On uniqueness of the q-state Potts model on a self-dual family of graphs

This paper deals with the location of the complex zeros of the Tutte polynomial for a class of self-dual graphs. For this class of graphs, as the form of the eigenvalues is known, the regions of the complex plane can be focused on the sets where there is only one dominant eigenvalue in particular containing the positive half plane. Thus, in these regions, the analyticity of the pressure can be derived easily. Next, some examples of graphs with their Tutte polynomial having a few number of eigenvalues are given. The cases of the strip of triangles with a double edge, the wheel and the cycle with an edge having a high order of multiplicity are presented. In particular, for this last example, we remark that the well known conjecture of Chen et al. is false in the finite case

Continuum Percolation in the Relative Neighborhood Graph

In the present study, we establish the existence of nontrivial site percolation threshold in the Relative Neighborhood Graph (RNG) for Poisson stationary point process with unit intensity in the plane

Continuum percolation in proximity graphs

14 pagesWe establish a sufficient condition to obtain continuum percolation on a class of proximity graphs when their vertices are distributed under a stationary Poisson point process with unit intensity in the plane. We apply this result on a family of graphs which generalizes $\beta$-skeleton graphs

Reyner Banham, Théorie et design à l’ère industrielle

En introduisant The Architecture Of The Well-tempered Environment, Reyner Banham annonçait qu’il n’y aurait pas dû avoir nécessité à écrire un tel livre si « ces équipements des bâtiments qui assurent le confort et le bien-être des humains avaient toujours fait partie de l’histoire de l’architecture ». On pourrait faire un constat identique à propos du premier ouvrage de Banham, Theory and Design in the First Machine Age, paru en 1960 : l’auteur aurait eu comme une obligation d’écrire cette h..

Motor Exit Point (MEP) Glia: Novel Myelinating Glia That Bridge CNS and PNS Myelin

Oligodendrocytes (OLs) and Schwann cells (SCs) have traditionally been thought of as the exclusive myelinating glial cells of the central and peripheral nervous systems (CNS and PNS), respectively, for a little over a century. However, recent studies demonstrate the existence of a novel, centrally-derived peripheral glial population called motor exit point (MEP) glia, which myelinate spinal motor root axons in the periphery. Until recently, the boundaries that exist between the CNS and PNS, and the cells permitted to cross them, were mostly described based on fixed histological collections and static lineage tracing. Recent work in zebrafish using in vivo, time-lapse imaging has shed light on glial cell interactions at the MEP transition zone and reveals a more complex picture of myelination both centrally and peripherally

Une approche récursive pour construire des polynômes à racines réelles

In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.Dans cette étude, nous donnons des conditions nécessaires et suffisantes sur les coefficients d'un polynôme de manière à ce que ce denier n'ait que des racines réelles

The Neuromodulator Adenosine Regulates Oligodendrocyte Migration at Motor Exit Point Transition Zones

During development, oligodendrocyte progenitor cells (OPCs) migrate extensively throughout the spinal cord. However, their migration is restricted at transition zones (TZs). At these specialized locations, unique glial cells in both zebrafish and mice play a role in preventing peripheral OPC migration, but the mechanisms of this regulation are not understood. To elucidate the mechanisms that mediate OPC segregation at motor exit point (MEP) TZs, we performed an unbiased small-molecule screen. Using chemical screening and in vivo imaging, we discovered that inhibition of A2a adenosine receptors (ARs) causes ectopic OPC migration out of the spinal cord. We provide in vivo evidence that neuromodulation, partially mediated by adenosine, influences OPC migration specifically at the MEP TZ. This work opens exciting possibilities for understanding how OPCs reach their final destinations during development and identifies mechanisms that could promote their migration in disease

The Neuromodulator Adenosine Regulates Oligodendrocyte Migration at Motor Exit Point Transition Zones

During development, oligodendrocyte progenitor cells (OPCs) migrate extensively throughout the spinal cord. However, their migration is restricted at transition zones (TZs). At these specialized locations, unique glial cells in both zebrafish and mice play a role in preventing peripheral OPC migration, but the mechanisms of this regulation are not understood. To elucidate the mechanisms that mediate OPC segregation at motor exit point (MEP) TZs, we performed an unbiased small-molecule screen. Using chemical screening and in vivo imaging, we discovered that inhibition of A2a adenosine receptors (ARs) causes ectopic OPC migration out of the spinal cord. We provide in vivo evidence that neuromodulation, partially mediated by adenosine, influences OPC migration specifically at the MEP TZ. This work opens exciting possibilities for understanding how OPCs reach their final destinations during development and identifies mechanisms that could promote their migration in disease