Optimal Re-Embeddings of Border Basis Schemes

Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of $\mathbb{P}^n$ of given length. They yield open coverings and are easy to describe and to compute with. Our topic is to find re-embeddings of border basis schemes into affine spaces of minimal dimension. Given $P = K[X] = K[x_1,\dots,x_n]$, an ideal $I\subseteq \langle X \rangle$, and a tuple $Z$ of indeterminates, in previous papers the authors developed techniques for computing $Z$-separating re-embeddings of $I$, i.e., of isomorphisms $\Phi: P/I \rightarrow K[X\setminus Z] / (I\cap K[X\setminus Z])$. Here these general techniques are developed further and improved by constructing a new algorithm for checking candidate tuples $Z$ and by using the Gr\"obner fan of the linear part of $I$ advantageously. Then we apply this to the ideals defining border basis schemes $\mathbb{B}_{\mathcal{O}}$, where $\mathcal{O}$ is an order ideal of terms, and to their natural generating polynomials. The fact that these ideals are homogeneous w.r.t. the arrow grading allows us to look for suitable tuples $Z$ more systematically. Using the equivalence of indeterminates modulo the square of the maximal ideal, we compute the Gr\"obner fan of the linear part of the ideal quickly and determine which indeterminates should be in $Z$ when we are looking for optimal re-embeddings. Specific applications include re-embeddings of border basis schemes where $\mathcal{O}\subseteq K[x,y]$ and where $\mathcal{O}$ consists of all terms up to some degree.Comment: This preprint will not be published. It has been split into several parts which will be extended and published separately. When the last part is finished, this preprint will be withdraw

The X-CLASS - redMaPPer galaxy cluster comparison: I. Identification procedures

We performed a detailed and, for a large part interactive, analysis of the matching output between the X-CLASS and redMaPPer cluster catalogues. The overlap between the two catalogues has been accurately determined and possible cluster positional errors were manually recovered. The final samples comprise 270 and 355 redMaPPer and X-CLASS clusters respectively. X-ray cluster matching rates were analysed as a function of optical richness. In a second step, the redMaPPer clusters were correlated with the entire X-ray catalogue, containing point and uncharacterised sources (down to a few 10^{-15} erg s^{-1} cm^{-2} in the [0.5-2] keV band). A stacking analysis was performed for the remaining undetected optical clusters. Main results show that neither of the wavebands misses any massive cluster (as coded by X-ray luminosity or optical richness). After correcting for obvious pipeline short-comings (about 10% of the cases both in optical and X-ray), ~50% of the redMaPPer (down to a richness of 20) are found to coincide with an X-CLASS cluster; when considering X-ray sources of any type, this fraction increases to ~ 80%; for the remaining objects, the stacking analysis finds a weak signal within 0.5 Mpc around the cluster optical centers. The fraction of clusters totally dominated by AGN-type emission appears to be of the order of a few percent. Conversely ~ 40% of the X-CLASS clusters are identified with a redMaPPer (down to a richness of 20) - part of the non-matches being due to the fact that the X-CLASS sample extends further out than redMaPPer (z<1 vs z<0.6); extending the correlation down to a richness of 5, raises the matching rate to ~ 65%.Comment: 15 pages, 20 figures, 2 table

Animal lameness detection with radar sensing

Lameness is a significant problem for performance horses and farmed animals, with severe impact on animal welfare and treatment costs. Lameness is commonly diagnosed through subjective scoring methods performed by trained veterinary clinicians, but automatic methods using suitable sensors would improve efficiency and reliability. In this paper, we propose the use of radar micro-Doppler signatures for contactless and automatic identification of lameness, and present preliminary results for dairy cows, sheep, and horses. These proof-of-concept results are promising, with classification accuracy above 85% for dairy cows, around 92% for horses, and close to 99% for sheep

3D density reconstruction of a screeching supersonic jet by synchronized multi-camera Background Oriented Schlieren

International audienceThis work describes the application of 3D Background Oriented Schlieren (3DBOS) to the experimental analysis of the mean and instantaneous 3D structures of supersonic under-expanded screeching jets. These jets feature various dynamical states as the jet nozzle pressure ratio (NPR) is varied. Hence, six flow conditions were considered using acoustic measurements and 3D density reconstructions. Relying on the latter and on Proper Orthogonal Decomposition (POD) to isolate the main flow features, clear visualizations of the instantaneous 3D state and the reconstructed average dynamics of modes A1 and C, that are respectively axisymmetric and helical, were obtained

An Updated View on an Emerging Target: Selected Papers from the 8th International Conference on Protein Kinase CK2

The 8th International Conference on Protein Kinase CK2 took place in Homburg, Germany, from 6 September to 9 September 2016. Over 80 scientists from Australia, China, Japan, USA, Canada, Denmark, France, Italy, Spain, Poland and Germany participated. After the opening lecture by Lorenzo A. Pinna, Padova, Italy, entitled Exploring the CK2 Paradox: Restless, Dangerous, Dispensable, the scientists reported their latest research on the structural characterization of CK2, hence leading directly to the development of CK2 inhibitors. The driving force behind the development of inhibitors is their use in the treatment of various diseases, which was the next topic of the conference. New findings on protein kinase CK2 were addressed in the following session. The final topic of the conference addressed the role of CK2 in differentiation and development