Bootstrap percolation on a graph with random and local connections

Let $G_{n,p}^1$ be a superposition of the random graph $G_{n,p}$ and a one-dimensional lattice: the $n$ vertices are set to be on a ring with fixed edges between the consecutive vertices, and with random independent edges given with probability $p$ between any pair of vertices. Bootstrap percolation on a random graph is a process of spread of "activation" on a given realisation of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at least $r \geq 2$ active neighbours become active as well. We study the size of the final active set in the limit when $n\rightarrow \infty$. The parameters of the model are $n$, the size $A_0=A_0(n)$ of the initially active set and the probability $p=p(n)$ of the edges in the graph. Bootstrap percolation process on $G_{n,p}$ was studied earlier. Here we show that the addition of $n$ local connections to the graph $G_{n,p}$ leads to a more narrow critical window for the phase transition, preserving however, the critical scaling of parameters known for the model on $G_{n,p}$. We discover a range of parameters which yields percolation on $G_{n,p}^1$ but not on $G_{n,p}$.Comment: 38 pages, 2 figure

Femmes africaines-américaines : identités et identifications multiples, une cause commune (1865-1920)

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CKM angle γ measurements at LHCb

International audienceThe CKM angle γ remains the least known parameter of the CKM mixing matrix. The precise measurement of this angle, as a Standard Model benchmark, is a key goal of the LHCb experiment. We present four recent CP violation studies related to the measurement of γ, including amplitude analysis of B± → DK± decays, the ADS/GLW analysis of B± → DK*0 decays and the time-dependent analysis of B± → DK±sK± decays

Activin/Nodal signalling in stem cells.

Activin/Nodal growth factors control a broad range of biological processes, including early cell fate decisions, organogenesis and adult tissue homeostasis. Here, we provide an overview of the mechanisms by which the Activin/Nodal signalling pathway governs stem cell function in these different stages of development. We describe recent findings that associate Activin/Nodal signalling to pathological conditions, focusing on cancer stem cells in tumorigenesis and its potential as a target for therapies. Moreover, we will discuss future directions and questions that currently remain unanswered on the role of Activin/Nodal signalling in stem cell self-renewal, differentiation and proliferation.S.P. was supported by the EUFP7 grant InnovaLIV and an FEBS long-term fellowship. L.V. was supported by the ERC starting grant Relieve IMDs and the Cambridge Hospitals National Institute for Health Research Biomedical Research Centre.This is the accepted manuscript of a paper published in Development (Pauklin S, Vallier L, Development 2015, 142, 607-619, doi: 10.1242/dev.091769). The final version is available at http://dx.doi.org/10.1242/dev.09176

Biomechanical breast modelling to improve patient positioning during breast cancer radiotherapy.

International audienceThis paper introduces a 3D FInite Element model of the breast designed to improve patient positioning during breast cancer radiotherapy. The model is used here for the design of a realistic breast phantom developed to quantify the positioning accuracy during radiotherapy