TS-Reconfiguration of Dominating Sets in circle and circular-arc graphs

We study the dominating set reconfiguration problem with the token sliding rule. It consists, given a graph G=(V,E) and two dominating sets D_s and D_t of G, in determining if there exists a sequence S= of dominating sets of G such that for any two consecutive dominating sets D_r and D_{r+1} with r<t, D_{r+1}=(D_r\ u) U v, where uv is an edge of G. In a recent paper, Bonamy et al studied this problem and raised the following questions: what is the complexity of this problem on circular arc graphs? On circle graphs? In this paper, we answer both questions by proving that the problem is polynomial on circular-arc graphs and PSPACE-complete on circle graphs.Comment: This work was supported by ANR project GrR (ANR-18-CE40-0032) and submitted to the conference WADS 202

COULD BIPOLARITY BE INFLUENCED BY STRESSFUL LIFE EVENTS? A REFLECTION BASED ON A CASE REPORT

Introduction: Bipolar disorder (BPD) has over the last fifteen years been considered as a biological disease with genetic bases, possibly triggered by stress factors. On the basis of a clinical case, we will question this theory. Subject and methods: Mrs. X, a patient with a history of domestic violence, has two manic episodes that corresponded with conjugal difficulties. This would lead us to believe that stressful life events may have triggered the onset and the relapse of the illness of our patient. To confirm this , we made a literature review with the keywords bipolar disorder, stress, family functioning and domestic violence on three databases: PubMed, PsycInfo and PsycArticles. Results: Studies show that BPD has likely genetic and biological origins. It is also established in the literature that stressful life events influence the course of the disease, with for example the “Kindling” effect. However, there is very few data regarding the precise nature of these events. It is also established that the family interactions are affected by the BPD. Nonetheless, little is known about the influence of the family’s interactions on the onset of the disease. Conclusions: Our clinical case raises the question of the stress factors that may influence the onset and the course of BPD. It also raises the question of the possible link between BPD and domestic violence and the question of theeffect of stressors on the genetic and biological factors, introducing a more psychodynamic view of BPD. Further research on this subject should allow us to expand the treatment to more comprehensive care

Linear Transformations Between Dominating Sets in the TAR-Model

Given a graph $G$ and an integer $k$, a token addition and removal ({\sf TAR} for short) reconfiguration sequence between two dominating sets $D_{\sf s}$ and $D_{\sf t}$ of size at most $k$ is a sequence $S= \langle D_0 = D_{\sf s}, D_1 \ldots, D_\ell = D_{\sf t} \rangle$ of dominating sets of $G$ such that any two consecutive dominating sets differ by the addition or deletion of one vertex, and no dominating set has size bigger than $k$. We first improve a result of Haas and Seyffarth, by showing that if $k=\Gamma(G)+\alpha(G)-1$ (where $\Gamma(G)$ is the maximum size of a minimal dominating set and $\alpha(G)$ the maximum size of an independent set), then there exists a linear {\sf TAR} reconfiguration sequence between any pair of dominating sets. We then improve these results on several graph classes by showing that the same holds for $K_{\ell}$-minor free graph as long as $k \ge \Gamma(G)+O(\ell \sqrt{\log \ell})$ and for planar graphs whenever $k \ge \Gamma(G)+3$. Finally, we show that if $k=\Gamma(G)+tw(G)+1$, then there also exists a linear transformation between any pair of dominating sets.Comment: 13 pages, 6 figure

Arctic Ecology: What does one need for a sustainable future?

The future sustainable development of the Arctic region and its environmental protection require cooperation. Perhaps the greatest challenge is to balance the needs of the local population and the need to maintain the pristine nature of the region against the degradation caused by anthropogenic pressures. Here a short discussion is given of a future that allows both economic exploitation but, at the same time, holds the development in check by balancing all requirements to the overarching good of the whole

Three-dimensional modelling of turbine wake interactions at a tidal stream energy site

One of the biggest uncertainties in tidal stream energy resource assessment is how tidal energy conversion, particularly at large scale, will interact with the resource. As few arrays are currently operational, data collected from these developments tends to be commercially sensitive. Therefore, array interaction with the resource is generally assessed using numerical models. A fully three-dimensional numerical approach based on Actuator Disk theory was implemented into the Regional Ocean Modelling System (ROMS) to simulate the energy extraction by tidal stream turbines. Emphasis was placed on wake interactions and cumulative effects of individual devices on energy extraction at array scale. This model was applied at the tidal stream energy site of the Fromveur Strait (western Brittany, France) considering an array of horizontal-axis turbines of 10-m diameter, matching the device technology currently operating in the Strait. Two tidal energy metrics were considered to describe asymmetries in tidal current magnitude and direction. The area with reduced asymmetry in current magnitude was selected to implement the turbine array. A nested grid technique was adopted to cascade processes from the regional scale to the high-resolution local farm domain. The computation was conducted over the inner-nested array domain covering the tidal farm with horizontal and vertical resolutions of 1 m, matching the 1/10th turbine diameter (D) recommended to resolve velocity and turbulence intensity along device wakes. The array layout initially followed recommended staggered configurations with longitudinal and lateral spacings of 10D and 5D, respectively. However, during mean spring tidal conditions, the misalignment of peak flood currents induced significant wake interactions that reduced the array output by about 15% in comparison to peak ebb. These interactions were investigated to adapt array layouts, minimise wake interactions, and optimise the energy conversion. By reducing the lateral spacing between devices to 3D (measured centre to centre rather than tip to tip), the flood ebb asymmetry in energy extraction was lowered from 15% to 2%

Eve, Adam and the Preferential Attachment Tree

We consider the problem of finding the initial vertex (Adam) in a Barab\'asi--Albert tree process $(\mathcal{T}(n) : n \geq 1)$ at large times. More precisely, given $\varepsilon>0$, one wants to output a subset $\mathcal{P}_{ \varepsilon}(n)$ of vertices of $\mathcal{T}(n)$ so that the initial vertex belongs to $\mathcal{P}_ \varepsilon(n)$ with probability at least $1- \varepsilon$ when $n$ is large. It has been shown by Bubeck, Devroye & Lugosi, refined later by Banerjee & Huang, that one needs to output at least $\varepsilon^{-1 + o(1)}$ and at most $\varepsilon^{-2 + o(1)}$ vertices to succeed. We prove that the exponent in the lower bound is sharp and the key idea is that Adam is either a ``large degree" vertex or is a neighbor of a ``large degree" vertex (Eve).Comment: 11 pages, comments are welcome