3 figures, to be published in "Journal of Physics: Conference Series

Vacuum configurations for renormalizable non-commutative scalar models

In this paper we find non-trivial vacuum states for the renormalizable non-commutative $\phi^4$ model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.Comment: 17 page

Renormalization of the commutative scalar theory with harmonic term to all orders

The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders by using multiscale analysis in the momentum space. Then, we consider and compute its one-loop beta function, as well as the one on the degenerate Moyal space. We can finally compare both to the vanishing beta function of the theory with harmonic term on the Moyal space.Comment: 16 page

Visual Integration of Genome-Wide Association Studies and Differential Expression Results with the Hidecan R Package.

Background/Objectives: We present hidecan, an R package for generating visualisations that summarise the results of one or more genome-wide association studies (GWAS) and differential expression analyses, as well as manually curated candidate genes, e.g., extracted from the literature. This tool is applicable to all ploidy levels; we notably provide functionalities to facilitate the visualisation of GWAS results obtained for autotetraploid organisms with the GWASpoly package. Results: We illustrate the capabilities of hidecan with examples from two autotetraploid potato datasets. Conclusions: The hidecan package is implemented in R and is publicly available on the CRAN repository and on GitHub. A description of the package, as well as a detailed tutorial, is made available alongside the package. It is also part of the VIEWpoly tool for the visualisation and exploration of results from polyploids computational tools.fals