Partial recovery bounds for clustering with the relaxed KKmeans

We investigate the clustering performances of the relaxed $K$means in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the misclassification error decay exponentially fast with respect to this SNR. These partial recovery bounds for the relaxed $K$means improve upon results currently known in the sGMM setting. In the SBM setting, applying the relaxed $K$means SDP allows to handle general connection probabilities whereas other SDPs investigated in the literature are restricted to the assortative case (where within group probabilities are larger than between group probabilities). Again, this partial recovery bound complements the state-of-the-art results. All together, these results put forward the versatility of the relaxed $K$means.Comment: 39 page

Tetragonal to orthorhombic phase transition in SmFeAsO: a synchrotron powder diffraction investigation

The crystal structure of SmFeAsO has been investigated by means of Rietveld refinement of high resolution synchrotron powder diffraction data collected at 300 K and 100 K. The compound crystallizes in the tetragonal P4/nmm space group at 300 K and in the orthorhombic Cmma space group at 100 K; attempts to refine the low temperature data in the monoclinic P112/n space group diverged. On the basis of both resistive and magnetic analyses the tetragonal to orthorhombic phase transition can be located at T about 140 K.Comment: Submitted to: Superconductor Science and Technology PACS: 61.05.cp, 61.66.Fn, 74.10.+v, 74.62.Dh, 74.70.D

No Riemann-hurwitz formula for the p-ranks of relative class groups

We disprove, by means of numerical examples, the existence of a Riemann-Hurwitz formula for the p-ranks of relative class groups in a p-ramified p-extension K/k of number fields of CM-type containing ?\_p. In the cyclic case of degree p, under some assumptions on the p-class group of k, we prove some properties of the Galois structure of the p-class group of K; but we have found, through numerical experimentation, that some theoretical group structures do not exist in this particular situation, and we justify this fact. Then we show, in this context, that Kida's formula on lambda invariants is valid for the p-ranks if and only if the p-class group of K is reduced to the group of ambiguous classes, which is of course not always the case.Comment: 6 pages + tables num\'erique

Understanding stakeholder values using cluster analysis

The K-Means and Ward’s Clustering procedures were used to categorize value similarities among respondents of a public land management survey. The clustering procedures resulted in two respondent groupings: an anthropocentrically focused group and an ecocentrically focused group. While previous studies have suggested that anthropocentric and ecocentric groups are very different, this study revealed many similarities. Similarities between groups included a strong feeling towards public land and national forest existence as well as the importance of considering both current and future generations when making management decisions for public land. It is recommended that land managers take these similarities into account when making management decisions. It is important to note that using the Ward’s procedure for clustering produced more consistent groupings than the K-Means procedure and is therefore recommended when clustering survey data. K-Means only showed consistency with datasets of over 500 observations

Trimness of Closed Intervals in Cambrian Semilattices

In this article, we give a short algebraic proof that all closed intervals in a $\gamma$-Cambrian semilattice $\mathcal{C}_{\gamma}$ are trim for any Coxeter group $W$ and any Coxeter element $\gamma\in W$. This means that if such an interval has length $k$, then there exists a maximal chain of length $k$ consisting of left-modular elements, and there are precisely $k$ join- and $k$ meet-irreducible elements in this interval. Consequently every graded interval in $\mathcal{C}_{\gamma}$ is distributive. This problem was open for any Coxeter group that is not a Weyl group.Comment: Final version. The contents of this paper were formerly part of my now withdrawn submission arXiv:1312.4449. 12 pages, 3 figure