Early initiation of breastfeeding was associated with a marked reduction of the rate of diarrhea throughout the first 6 months of life, possibly because of the salutary effects of human colostrum. These data highlight the need for interventions to encourage early initiation of breastfeeding in less developed settings.

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

International audienceWe show that a class of vertex partitioning problems that can be expressed in monadic second order logic (MSOL) are polynomials on graphs of bounded clique-width. This class includes coloring, H-free coloring, domatic number and partition into perfect graphs. Moreover we show that a class of vertex and edge partitioning problems are polynomials on graphs of bounded treewidth

a b s t r a c tDejean conjectured that the repetition threshold for a k-letter alphabet is k k−1 when k ≥ 5. Dejean's conjecture has already been proved for k ≤ 14 and for k ≥ 27. We present here a proof for 8 ≤ k ≤ 38. The same technique is also applied to prove Ochem's stronger version of the conjecture for 9 ≤ k ≤ 38.

This study presents a comprehensive evaluation of five widely used multisatellite precipitation estimates (MPEs) against 1° × 1° gridded rain gauge data set as ground truth over India. One decade observations are used to assess the performance of various MPEs (Climate Prediction Center (CPC)‐South Asia data set, CPC Morphing Technique (CMORPH), Precipitation Estimation From Remotely Sensed Information Using Artificial Neural Networks, Tropical Rainfall Measuring Mission's Multisatellite Precipitation Analysis (TMPA‐3B42), and Global Precipitation Climatology Project). All MPEs have high detection skills of rain with larger probability of detection (POD) and smaller “missing” values. However, the detection sensitivity differs from one product (and also one region) to the other. While the CMORPH has the lowest sensitivity of detecting rain, CPC shows highest sensitivity and often overdetects rain, as evidenced by large POD and false alarm ratio and small missing values. All MPEs show higher rain sensitivity over eastern India than western India. These differential sensitivities are found to alter the biases in rain amount differently. All MPEs show similar spatial patterns of seasonal rain bias and root‐mean‐square error, but their spatial variability across India is complex and pronounced. The MPEs overestimate the rainfall over the dry regions (northwest and southeast India) and severely underestimate over mountainous regions (west coast and northeast India), whereas the bias is relatively small over the core monsoon zone. Higher occurrence of virga rain due to subcloud evaporation and possible missing of small‐scale convective events by gauges over the dry regions are the main reasons for the observed overestimation of rain by MPEs. The decomposed components of total bias show that the major part of overestimation is due to false precipitation. The severe underestimation of rain along the west coast is attributed to the predominant occurrence of shallow rain and underestimation of moderate to heavy rain by MPEs. The decomposed components suggest that the missed precipitation and hit bias are the leading error sources for the total bias along the west coast. All evaluation metrics are found to be nearly equal in two contrasting monsoon seasons (southwest and northeast), indicating that the performance of MPEs does not change with the season, at least over southeast India. Among various MPEs, the performance of TMPA is found to be better than others, as it reproduced most of the spatial variability exhibited by the reference.

A [Wang tile](https://en.wikipedia.org/wiki/Wang_tile) is a square tile such that each of its edges is colored. The plane can be _tiled_ with a set of Wang tiles if tiles contained in the set can be placed in the plane without rotations and reflections such that the whole plane is covered and the colors of their edges match at adjacent tiles. Wang tiles were introduced by [Wang](https://en.wikipedia.org/wiki/Hao_Wang_(academic)) in 1961 to study decidability in mathematical logic, and they are also of relevance to other areas of theoretical computer science. Wang conjectured that if the plane can be tiled with a set of Wang tiles, then it can be tiled in a periodic way. This was refuted by [Berger](https://en.wikipedia.org/wiki/Robert_Berger_(mathematician)) in 1966 who described how a Turing machine computation can be emulated by Wang tilings and constructed a set of 104 Wang tiles for which the plane can be tiled with the set but only aperiodically. In the first volume of [The Art of Computer Programming](https://en.wikipedia.org/wiki/The_Art_of_Computer_Programming), Knuth presented a simplified version of Berger's set with 92 Wang tiles. Smaller sets of Wang tiles that tile the plane only aperiodically were subsequently constructed with the smallest set containing 13 Wang tiles, found by Culik II in 1996. The authors construct a set of 11 Wang tiles with edges colored with four colors such that the plane can be tiled with the set but each tiling is aperiodic. Moreover, they establish that there is no set of at most 10 Wang tiles with this property. The number of colors is also the best possible as it is known that every set of Wang tiles with edges colored with at most three colors either can tile the plane periodically or cannot tile the plane at all.

International audienceWe define NLC Fk to be the restriction of the class of graphs NLC k , where relabelling functions are exclusively taken from a set F of functions from {1,...,k} into {1,...,k}. We characterize the sets of functions F for which NLC Fk is well-quasi-ordered by the induced subgraph relation ≤ i . Precisely, these sets F are those which satisfy that for every f,g∈F , we have Im(f ∘ g) = Im(f) or Im(g ∘ f) = Im(g). To obtain this, we show that words (or trees) on F are well-quasi-ordered by a relation slightly more constrained than the usual subword (or subtree) relation. A class of graphs is n-well-quasi-ordered if the collection of its vertex-labellings into n colors forms a well-quasi-order under ≤ i , where ≤ i respects labels. Pouzet (C R Acad Sci, Paris Sér A-B 274:1677-1680, 1972) conjectured that a 2-well-quasi-ordered class closed under induced subgraph is in fact n-well-quasi-ordered for every n. A possible approach would be to characterize the 2-well-quasi-ordered classes of graphs. In this respect, we conjecture that such a class is always included in some well-quasi-ordered NLC Fk for some family F . This would imply Pouzet's conjecture

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