Decomposition of bounded degree graphs into C4C_4-free subgraphs

We prove that every graph with maximum degree $\Delta$ admits a partition of its edges into $O(\sqrt{\Delta})$ parts (as $\Delta\to\infty$) none of which contains $C_4$ as a subgraph. This bound is sharp up to a constant factor. Our proof uses an iterated random colouring procedure.Comment: 8 pages; to appear in European Journal of Combinatoric

Radiative capture on 242Pu for MOX fuel reactors

Proposal: Radiative capture on 242Pu for MOX fuel reactorsThe use of MOX fuel (mixed-oxide fuel made of UO2 and PuO2) in nuclear reactors allows substituting a large fraction of the enriched Uranium by Plutonium reprocessed from spent fuel. Indeed around 66% of the plutonium from spent fuel is made of 239Pu and 241Pu, which are fissile in thermal reactors. A typical reactor of this type uses a fuel with 7% reprocessed Pu and 93% depleted U, thus profiting from both the spent fuel and the remaining 238U following the 235U enrichment. With the use of such new fuel compositions rich in Pu the better knowledge of the capture and fission cross sections of the Pu isotopes becomes very important. This is clearly stated in the recent OECD NEA’s “High Priority Request List” and in the WPEC-26 “Uncertainty and target accuracy assessment for innovative systems using recent covariance data evaluations” report. In particular, a new series of cross section evaluations have been recently carried out jointly by the European (JEFF) and United States (ENDF) nuclear data agencies. As the new evaluations on 240Pu and 241Am have been already completed, 242Pu is the next to be reevaluated, and the scarceness of capture data (only two TOF measurements from 1973 and 1976 are available and disagree with each other) calls for a new time-of flight capture cross section measurement. This will be the first measurement in 40 years and, with the use of more advanced techniques, shall provide a more reliable and accurate result. We propose to measure the capture cross section of 242Pu in the region from thermal up to at least 60 keV, aiming for a high energy limit of 500 keV. The experiment would make use of an array of 4 low neutron sensitivity C6D6 detectors and be carried out at the n_TOF EAR-1 (185 m flight path) measuring station. Compared to the current uncertainty of 35%, this measurement aims at an improved accuracy between 7% and 12% depending on the energy region.Preprin

Controlled Heterometallic Composition in Linear Trinuclear [LnCeLn] Lanthanide Molecular Assemblies.

The combination of two different β-diketone ligands facilitates the size-controlled assembly of pure heterometallic [LnLn'Ln] linear compounds thanks to two different coordination sites present in the molecular scaffold. [HoCeHo], [ErCeEr], and [YbCeYb] analogues are presented here and are characterized both in the solid state and in solution, demonstrating the selectivity of this unique method to produce heterometallic 4f molecular entities

A Weakly Supervised Approach for Estimating Spatial Density Functions from High-Resolution Satellite Imagery

We propose a neural network component, the regional aggregation layer, that makes it possible to train a pixel-level density estimator using only coarse-grained density aggregates, which reflect the number of objects in an image region. Our approach is simple to use and does not require domain-specific assumptions about the nature of the density function. We evaluate our approach on several synthetic datasets. In addition, we use this approach to learn to estimate high-resolution population and housing density from satellite imagery. In all cases, we find that our approach results in better density estimates than a commonly used baseline. We also show how our housing density estimator can be used to classify buildings as residential or non-residential.Comment: 10 pages, 8 figures. ACM SIGSPATIAL 2018, Seattle, US