Safe sets, network majority on weighted trees

Let G = (V, E) be a graph and let w : V → ℝ>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X) ≔ ∑v∈Gw(v). A non-empty subset ∑ is a weighted safe set if, for every component C of the subgraph induced by S and every component D of G/S, we have w(C) ≥ w(D) whenever there is an edge between C and D. If the subgraph G(S) induced by a weighted safe set S is connected, then the set S is called a weighted connected safe set. In this article, we show that the problem of computing the minimum weight of a safe set is NP-hard for trees, even if the underlying tree is restricted to be a star, but it is polynomially solvable for paths. We also give an O(n log n) time 2-approximation algorithm for finding a weighted connected safe set with minimum weight in a weighted tree. Then, as a generalization of the concept of a minimum safe set, we define the concept of a parameterized infinite family of proper central subgraphs on weighted trees, whose polar ends are the vertex set of the tree and the centroid points. We show that each of these central subgraphs includes a centroid point. © 2017 Wiley Periodicals, Inc

The sub-seasonal to seasonal prediction (S2S) project database

A database containing sub-seasonal to seasonal forecasts from 11 operational centres is available to the research community and will help advance our understanding of the sub-seasonal to seasonal time range. Demands are growing rapidly in the operational prediction and applications communities for forecasts that fill the gap between medium-range weather and long-range or seasonal forecasts. Based on the potential for improved forecast skill at the sub-seasonal to seasonal time range, a sub-seasonal prediction (S2S) research project has been established by the World Weather Research Program/World Climate Research Program. A main deliverable of this project is the establishment of an extensive database, containing sub-seasonal (up to 60 days) forecasts, 3-weeks behind real-time, and reforecasts from 11 operational centers, modelled in part on the THORPEX Interactive Grand Global Ensemble (TIGGE) database for medium range forecasts (up to 15 days). The S2S database, available to the research community since May 2015, represents an important tool to advance our understanding of the sub-seasonal to seasonal time range that has been considered for a long time as a “desert of predictability”. In particular, this database will help identify common successes and shortcomings in the model simulation and prediction of sources of sub-seasonal to seasonal predictability. For instance, a preliminary study suggests that the S2S models underestimate significantly the amplitude of the Madden Julian Oscillation (MJO) teleconnections over the Euro-Atlantic sector. The S2S database represents also an important tool for case studies of extreme events. For instance, a multi-model combination of S2S models displays higher probability of a landfall over Vanuatu islands 2 to 3 weeks before tropical cyclone Pam devastated the islands in March 2015

How to design graphs with low forwarding index and limited number of edges

International audienceThe (edge) forwarding index of a graph is the minimum, over all possible rout-ings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question: Given a number e of edges and a number n of vertices, what is the least congested graph that we can construct? and what forwarding-index can we achieve? Our problem has some distant similarities with the well-known (∆, D) problem, and we sometimes build upon results obtained on it. The goal of this paper is to study how to build graphs with low forwarding indices and to understand how the number of edges impacts the forwarding index. We answer here these questions for different families of graphs: general graphs, graphs with bounded degree, sparse graphs with a small number of edges by providing constructions, most of them asymptotically optimal. For instance, we provide an asymptotically optimal construction for (n, n + k) cubic graphs-its forwarding index is ∼ n 2 3k log 2 (k). Our results allow to understand how the forwarding-index drops when edges are added to a graph and also to determine what is the best (i.e least congested) structure with e edges. Doing so, we partially answer the practical problem that initially motivated our work: If an operator wants to power only e links of its network, in order to reduce the energy consumption (or wiring cost) of its networks, what should be those links and what performance can be expected

Epithelial-immune cell interplay in primary Sjogren syndrome salivary gland pathogenesis

In primary Sjogren syndrome (pSS), the function of the salivary glands is often considerably reduced. Multiple innate immune pathways are likely dysregulated in the salivary gland epithelium in pSS, including the nuclear factor-kappa B pathway, the inflammasome and interferon signalling. The ductal cells of the salivary gland in pSS are characteristically surrounded by a CD4(+) T cell-rich and B cell-rich infiltrate, implying a degree of communication between epithelial cells and immune cells. B cell infiltrates within the ducts can initiate the development of lymphoepithelial lesions, including basal ductal cell hyperplasia. Vice versa, the epithelium provides chronic activation signals to the glandular B cell fraction. This continuous stimulation might ultimately drive the development of mucosa-associated lymphoid tissue lymphoma. This Review discusses changes in the cells of the salivary gland epithelium in pSS (including acinar, ductal and progenitor cells), and the proposed interplay of these cells with environmental stimuli and the immune system. Current therapeutic options are insufficient to address both lymphocytic infiltration and salivary gland dysfunction. Successful rescue of salivary gland function in pSS will probably demand a multimodal therapeutic approach and an appreciation of the complicity of the salivary gland epithelium in the development of pSS. Salivary gland dysfunction is an important characteristic of primary Sjogren syndrome (pSS). In this Review, the authors discuss various epithelial abnormalities in pSS and the mechanisms by which epithelial cell-immune cell interactions contribute to disease development and progression

TLR3-mediated apoptosis and activation of phosphorylated Akt in the salivary gland epithelial cells of primary Sjögren’s syndrome patients

This study aimed at ascertain whether innate immunity is involved in the apoptosis of primary cultured salivary gland epithelial cells (SGECs) in primary Sjögren\u27s syndrome (pSS). Induction of apoptosis of SGECs was performed using a TLR3 ligand, poly (I:C). Activation of phosphorylated-Akt (pAkt) and cleaved-caspase 3 was determined by Western blotting or immunofluorescence. Expression of TLR2 and TLR3 with pAkt was observed in cultured SGECs after 24-h stimulation with each ligand. Compared with stimulation with the peptidoglycan or lipopolysaccharide, that with poly (I:C) induced significant nuclear fragmentation, as determined by Hoechst staining (p = 0.0098). Apoptosis was confirmed by terminal deoxynucleotidyltransferase-mediated dUTP nick end-labeling (TUNEL) staining of SGECs from pSS patients and a normal subject. A significant increase in TUNEL-positive cells was observed by the addition of a PI3K inhibitor, LY294002. Poly (I:C) phosphorylated stress-activated protein kinase/Jun-terminal kinase and p44/42 MAP kinase as well as Akt. Furthermore, poly (I:C)-induced caspase 3 cleavage in SGECs was also inhibited by LY294002. Similar results were obtained using SGECs obtained from a normal subject. The results demonstrated for the first time that TLR3 induces the apoptotic cell death of SGECs via the PI3K-Akt signaling pathway